Download Chapter 5, Meaning

What is Philosophy Chapter 5
by Richard Thompson
Analysis and Meaning
(revised on 16 August 2011)
Meaning
Ask someone to explain ‘meaning’ off the cuff, without giving them time for thought,
and the answer would most likely be one of the following. The meaning of a word is said
to be one of:
(1) Something that the word ‘stands for’ as ‘Lenin’ stands for my friend Jon’s cat,
(2) An idea either in the mind of the person using the word, or to be evoked in the
mind of the person hearing the word, or both, or
(3) A definition of the word.
The meaning of a phrase or sentence, people are likely to continue, is a construct
from the meanings of the component words.
None of those explanations is satisfactory.
(1) does not explain the meaning of a word like ‘Santa Claus’, that, despite
appearances, does not stand for anything, or a word like ‘if’ that doesn’t even look as if it
stands for anything. The theory also generates a feeling that there ought to be general
objects corresponding to general words like ‘cat’ or ‘pink’. What could such objects be?
Not the set of all pink things because it is the members of that set that are pink, not the
set itself. Plato would have said it was the Form of Pink. That leads to the problem of
universals, which I’ll discuss later in this chapter.
(2) fails because there is no constant mental component that can be relied upon to
correspond to the use of the word. It’s quite possible to say one thing while thinking quite
another. One might say to an unexpected visitor ‘How lovely to see you after so long’
while thinking ‘If he doesn’t shut up soon so that I can get back to the kitchen, the
potatoes will be overcooked’
Even if we restrict ourselves to cases where people are thinking about what they are
saying, rather than something different, there is no simple correspondence between
words and mental activity. When thinking of tangible objects many people ‘see’ mental
pictures or diagrams, but they need not associate the same picture with every use of the
same word and different people may have different galleries mental pictures, or none at
all.
I used to find it hard to remember the word ‘hydrangea’ until I devised a mnemonic,
in which I associated the word with a picture of my grandmother watering the hydrangea
she used to keep in a tub. ( = water) The hydrangea itself is hardly visible in that
picture, the prominent features are grandmother, the watering can and the tub. I suspect
very few people associate ‘hydrangea’ with that mental image. Many people have very
little mental imagery, and I suspect auditory, tactile and olfactory images are uncommon.
Even for someone with a rich mental imagery it’s hard to think of a suitable image to
associate with a word that doesn’t refer either to physical objects or to processes. What
does ‘or’ look like? Someone might visualise a Venn Diagram or the symbol ‘’, but that is
just to visualise another symbol with the same meaning as ‘or’ and in any case correct
use of the word doesn’t require any image.
If we want to check whether someone understands a word, we don’t usually ask
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what mental images they associate with it, and if we did ask them it would only be a
roundabout and unreliable way of trying to find out what they meant.
(3) applies to a few special cases; it is the correct explanation of how many technical
words enter our vocabulary, but definition presupposes a supply of words that enter our
vocabulary without being formally defined, so it is at most a partial explanation of
meaning, telling us how to find out the meanings of some words from the meanings of
other words, without explaining what a meaning is.
People influenced by behaviourist psychology may favour a ‘stimulus-response’
analysis of meaning. Say ‘sit’ to the dog and, if properly trained, in good health, and not
distracted by overwhelming carnal desire when it hears the command, it sits. Soldiers
seem to be trained to respond to some command words like that, but I can’t imagine how
that account could be generalised to cover all words. The behaviourist account of
meaning seems applicable only to cases where a command is used to elicit a precisely
defined response. It could not be extended to analyse the complexities of a discussion
between several people wondering how best to do something. How could there be a
stimulus-response analysis of a discussion about how to site the raised beds and how to
arrange the plants in the garden, or what to put on the menu of the dinner party and how
to seat the guests?
Descartes believed a version of theory (2), but was disinclined to develop it very far.
“For the use of speech we attach all our conceptions to words by which to express them, and
commit to memory our thoughts in connection with these terms, and as we afterwards find it more
easy to recall the words than the things signified by them, we can scarcely conceive anything with
such distinctness as to separate entirely what we conceive from the words that were selected to
express it. On this account the majority attend to words rather than to things; and thus very
frequently assent to terms without attaching to them any meaning, either because they think they
once understood them, or imagine they received them from others by whom they were correctly
understood. This, however, is not the place to treat of this matter in detail.. ” (A Discourse On
Method p. 197 in the Everyman edition)
Hobbes believed (1) but seems to have combined it with a form of (2)
“the most noble and profitable invention of all other, was that of speech, consisting of names or
appellations, and their connexion; whereby men register their thoughts; recall them when they are
past; and also declare them one to another for mutual utility and conversation; (Leviathan. 73)
Locke also favoured (2)
“1. God, having designed man for a sociable creature, made him not only with an inclination
and under a necessity to have fellowship with those of his own kind, but furnished him also with
language, which was to be the great instrument and common tie of society. Man therefore, had by
nature his organs so fashioned as to be fit to frame articulate sounds, which we call words. But this
was not enough to produce language; for parrots and several other birds will be taught to make
articulate sounds distinct enough, which yet by no means are capable of language.
2. Besides articulate sounds, therefore, it was further necessary that he should be able to use
these sounds as signs of internal conceptions, and so to make them stand as marks for the ideas
within his own mind, whereby that might be made known to others and the thoughts of men’s minds
be conveyed from one to another.” (An Essay Concerning Human Understanding Part III Chapter 1)
Mental life is pictured as a ballet. We observe ideas gliding wordlessly through our
consciousness. Only when we want to communicate them to others do we try to express
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them in words, and that communication, if successful, somehow produces in the other
mind a ballet similar to that in our own.
Berkeley recommended concentrating on the way words are used.
“And a little attention will discover that it is not necessary (even in the strictest reasonings)
significant names which stand for ideas should, every time they are used, excite in the
understanding the ideas they are made to stand for - in reading and discoursing, names being for
the most part used as letters are in Algebra, in which, though a particular quantity be marked by
each letter, yet to proceed right it is not requisite that in every step each letter suggest to your
thoughts that particular quantity it was appointed to stand for. (The Principles of Human
Knowledge p. 59)
Recent discussions of meaning have concentrated on use. If someone habitually
uses the word ‘blue’ to refer to things that taste sweet, that is an error, however exquisite
a shade of blue they may be visualising as they speak, and however elegant their
definition of ‘blue’ in terms of the wavelengths of incident and reflected light.
In practice most words are learnt by a combination of an approximate definition,
some words of description, and a number of examples. For example ‘maroon is a colour,
a rather deep red, like this or this, but not quite that’. Ostensive definition, through
exposure to examples is made much of in the philosophical literature and is indeed very
important, though it works best when aided by a few words. Showing lots of examples of
things that are maroon should get the idea across eventually, but first telling people that
‘maroon’ is a colour word would speed things up immensely.
Describing how meanings are learnt is interesting and instructive, but not the same
as saying what meanings are. The use of the noun ‘meaning’ may be question begging if
it suggests that the answer to the problem of meaning must be the discovery of a
collection of entities to be called ‘meanings’. I don’t want to involve myself in inelegant
verbal contortions to avoid use of ‘meaning’ , so I’ll just state that my use of the word
involves no such assumption.
C. S. Peirce
A notable contribution to the study of use as a key to meaning was that of C. S.
Peirce who developed an elaborate theory of signs, that was embedded in a little
discussed theory of categories.
Peirce thought that everything that we can discuss can be assigned according to its
complexity to one of three categories.
Firstness encompassed what involves only one element viewed independently of
any relation it might have to anything else. Peirce did not seem completely sure that there
are any examples of Firstness, but thought that a quality of a component of sense
experience , though not the experience itself, would be a strong candidate.
Secondness was something involving relations between two components but
nothing of greater complexity, examples were cause, constraint, sense experience. “It is
the compulsions, the absolute constraining on us to think otherwise than we have been
thinking that constitutes experience” (Collected papers, voln I §336)
Thirdness is whatever involves the relation of three things in a way that cannot be
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analysed into relations of pairs. Peirce held that any relation involving more than three
components could be analysed into the conjunction of relations none of them involving
more than three, so Thirdness represents the greatest possible complexity. Examples are
process, legislation, generality, and, most important, signs.
A sign involves Thirdness because it must always have three components:
(1) the object, whatever it is about
(2) the ground, that aspect of the object that the sign invoked
(3) the interpretant, another sign that the original sign evokes (or possibly that it
is intended to evoke) in the person with whom we are communication.
The interpretant must bear the same relation to the object that original sign bears to
it.
Peirce’s system of classification was most elaborate, using three interlocking triadic
divisions of signs, each related to his three categories. The most important and often
quoted division was into Icon, Index and Symbol.
An icon has a form and meaning belonging to the category of Firstness. Just as
Peirce was not quite sure that there were any unequivocal examples of Firstness, so he
was rather hesitant about producing examples of icons, but the main idea seemed to be
that an Icon represented its object by resembling it, like a picture.
An Index bears a causal relationship to its object. Peirce’s example was the
weathercock that points into the wind because it is so constructed that the effect of the
wind is to make it point in that direction. Other examples would be compasses, and
possibly also thermometers, pressure gauges and voltmeters.
A Symbol represents its object by convention - because we say it does, or because
custom so dictates.
The status of logical truths
Any theory of meaning must include an account of logical truth, since the notion of
logical truth depends on the notion of meaning; a sentence expresses a logical truth
when we can tell that the sentence is true without attending to anything more than its
meaning.
First some terminology: logically true propositions are often referred to as logically
necessary. Propositions that are not necessary are called contingent, so a contingent
proposition might be true, or might be false, depending on the way things are, but a
necessary proposition is true whatever the way things are.
Leibnitz said that necessary propositions are those ‘true in all possible worlds’, a
view that attracted a lot of interest among 20th century modal logicians. A proposition is
contingent if it would be true in some possible worlds but false in others. A proposition is
possible if it is true in at least one possible world.
The related terms a priori and a posteriori are used to distinguish the ways in which
propositions can be known to be true, or false. A priori propositions can be known
independently of sense of experience while a posteriori propositions cannot. Most
logicians use the terms so that necessary = a priori and contingent = a posteriori.
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If we are to follow that usage we must take care not to say that a priori propositions
cannot be known through experience, since necessary propositions sometimes can be
known by experience. If Q is logically necessary, P  Q is valid for any proposition P, so
that anything could conceivably be presented as a ground for believing Q. Even if we
manage to eliminate some P as irrelevant, there will be some incontestable cases where
the evidence of our senses gives us reasonable grounds for believing a proposition which
could be known a priori. For instance if I key ‘713*859’ into my calculator and see that it
then displays ‘612467’, my seeing that gives me some reason for believing that 713*859
= 612467.
Sometimes Mathematicians avoid the tedium of personally attending to every stage
in a long and repetitive proof by programming a computer to carry out some of the steps.
For example the proof of the four colour theorem for plane maps 1 involved checking
through several thousand geometrical configurations. The mathematicians did not check
every case themselves but trusted the computer’s conclusions. That the computer
produced the output it did was something the mathematicians new by experience so their
knowledge was a posteriori, yet the conclusion they drew from it - namely the truth of the
four colour theorem, is logically necessary.
Another example of proof by computer is the identification of large primes, which is
always done by computer. Thus our knowledge that some large Mersenne number is
prime is based on our knowledge of how computers work, and of the logic of the program
used to test for primes, and our knowledge that a computer running the program identified
n
the number in question as prime. (A Mersenne number is of the form 2 - 1 so that in the
binary scale it is represented by an unbroken sequence of 1’s. It cannot be prime unless
n is prime, though that is only a necessary, not a sufficient, condition)
When we know a necessary truth by experience, there is a sense in which the
experience is only the secondary support for our belief. Reading the computer output or
the calculator display shows us the result of a process which we believe to be logically
valid, in other words our observations of the calculator or computer suggest that there are
a priori grounds for believing the proposition in question. Those a priori grounds are
embedded in the logic of the computer program or the calculator circuits. So it appears
that we can know a necessary truth by experience only if we also know, at least in
general terms, of a way in which it could be known without reference to experience.
To sum up, if the distinction between a priori and a posteriori is to be useful, the a
priori must be what can be known without reference to experience not what cannot be
known by experience, for there is nothing that cannot be known by experience.
We must also be careful how we define a posteriori. How far we can verify a
proposition by appealing to the evidence of the senses? ‘The Charge on the electron is
1
The four colour theorem concerns the minimum number of colours needed to
colour a map so that no two regions with a common edge have the same colour. It is
easily shown that on a plane at least four colours are needed, and once mathematicians
took an interest in the problem, it was soon proved that five colours suffice, but that four
colours suffice was proved only quite recently by a proof running to several hundred
pages and depending on a computer to check many of the details.
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-19
1.602192 x 10 Coulombs’ is almost universally considered to be a posteriori, but it has
been plausibly argued that it has never been conclusively verified, and never could be.
When I discuss science in the next chapter it will become apparent that almost everyone
interested in the logical basis of science now agrees with the late Sir Karl Popper that the
relation of scientific theories to experience and experiment is that theories are liable to
refutation by experiment. If we want ‘a posteriori’ to stand for anything definite, we could
define it as meaning ‘capable of being refuted by observation’. However that would make
all logically false propositions contingent, since if P is logically false P & Q is logically
false for every Q, so that Q  ~P, in other words, for every proposition Q, Q refutes P. An
amended definition of ‘contingent’ that excludes necessarily false propositions is ‘Capable
of being refuted by observation, but not refuted by every possible observation’
If we adopt that definition we may then assert ‘a posteriori = contingent’,
‘a priori = necessary’ still requires a little more discussion. Any a priori proposition
must be necessary, but is the converse true? Any necessary proposition that we know,
must be a priori, for as we noted, to know a necessary proposition a posteriori is to have
a posteriori grounds for thinking that there is an a priori reason on which we could base
our belief had we the time and energy to work out the details. So if there are any
necessary truths that are not a priori we do not know them to be necessary.
Kant proposed another division of propositions into the analytic and the synthetic.
Analytic propositions were those that (1) assert only the implications of their
component parts and (2) are such that their denial leads to a contradiction. Kant
considered (1) and (2) equivalent, at least in any case to which both apply. Synthetic
propositions are those that are not analytic. For instance ‘Mammals suckle their young’ is
analytic as the disposition to suckle their young is part of the definition of mammal. On the
other hand ‘Jacques Chirac is President of France’ is synthetic, true when I first wrote this
chapter, but false when I revise in in August 2011.
Kant thought that only synthetic propositions convey genuine information - another
example of the assumption that logic must be trivial. Kant assumed that a priori =
necessary and a posteriori = contingent and went on to compare the analytic/synthetic
distinction with that between the a priori and the a posteriori. There is clearly some
connection. In principle we could envisage that applying both distinctions could define
four categories of proposition:
(1) analytic and a priori
(2) analytic and a posteriori
(3) synthetic and a priori
(4) synthetic and a posteriori
Kant ruled out combination (2) on the grounds that any analytic judgement must be
a priori, but thought that all the other three combinations were admissible. Subsequently
philosophers have accepted (1) and (4) but have argued about combination (3), the
synthetic a priori.
Critics of Kant argued that all logical truths are analytic, for if not how can we know
them to be true? This is one of the issues that have divided Empiricists from Rationalists.
Empiricists have usually said that logically necessary propositions are analytic, while
Rationalists have suggested counter-examples such as ‘Every event has a cause’, or
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even the laws of Newtonian mechanics.
Kant offered ‘5 + 7= 12’ as a example of a non-analytic proposition that is true a
priori. The claim is dubious. Taking Kant’s first criterion of analyticity, if we follow both
pedagogical practice and Peano in defining numbers by counting, 5 and 7 are both parts
of 12, since 5 = 1+1+1+1+1, and 7 and 12 may be similarly defined. This does indeed
assume the associative rule, that lets us dispense with brackets, otherwise we should
have to write 5 = ((((1+1)+1)+1)+1, and
12=((((((( ((((1+1)+1)+1)+1+1)+1)+1)+1+1)+1)+1. I have shown in green the part of
the expression for 12 corresponding to 5. Omitting that part would leave behind an
expression for 7. Similarly we could find in the expression for 12 an expression for 7, and
if we removed that, we should be left with be an expression for 5. However, although we
can pick out either a 5 or a 7 in the Peano expression for 12, the 7 and the 5 that we can
pick out overlap; we can’t see them side by side. That may leave a Kantian a little room to
wriggle, but not, in my opinion very much.
To get further than that we should need to assume the associative rule for addition.
But the associative rule is provable from Peano’s axioms, so it seems perfectly
reasonable to assume it. Once we are able to use the associative rule we may remove
most of the brackets to write:
12 = 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1+ 1
= ( 1+ 1+ 1+ 1+ 1) + (1+ 1+ 1+ 1+ 1+ 1+ 1)
= 5 + 7.
Taking instead Kant’s second criterion, the denial of 5 + 7 = 12 certainly produces a
contradiction in Peano’s system, so anyone wishing to deny that the proposition is
analytic would have to reject at least one of Peano’s axioms.
Other proposed examples of propositions that are synthetic and a priori are ’Every
Event has a Cause’ and ‘Everything coloured is extended’. I discuss cause in Chapter 6.
Discussion of ‘Everything coloured is extended’ encourages many complicating
digressions in the course of which it is hard for either side to prove their point
conclusively, so I shall not grapple with the traditional debate here, preferring a different
approach.
If it is necessary that ‘Everything coloured is extended’ then the pattern of inference:
(RI) From A is coloured, infer A is extended, is valid.
In that case, the supposition that anything might be coloured but not extended does
entail a contradiction.
For suppose:
(1) A is coloured & A is not extended, then
(2) A is not extended, from (1)
(3) A is coloured, from (1)
(4) A is extended from (3) using (RI)
(5) A is extended & A is not extended, from (2) and (4)
Hence the supposition that something is coloured but not extended entails a
contradiction, so that by Kant’s criterion, the supposition that ‘Everything coloured is
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extended’ is false entails a contradiction, so that ‘Everything coloured is extended’ is
analytic.
Note that the argument is not circular. I nowhere assumed that ‘everything coloured
is extended’ is analytic, only that it is necessary, in the sense of being true in all possible
worlds. Necessity is all that is needed to make the argument valid, and an a priori
proposition must be true in all possible worlds, otherwise it would be possible for it to be
falsified by experience, in which case it could not be known independently of experience.
Another commonly cited example of a proposition that may be synthetic a priori is
‘nothing can be red and green all over’ . I am not sure quite what that means, and can
think of a plausible interpretation for which it is contingent.
Imagine the following test. Sources of red and green light are focussed onto a white
screen to produce a red circle and a green circle, which are initially separate.
Then the beams of light are redirected so that the two circles overlap. If anything
could be both red and green we might expect it to be the part of the screen where the red
lit and the green light overlap. However that region will appear to us to be neither red nor
green but yellow.
Yet there is a sense in which the appearance of yellow is an optical illusion. There is
a band in the spectrum in which light appears yellow, without any mixture of colours. That
a mixture of red light and green can look to us the same as pure yellow, is just a sign that
our eyes cannot distinguish such a mixture from the pure yellow.
It is conceivable that eyes might work differently, performing a spectral analysis of
the light coming into our eyes from a particular source. I imagine it would be possible to
construct a robot that performed such an analysis. An intelligence with such an eye would
be able to see a mixture of red light and green for what it is, and would be able to see a
surface as both red and green. That nothing can do so at the moment is contingent, not
necessary.
Of course, we could define ‘red’ as ‘red and nothing else’ and ‘green’ as ‘green and
nothing else’ . With the words so defined ‘nothing can be red and green all over’ would be
necessary, but it would also clearly be analytic.
Another proposition that has been alleged to be synthetic a priori is ‘two bodies
cannot occupy the same space at the same time’
I should like to approach that claim by considering how someone who considered
the proposition synthetic a priori might deal with one possible counter example.
Suppose we take a litre each of oxygen and nitrogen at atmospheric pressure, each
in a separate container, Now pump the oxygen into the container holding the nitrogen,
and compress till the volume of the mixed gases is one litre. The litre of oxygen and the
litre of nitrogen now occupy the same space.
Someone who wanted to maintain that it is impossible for two objects to occupy the
same space at the same time, might deal with the apparent counter example in either of
two ways.
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(1) He might say that ‘objects’ refers only to solids. However, having a definite
shape and being relatively impenetrable are defining properties of ‘solid’ so that
interpretation of the word would make the principle analytic.
(2) He might say that, even though the gases have mingled, the individual
molecules composing the gases follow the principle, because no two molecules can
occupy the same space at the same time. However, in the realm of particle physics,
physicists distinguish fermions and bosons. Fermions, such as the electron and the
proton, are subject to an exclusion principle so that no two can occupy the same space at
the same time. On the other hand bosons, such as mesons and photons are not subject
to an exclusion principle. Molecules are composed of atoms, which are in turn composed
of fermions, so it is impossible for two molecules to occupy the same space at the same
time. That is a consequence of the principle that two fermions cannot occupy the same
space at the same time. We could therefore think of the principle applied to molecules as
analytic, since following an exclusion principle is part of the definition of a fermion.
Alternatively we could class the principle as contingent, since molecules could
conceivably not have been composed of fermions, or perhaps protons and electrons
might not have been fermions.
Thus ‘two objects cannot occupy the same space at the same time’ appears to be
either analytic, or synthetic and contingent.
There appears to be a deadlock. Although it is hard for rationalists to prove that
any particular proposition is both logically true and not analytic, it has been thought that
the empiricists can sustain the claim that logical truths are analytic only by replacing key
terms by definitions - for instance by showing that ‘A vixen is female’ is analytic by
replacing ‘vixen’ by ‘female fox’. Sometimes a proposed rephrasing can be questioned;
the strategy invites disputes about whether a rephrasing just expresses the original
proposition in different words, or produces a new proposition. That leads to another
question:
What constitutes identity between two propositions?
The simplest candidate is mutual entailment so that propositions P and Q are the same iff
P  Q but P  Q is always true if P and Q are both logically necessary, hence that
analysis would imply that all necessary propositions have the same meaning.
These points were been debated at length in the philosophical literature during
most of the twentieth century and I shall return to them later, but for the moment I’ll
concentrate on Kant.
There seems to be an obscurity in Kant’s notion of analyticity. Much of the
discussion is carried out in terms of clause (1) of his definition, that analytic propositions
reveal only the implications of their component parts, yet that applies only to propositions
of the form ‘All A are B’ and requires some criterion for determining whether or not B is
contained in A. That is much harder than it may at first sight seem, because the meanings
of words are rarely precise and tend to change gradually in the light of our knowledge and
experience. The truth of ‘All A are B’ can itself be a reason for supposing B to be
contained in A.
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Consider, for example ‘all birds lay eggs’. As successive generations of humans
have observed that birds lay eggs they have come to take this for granted and eventually
to use the word ‘bird’ to mean, among other things, ‘oviparous animal’, so that ‘all birds
lay eggs’ may have changed from once being contingent to being necessary. I think Kant
had a picture in which A might be defined as P&Q&R, so than All A are B is analytic iff we
can find B, or something equivalent to B, among the P, Q, R, or if B is the conjunction of
some of those. Yet that is circular for ‘A can be defined as P&Q&R…’ is equivalent to ‘All
A are P&Q&R’ is necessary’. Such an analysis risks making the attribution of necessity
trivial, because, whenever it as a matter of fact true that ‘all A are B’, it is always an option
to give A a definition of the required form, namely A=B&(A~B), so that ‘all A are B’
becomes necessary.
The second clause in Kant’s definition of analyticity says that a proposition is analytic
if its denial entails a contradiction. That makes analyticity dependent on the particular
logical system in use. It can be plausibly argued that that he necessity of any proposition
P validates a rule of inference making it possible to prove that P is analytic,
For if P is necessary, the rule of inference:
(RP) From any proposition deduce P,
Is valid.
(1) Suppose ~ P
(2) P, from (1), using rule (RP)
(3) P & (~ P) from (1) and (2)
So the negation of P entails a contradiction, thus P is analytic.
For Kant there was just one logic, so he didn’t realize there was any need to choose
a system appropriate to whatever particular proposition was under consideration. Yet he
should still have seen a difficulty in his further assertion that analytic propositions are
uninformative, for as all the theorems of the logic he knew were by his criterion analytic,
he was committing himself to saying that all logical inference was uninformative.
The only plausible criterion for a proposition’s being informative about the world is
falsifiability. Yet if we use non falsifiability as the criterion of analyticity that makes the
analytic identical with the a priori, so Kant’s case would collapse.
Gradually both Empiricists and Rationalists came to place less emphasis on
analyticity and instead identified their key point of disagreement as whether or not a
logically necessary proposition can give us any information about the world.
Hume thought necessary propositions recorded ‘relations of ideas’. Russell in
Problems of Philosophy said they describe ‘relations between concepts’ - referring to the
concepts in question as ‘universals’. He said concepts were abstract entities that subsist
timelessly and unchanging, in contrast to ‘objects’ that exist in time and are subject to
change. Russell did not explain how we learn about such entities and later abandoned
the idea. Possibly the ‘universals’ could have been identified with sets of rules for using
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words.
Another claim sometimes encountered is that necessary propositions are true
solely by virtue of the way the their constituent words are used, so that to understand the
words is a sufficient basis for assenting to their truth. That claim has sometimes been
confused with the claim that necessary propositions are verbal in the sense of being
about words. In that form the claim is clearly false. For instance ‘5 + 7= 12’ cannot
actually be about the words ‘7’, ‘+’ ‘5’ ‘=’ and ‘12’ because precisely the same proposition
could be made in different words, such as ‘seven plus five equals 12’ or ‘VII added to V
gives XII’ Indeed, a proposition does not contain any particular words. What do contain
words are the various sentences in various languages which could be used to express
the proposition.
It is still open to someone who wishes to connect necessity to linguistic usage to
argue that, although logically necessary propositions are not about words, they are
typically used in contexts where people wish to convey information about the meaning of
words. Perhaps someone who says ‘There are 16 ounces to a pound’ really wants to
draw attention to the fact that ‘pound’ is defined as ‘16 ounces’. Certainly the point of
asserting ‘obvious’ necessary truths may be to draw attention to the connections between
the meanings of some of the words used to express those necessary truths. The
grammatical form of a sentence need not always correctly indicate the type of information
people using the sentence which to convey.
However those observations do not explain logical truth, but at best only explain
why people often give a particular false account of it. Furthermore it has no relevance to
necessary truths that are not immediately obvious, such as many propositions of
arithmetic, or complicated tautologies.
The difficulty of establishing precise criteria for meaning and for the identity of
propositions have suggested to some logicians that ‘necessary truth’ can only be applied
to the sentences of formal systems. From that point of view, if the concept applies at all to
statements made in natural languages, it does so only by identifying them with sentences
in some formal system.
Modal Logic
If necessity is a precise logical notion we might expect to be able to treat it formally.
Systems constructed to formalise our intuitions of necessity, possibility and entailment are
called ‘modal logics’
In the second and third decades of the twentieth century some logicians started to
construct formal systems for modal logic. It was hoped such systems might, among other
things, provide a notion of entailment free from the so called ‘paradoxes’.
Much recent argument about logical necessity has involved the status and
interpretation of modal logic, so I shall outline some of the work on modal logic before
returning to the discussion of necessity.
There are some results that any modal logic clearly must include, either as axioms
or as theorems. Using ‘’ to represent entailment,
(1) (necessarily P) P,
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(2) P (possiblyP) .
There is also a connection between ‘necessary’ and ‘possible’. If P is necessary,
then ~P is not possible, and if P is possible, then ~P is not necessary so that either of
‘necessary’ and ‘possible’ may be defined in terms of the other.
That gives us a fragment of modal logic, but there is still a wide choice what else
should be included.
C. I. Lewis (1883 - 1964) produced eight modal logics, called S1...S8, of which S4
and S5 have attracted most interest, though Lewis himself preferred S2. Using  for
necessary,  for possible and  for ‘strict implication’ (in other words entailment):
S1 was: Definitions for S1 
 = ~~
(P  Q) = ~(P  ~Q), equivalent to necessarily (P  Q)
(P  Q) = [(P  Q)  (Q  P)]
‘’ is called ‘strict equivalence and represents logical equivalence
Rules of inference for S1
(1) Substitution for propositional variables: From any theorem a
new theorem may be obtained by substituting any wff for every
occurrence of any propositional variable appearing in the theorem.
(2) Substitution of strict equivalents. If formula F appears
somewhere in a theorem, and if F  G, a new theorem may be
obtained by replacing any (not necessarily all) occurrences of F by
G.
(3) If F and G are theorems then so is F  G
(4) If F and F  G are both theorems, then so is G (detachment)
Axioms for S1
(P  Q)  (Q  P)
(P  Q)  P
P  (P  P)
[(P  Q)  R)]  [P  (Q R)]
[(P  Q)  (Q  R)]  (P  R)
P  ~~P
PP
S2 had the axioms of S1 and also (P  Q)  P
S3 had the axioms of S2 and also (P  Q)  ( P  Q)
S4 had the axioms of S2 and also P  P
S5 had the axioms of S2 and also P  P
S5 is stronger than S4 in the sense that all theorems of S4 are theorems of S5, but
not vice versa. Similarly S4 is stronger that S3, S3 than S2 and S2 than S1.
The Lewis systems do not include all the usual truth functional connectives, but if 
and  are introduced using the definitions P  Q = ~(P  ~Q) and
P  Q = [(P  Q )(Q  P )], all the tautologies are provable.
While S1 and S2 seem to do no more than formalise the obvious assumptions about
necessity and possibility, the stronger systems include controversial material.
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The special axiom for S4 implies the theorem P  P, a necessary proposition is
necessarily necessary.
P  P
~P  P, by contraposition (not a rule of inference in S4, but deducible in it)
~~Q  ~Q, substituting ~Q for P
~~Q  ~Q
Q  Q, using the definition for 
That result is questionable. Lewis himself was doubtful about it. In favour of the
theorem it is argued that if a proposition P is necessary, it is true in every possible world.
Suppose now that P is not necessary, there must then be some possible world in which
Pis not true, and from the point of view of that world there is a possible world in which P
is not true, which contradicts P.
S5 goes further by collapsing all iterated modalities to single modalities so that in
S5P and P are both equivalent to P, P and P are both equivalent to P, and in
general M1M2...MjP is equivalent to MjP, where each of M1...Mj is either  or . Also
entailment in S5 is the same as strict implication.
Alternative formulations of modal logic generally took the propositional logic as a
basis and added extra rules and axioms. Von Wright suggested defining a basic modal
logic as follows.
Taking  as undefined, with  defined as ~~ his two axioms were:
P  P, and (P  Q)  (P  Q)
his two rules of inference were:
(Rule 1) from F  G infer F  G and
(rule 2) if F is a theorem infer F - so that any theorem is logically necessary
The additional axiom P  P gives a system equivalent to S4.
Adding instead the axiom P  P gives a system equivalent to S5
Most work in modal logic has consisted of adding modal operators and axioms to
the propositional logic, but there have been some attempts to extend modal logic to
include quantification and the predicate logic. That produced the strange theorem,
provable using von Wright’s rule 2, that all true identity statements are logically true. In S5
it is possible to prove the stronger and stranger result that if an identity statement is false
it is necessarily false. Thus in S5, for any two individuals a and b, either they are
necessarily identical, or they are necessarily not identical so that in all cases either (a =
b) or (a  b).
It is interesting to find controversial material in a fairly elementary part of logic, so I
give a proof that any true identity is necessary. I have taken it from A. N. Prior’s Formal
Logic changing the notation from the Polish notation he used.
The proof starts with a definition of equality, according to which two individuals are
identical when all their properties are the same. That is a second order proposition and
the proof is conducted in second order logic.
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Definition: a = b is an abbreviation of (F)(F(a)  F(b))
1. (F)(F(a))  F(a)
(premiss) (axiom of predicate logic)
2. [P  (Q  R)]  [Q  (P  R)]
(premiss) (tautology)
3. x = x
(premiss) (given)
4. x = y  [F(x)  F(y)]
from 3 and definition of '='
5. [x=y (F(x)  F(y) )]  [F(x)  (x=y  F(y) )]
from 2 subs x=y for P, F(x) for Q, F(y) for R
6. F(x)  [(x = y)  F(y)]
using detachment with 4 and 5
7. (x = x)
from 3
8. (x = x)[ (x = y)  (x = y)] from 6 replacing F(z) by (x = z)
9. x = y (x= y)
from 8 using detachment with 7
Notice that in line 8 it is assumed that the properties of individuals can include ones
defined in terms of modal operators, yet in the definition we are required to quantify over
such properties. For the definition to be acceptable we’d expect the values of F to be
restricted to extensional properties - ones that could be identified with membership of
some set, since if F is the non extensional property such as ‘is believed by Samuel to
equal the number of planets’ F(9) might not be true even though 9 = the number of
planets.
Underlying the argument is the presupposition that, if x = y, then asserting x = y is
equivalent to asserting x = x. That is a suggestion that has often cropped up in
philosophical thought. It seems to lead to the strange conclusion that identity statements
are useless because, if true, they assert only the obvious identity of something with itself.
I have more to say about that later, in connection with what G. E. Moore called ‘The
Paradox of Analysis’ but for future reference note that the thesis that true identity
statements are necessary is dependent on the assumption that any true identity
statement is equivalent to one of the form x = x.
Entailment
There have been several attempts to find a relation of entailment that avoids the
apparent paradoxes that a contradiction entails anything, and anything entails a
tautology.
As noted in chapter 2 both those results hold for strict implication.
Attempts to avoid those paradoxes often produced even worse paradoxes,
sometimes without even avoiding the originals. I shall consider only two proposed
alternatives to strict implication, both of which did avoid the paradoxes.
John Wisdom and others suggested that P  Q be defined as:
P  Q is logically necessary, P is not a contradiction, and Q is not logically
necessary.
That identifies entailment with strict implication provided P and Q are both
contingent. However we frequently make deductions in which the conclusions are
logically necessary - we do so every time we prove a mathematical theorem. We also
sometimes need to make deductions from contradictory premises, we do so every time
we disprove a mathematical proposition by showing that it entails a contradiction. The
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proposed restriction on entailment is therefore a severe inconvenience.
Tim Smiley proposed a more permissive definition, obtained by extending the one
just rejected.
He suggested that we define entailment so that P  Q when
(1) P  Q is a tautology, P is not a contradiction, and Q is not a tautology
(2) P  Q can be obtained by substitution from an expression satisfying (1)
That would allow P  P V Q because P  P V Q it is a tautology satisfying (1)
Substituting  P for Q we have P  P V P
However we can't get Q  P V P
Also we have P & Q P , so substitution of  P for Q gives P & P  P
but we can't get P & P  Q
Entailment so defined is intransitive. Consider:
1: (P & Q) (P & (Q V R))
2 : (P & P) (P & (P V R))
3: (P & (P V R))  R
1 and 3 are both tautologies in which neither the consequent not the negation of the
antecedent is a tautology
2 may be obtained from 1 by substitution.
Hence all of 1, 2 and 3 satisfy Smiley’s condition.
so that
S1: (P & Q) (P & (Q V R))
S2 : (P & P) (P & (P V R))
S3: (P & (P V R))  R
However, if the relation were transitive, S2 and S3 taken together would give:
S4: (P & P) R which does not hold since, although (P & P) R is a tautology it
does not satisfy Smiley’s condition.
Entailment and the identity of propositions. One reason for seeking a form of
entailment stronger than strict implication, is to establish the identity of propositions. One
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approach to that questions would be to say that two propositions are equivalent (or
perhaps that two sentences express the same proposition) if each entails the other.
However that would make all logically necessary propositions identical.
Identity over propositions, and synonymy over sentences, must each be equivalence
relations, so neither relation could be built on an intransitive entailment relation.
I doubt whether it is possible to provide precise criteria for propositional identity
Quine’s criticism of Modal Logic
W. V. Quine (1908-2000) looked on modal logic with suspicion and argued that it is
impossible to give a coherent account of quantification into modal contexts. He took as
examples ‘9 > 7’ which is necessary and ‘the number of planets > 7’ which is contingent
even though 9 = the number of planets. If we allow quantification into modal contexts
(9 > 7) seems to imply (x)( (x > 7)), but what can be substituted for x in such an
expression? The obvious answer would be that x ranges over numbers, but the truth of a
sentence of the form ‘x > 7’ depends not just on which number is substituted for ‘x’ but on
how that number is specified. In other words the context is not extensional.
Quine thought that modal logic usually involves a confusion between use and
mention. One uses ‘nine’ in saying ‘there are nine planets’ but one mentions it in saying
‘the word ’nine’ has four letters’ or ‘the textbook includes the sentence ‘there are nine
planets’’.
In Three grades of Modal Involvement p 157 in The Ways of Paradox) he
distinguished:
(1) Necessity (he uses a capital ‘N’ for this sense) as a semantical predicate
applying to names of statements as in,
(1A)Pythagoras’ Theorem is necessary’ or
(1B)It is necessary that ‘5*6 = 30’, Quine treated ‘5*6 = 30’, a statement enclosed in
quotation marks, as the name of an arithmetical proposition so that it had the same
grammatical function as ‘Pythagoras’
(2) necessity (with a lower case ‘n’) as statement operator that applies to the
statement itself, that is to what the statement says as opposed to the list of words used to
express it, as in necessarily 5*6 = 30
(3) necessity as a sentence operator, appearing as part of the statement instead of
applying to the statement as a whole. For example
(3A) 5 is necessarily a factor of 30.
It is only in this third sense that ‘necessary’ can appear in an open sentence and
thus come within the scope of a quantifier. In the third sense only can we plausibly
present ‘necessarily 5*6 = 30’, as a special case of ‘necessarily x*6 = 30’ in a sense that
might legitimise the inference to (x)(necessarily x*6 = 30)
Quine thought that the three cases could be reduced to two by converting case (2)
into case (1) by inserting quotation marks, but he thought it very important to distinguish
cases (2) and (3). He considered (3) illegitimate and thought people often accept (3) only
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because they confuse it with (2). He blamed Whitehead and Russell for the confusion,
which they generated by confusing ‘’ which is a statement operator used to connect two
statements, with ‘implies’ which connects names of statements.
Quine continued his objection to quantification into a modal context by comparing it
to quantification into quoted text. Starting with
(S1)The sentence ‘25 is a perfect square’ has 18 characters
it would be absurd to derive
(x)(The sentence ‘x is a perfect square’ has 18 characters) (my example, and I am
not counting spaces as characters)
I think Quine’s point was that ‘implies’ and ‘necessary’ normally apply to completed
statements, and trying to use them as components of statements invites confusion, so
that people tend to confuse ‘it’s necessary that any square has four sides’ where the
necessity attaches to the inference from something’s being square to its having four
sides, with ‘any square necessarily has four sides’ where the necessity attaches to each
particular square individual, asserting that four sidedness is a necessary property of that
individual.
In sense (1) necessity is applied to sentences, and Quine thought it quite proper to
have some such term to describe the theorems of a formal system. ‘Necessary’ then
belongs to a meta language in which we discuss the formal system. That makes it hard to
find a use for iterated modalities. The only use for an iterated modality would be in a
meta-meta-language used to discuss a meta-language.
‘[“A square has four sides”] is necessary’
is a statement about the English language and so is presumably contingent, and the
same would apply to any modal proposition. So there might be a case for prefixing them
all with ‘possibly’ except that if we did that to all, the prefix ‘possibly’ would be pointless
because when applied indiscriminately it would mark no distinction.
In (3) necessity is not a metalinguistic concept and seems to be being applied to
propositions rather than sentences. Quine thought that there are no such individuals as
propositions, insofar as a proposition is anything more than a sentence, or at most a set
of equivalent sentences. It follows that for Quine logical truth in clearly defined only in the
context of a formal system.
That suggests to me another difficulty for modal logic. Within a formal system
necessity could be identified either with (A) provability, or with (B) truth under any
interpretation. However the latter criterion can only be used within a system if the
sentences true under any interpretation are also provable, so we are left with provability.
In that case ‘P’ is a theorem iff ‘P’ is a theorem. Since ‘P ~P’ is a theorem of any
system that includes the propositional logic, ‘(P ~P)’ is also a theorem. Consider now
the sentence ‘P~P)’ That is false since it implies ‘P~P’, which is false in any
consistent system. Therefore we have that ‘P~P)’ is a theorem, but if necessity is
the same as provability, that theorem is necessary and that in turn seems to assert that
no contradiction can be proved in the system; in other words we seem to have
constructed within the system a proof of its own consistency.
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That apparent proof could be constructed in any modal logic that includes the
propositional logic, and among such systems there could be some that contain a good
deal more than the propositional logic, possibly even Peano’s axioms. Yet Gödel proved
that such a system can only prove its own consistency if it is inconsistent. Not only that
but the sentence he constructed to represent the consistency of a system within the
system itself was not at all like our ‘(P ~P)’ so something seems to have gone very
wrong here. I suspect that the necessity formalised by modal logics cannot be identified
with provability.
Whatever the merits or demerits of the preceding argument, there is another reason
for not identifying ‘P’ with ‘P is a theorem. Take any single propositional letter F, then ‘F’
will not be a theorem, giving ~F which will be itself a necessary statement. However if
we allow ~F to be a theorem, we can generate other theorems from it by substituting
any well formed formula for F, in particular we can substitute ‘Pv~P’ giving ~(Pv~P),
but since Pv~P is a theorem we also have (Pv~P) so there is a contradiction. In the case
of the propositional logic we could avoid the paradox by dispensing with the rule of
substitution, or possibly just be restricting it to forbid the substitution of tautologies. That
would be possible in the case of the propositional logic because that is decidable so we
can identify all the tautologies by truth tables, hence a rule forbidding their substitution
would be effective. However, quantificational logic has no decision procedure, so
prohibiting the substitution of a theorem would fatally weaken it.
Logical Pragmatism
Quine’s scepticism about modal logic was part of a more extensive scepticism about
logical truth. He developed a theory that is generally known as ‘Logical Pragmatism’. He
thought that ‘necessary’, ‘a priori’, ‘analytic’, ‘synonymy’, and ‘meaning’ form a closed
circle of terms, any one of which may be defined in terms of the others but none of which
can be given watertight definitions, or even clear criteria for their use, without appealing
to other terms in the circle, so we cannot break out of the circle.
Starting with ‘analytic’ Quine distinguished two cases - the following examples are
mine.
(1) ‘A female fox is a fox’
(2) ‘A vixen is a fox’
(1) is clearly analytic. (2) is seen to be analytic when we replace ‘vixen’ by ‘female
fox’, permitted because ‘vixen’ and ‘female fox’ have the same meaning.
However ‘vixen’ is not always used to mean ‘female fox’, it sometimes means
‘ferocious human female’ and in that sense (2) is not even true and so is certainly not
analytic. We can meet that difficulty by saying there are really two meanings of ‘vixen’,
and in one sense, the standard sense, (2) is analytic. That sort of move is all right
provided we don’t make it too often, but we could make almost any true proposition
appear analytic by distinguishing sufficiently many senses for the component terms. In
any case there are more difficulties for meaning. Change the example to:
(3) ‘female human parents are female’ and
(4) ‘human mothers are female’
(4) would generally be considered analytic because it is equivalent to (3) since
‘human mother’ = ‘female human parent’.
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Now consider Simon’s mother Stephanie, who gradually became aware of the male
side of her personality and, after her family had grown up, had surgery and hormone
treatment which converted her to Stephen. Stephen isn’t just called ‘male’ as a sort of
courtesy title; we use the male personal pronoun in talking about him, he uses the gents
and has a beard. Yet if we use ‘mother’ to mean someone who gives birth to a child,
Stephen is Simon’s mother. It appears that while (4) used to be analytic, it is analytic no
longer.
That shows how ‘analytic’ depends on ‘meaning’. We could say that the meaning of
‘male’ has changed, or that the meaning of ‘mother’ has changed from ‘female parent’ to
‘parent female at the time of the child’s birth’ Alternatively we could save the analyticity of
(4) by defining ‘female’ as ‘has two X chromosomes’, though as the use of ‘female’
predates knowledge of genetics, that couldn’t count as maintaining the analyticity of (4) in
its original sense. That there is a choice what we say suggests that changes in meaning
are not the clearly defined events some logicians seem to suppose.
The problem is not confined to ‘analytic’ and ‘meaning’ but extends to ‘necessary’
Think of cases where people argue whether or not some sentence expresses a
necessary truth. Simon refers to David as ‘My husband’ and is rebuked on the grounds
that ‘husband’ refers to a male married to a female, so that only someone who is female
may correctly speak of anyone else as ‘my husband’ Simon points to another way of
using ‘husband’ in which the word does not have that implication. In the first sense of the
word ‘X is Y’s husband’ is equivalent to
H1: ‘X is male, & Y is female & X is married to Y’ so that
‘X is Y’s husband  Y is female’ is a necessary truth, while in the second sense the
conditional is not even generally true.
So, in order to identify the proposition expressed by some sentence containing the
word ‘husband’ we need to be able to tell in what sense the word is being used on that
particular occasion. How might we do that ? If the sentence is:
‘X is Y’s husband  Y is female’
one factor affecting our decision as to the meaning of ‘husband’ would be whether
or not the sentence appears to be being used to express a necessary truth. So we are
both appealing to the meanings of words to settle the logical status of sentences, and
also appealing to the logical status of sentences to settle the meanings of their
component words. The meaning of the words and the logical status of the proposition are
not separate questions.. To say ‘in one sense of the words that sentence expresses a
logically necessary proposition, but in another sense it does not’ offers little illumination
unless we can identify the senses of the words without first determining the logical status
of the proposition.
Sometimes we can distinguish meanings clearly. That is so when someone is
prepared to give a clear definition of their terms, such as the definition H1 for ‘X is Y’s
husband’ but when that happens we are really replacing a bit of natural language by a
fragment of formal logic. ‘X is Y’s husband  Y is female’ is presented as an inference of
the form:
(P  Q  R)  Q . It is logically necessary because we have specified that our
words shall be used in such a way that the sentence fits that logical pattern.
Quine did not deny that there is any distinction between necessary and contingent,
but held that it is a matter of degree not of kind. Except for propositions reporting
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individual sense impressions, our beliefs do not face the test of experience alone, but as
part of a complete world view. If we observe something contrary to our expectations, we
need to make some change in our belief system to accommodate that observations.
Often we’ll think there’s an obvious adjustment to make, but there will always be
alternatives. There are some beliefs we change quite readily; if I believe my visitor is in
the dining room, all it takes to change my mind is to look out of the window and see him in
the garden. Some beliefs we change only in extreme circumstances, like Newtonian
mechanics, and some we never seem to change at all. The latter, which Quine calls the
most deeply entrenched beliefs are the beliefs in the propositions that logicians
generally describe as logically necessary. While accepting that we are most unlikely to
revise any of those beliefs, Quine maintains that the bare possibility of our doing so must
be left open.
For example, suppose we perform a mass spectrometer 2 test on a sample of
specially purified iron, and find a line corresponding to mass number 51 we could infer:
(a) the spectrometer was contaminated
(b) the specimen of iron contained a little chromium,
51
(c) there is a hitherto undiscovered isotope Fe
(d) the theory of the mass spectrometer is all wrong
(e) matter is not atomic and the readings of scientific instruments are just the results
of baby angels playing computer games.
51
’
(f) logic is wrong and the two propositions ‘there is an isotope Fe and ‘there is no
51
’
isotope Fe can both be true .
(a) to (f) successively challenge progressively more deeply entrenched beliefs.
It is difficult for a Logical Pragmatist to explain either how a contradiction between
some of our beliefs and our observations impels us to review our belief system, or how
that review is carried out. What is the status of the propositions that record the
contradictions that start off the process? The contradictions they record must be of the
form:
C: ‘B & S is a contradiction’ where B is the set of our beliefs and S is the discordant
sensory experience,
so that C is equivalent to: ‘NOT (B&S) is logically necessary’
If logical necessity is a matter of degree C might not be necessary, implying that
there is after all no problem to be solved and no need even to consider revising any of our
beliefs.
2
The mass spectrometer vaporises minute quantities of materials, converting them
to stream of charged particles. A combination of electrical and magnetic fields spreads
the particles out into a spectrum in which the position of each particle depends on the
ratio of its charge to its mass. The particles produce a set of lines on a photographic film.
The instrument was extremely useful for identifying isotopes - atoms of different mass
that have the same chemical properties. Every atom is assigned a mass number, equal to
the total number of protons and neutrons in its nucleus. For instance most carbon atoms
have mass number 12, represented be 12C, but there is a radioactive isotope of mass number
14, represented as 14C. Naturally occurring iron is a mixture of 54Fe, 56Fe, 57Fe and 58Fe
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The entire process of reviewing our beliefs is guided by the need to avoid
contradiction, and the same considerations would apply to those contradictions too.
Quine on Synonymy and Propositions
Quine’s doubts about necessity made him doubt whether there can be any watertight
criteria for any of the related concepts such as synonymy, and propositions. If there were
propositions, the relation ‘express the same proposition’ would be an equivalence class
over sentences. In fact, Quine argues, there is no clear criterion for synonymy. Sentences
that are regarded as synonymous in one context may not be so regarded in another.
Consider:
(1) ‘I’m going for dinner at Simon’s’
(2) ‘I’m going for dinner with Simon’
(3) ‘I’m going to Simon’s for one of his lovely dinners’
(1) and (2) might be used to give precisely the same information. On the other hand
if Simon and I were planning to eat out together (2) could still be used but (1) could not.
(3) might for some purposes be considered to make the same factual claim as (1), but it
also gives the additional information that I like Simon’s dinners.
Quine pointed out that the practical implications of one belief may depend on what
other beliefs we have, so that it is often hard to divide up the factual content of our belief
system between the various sentences we believe. That is most strikingly true in the case
of a scientific theory where some sentences cannot be directly tested at all. So if the
result of an experiment contradicts our expectations there is a variety of ways our
knowledge could be adjusted to remove the inconsistency. For example, in the mass
spectrometer experiment that I imagined earlier, we can draw the conclusion that we
have discovered a new isotope of iron only if we assume the truth of the theory of the
spectrometer, and assume that it was functioning correctly, was not contaminated, and
that the sample of iron used was pure.
The difficulty of parcelling out the contents of our belief system amongst the various
sentences we use to express our beliefs, challenges the convention of treating our beliefs
as a set of distinct propositions.
Quine preferred not to use the word ‘proposition’. Although Quine’s arguments are
powerful I think it may be possible to rehabilitate propositions, at least to some extent.
But first I make a concession to Quine. Even the most enthusiastic partisan of
propositions must accept that it is usually through sentences that propositions are
communicated or recorded and that the same sentence may express different
propositions on different occasions. If someone seems to misunderstand a sentence, the
person who utters it may need to provide supplementary sentences. For instance if Felix
utters (2) and Algernon replies ‘where are you going?’ Felix may reply ‘Oh, we aren’t
going out, Simon’s cooking at his place’. Given sufficient explanation, clarity should
eventually be achieved. At any stage in such a discussion it is possible to imagine
someone still misunderstanding, but that does not imply there actually will be a
misunderstanding at that point. Once we have removed all the misunderstandings that
have actually arisen we have identified the proposition our sentence is expressing on
the occasion in question. We do not need to anticipate all the other misunderstandings
that might have arisen, but in fact did not. The latter task may well be infinite, it is certainly
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impractical, but the former is usually possible and often quite straightforward.
The ever present possibility of doubt is often referred to in philosophical discussions
whatever the particular subject under discussion. However carefully we have explained
the sense in which we were using the sentence, verified that the back door is locked,
checked that the frog has four legs, carried out the calculation six times using a different
method each time, there is always the bare possibility that we may still have made a
mistake, just imagined we’ve checked when we haven’t really, or are really dreaming it all
anyway. I’ll call such doubts the pervasive doubts. They represent the bare possibility of
error common to all cases where we claim to know anything.
In many cases there are also special reasons for suspecting error - we notice an
alternative interpretation of the sentence which we forgot to check at the time. I’ll call
those particular doubts. It is a common error to cite the pervasive doubts as reasons for
thinking there is a particular doubt in the case in hand, or for thinking that all belief is
equally doubtful. While all belief is subject to the pervasive doubts, some beliefs are also
open to particular doubts; it is those beliefs only that we usually call doubtful.
In the case of statements people actually make, it is usually possible to remove all
the misunderstandings that occur on any particular occasion, leaving the way open for a
sentence that has been so clarified to be used to identify a proposition. Supposing we
can identify propositions by combining a primary sentence with a series of secondary
sentences to clarify it, what is this proposition we have identified? Not a sentence, as the
same sentence might express any of a variety of propositions. I can think of two possible
answers:
(1) A tentative proposal, that I haven’t yet thought through is that a proposition might
be a theoretical entity, like the theoretical entities of science such as ‘fundamental’
particles. (see chapter 6 of these notes) There is no direct sense experience that can be
identified with encountering an electron, yet theories about electrons are used to predict
events that can be the subject of experience. Perhaps, even though we can’t define an
individual proposition by identifying it with a particular sentence or class of sentences, talk
of propositions could be part of a theory that helps to explain things we say. The relevant
theory could include the propositional logic and we could say that the letters P, Q, R...
that appear in its formulae represent propositions.
(2) A proposition is a pattern of linguistic usage. A proposition might be identified as
something that could be expressed by the sentence S 1, qualified by Q1...Qn, or by
*
*
*
sentence S 1, qualified by Q 1...Q n, or.... something that is considered true in such and
such circumstances, and false in certain other circumstances.
Whether or not such moves can rescue ‘proposition’ from Quine’s strictures, he is
correct in suggesting the use of the term is problematic. He might well have regarded the
arguments I’ve just deployed as a refinement of his position rather than an alternative to
it.
When we try to apply Logic to questions outside Logic and Mathematics, the hard
part of the work is not determining the logical relations between clearly defined
propositions, but determining precisely what propositions are being asserted so that their
logical relations can be determined. Very often the difficulty arises from people trying to
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talk their way through an issue instead of writing down their arguments. Talking instead of
writing is a very common source of confusion and intellectual error.
If one can get people to agree to write down their claims, and translate them into
formal logic, disagreement doesn’t usually persist for long. Very often careful analysis of a
dispute reveals that people were at cross purposes, using the same sentence to express
different propositions. The fact that we can verify that that is what is happening, shows
that the ambiguity of individual sentences need not prevent our determining what they are
being used to say.
Lewy's Reply to Quine
In Meaning and Modality (CUP 1975) Casimir Lewy discussed various questions
concerning logical truth, meaning and modal logic, and disputed Quine's claim that one
cannot quantify into a modal context.
Lewy started by attacking Quine's idea of substitutivity as a test for a word appearing
referentially.
Lewy (op cit p24) considered:
(g) 'The word "cat" has three letters'
he then supposed that it so happened that every synonym for "cat" in every
language happened to have three letters.
If that were true, substituting any of those synonyms for "cat" in (g) would preserve
the truth value of the sentence and so, argued Lewy, the appearance of "cat" in (g) would
satisfy Quine's criterion for being referential.
I think that is a misunderstanding of Quine. I do not think he intended ‘referential’ to
apply to a particular sentence, but to a particular context, to a sort of skeleton around
which many sentences could be built.
That context was:
(g*) ‘The word”.....” has three letters’
and Quine’s criterion for that context being referential was that substituting for “.....“
any two words with the same meaning should give the same truth value. So preservation
of truth value for synonyms of ‘cat’ would not suffice. the truth value would also have to
be the same for “dog” as for “chien”, the same “hat” as for “headgear”.
Lewy continued his argument by distinguishing two sorts of modality: modalities de
dicto, and modalities de re, criticising Quine for overlooking the distinction.
Lewy introduced the distinction with the examples:
() The proposition that the number of planets is greater than 7 is necessary
) The number of planets is necessarily greater than 7
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() is a modality de dicto, because it applies to a proposition
() a modality de re because it tells us that something is necessarily true of a
particular individual, namely the number 9. Note that ) does not assert that the
number of planets is 9
Lewy said that () is false, but () is true, since the number of planets was at the
time he wrote considered to be 9, and 9 is necessarily greater than 7. Today we should
have to say 8 is necessarily greater than 7. It is fortunate that Lewy left himself a margin
for error!
Quine, and many other logicians, recognise only modalities de dicto.
The only grounds Lewy seems to have for asserting any modality de re, is
substitution of terms of the same reference in a modality de dicto.
Lewy observed (op cit p 36) that propositions such as () are, if true, logically true, in
which case the corresponding proposition like () is also logically true.
A substitution based on a contingent identity may alter the modality of a ()
proposition, but will leave its truth value unchanged. If a () proposition is contingent
(whether true or false) the corresponding () proposition is false.
Because he believed the truth value of a modality de re to be preserved by
substitution of terms of the same reference, Lewy held that Quine’s objections to
quantification into a modal context did not apply to such modalities.
Thus Lewy’s explanation of modality de re suggests that:
‘a is necessarily F’ is equivalent to ‘a = x for some x satisfying necessarily F(x)’
so perhaps ‘a is necessarily F’ means (x)(F(x) is necessary & a=x)
which analyses the modality as a quantification into a modality de dicto. Yet Lewy
introduced modalities de re as a basis for just such quantification, suggesting that
quantification over a modality de re avoids the difficulties Quine believed he had found in
quantification into a modality de dicto. To analyse a modality de re in terms of a modality
de dicto therefore appears viciously circular.
In the context of a discussion of external and internal relations, Lewy later (op cit p
62) qualified his claim that a modality de re entails the corresponding modality de dicto,
giving the example:
(A) Necessarily there is a number which numbers the planets.
(B) There is a number that necessarily numbers the planets.
(A) does not entail (B)
Lewy excluded such cases by restricting the claim to the case:
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‘Necessarily F(t)’ entails ‘t is necessarily F’ where ’t’ is either a name or a definite
description.
I think Lewy could have chosen a better example. It is not clear to me what (A)
means. Is it the assertion that the number of planets is constant, and does not vary from
day to day, so that more than one number would be needed to number them. If that is
what (A) means A is false, because in that sense of the words ‘there is a number that
numbers the planets’ is not necessary but contingent.
Definite Descriptions
Phrases such as ‘the tallest mountain on earth’, ‘the smallest Mersenne number that
is not prime’ and ‘the king of France’ are called definite descriptions. Problems about
descriptions first became apparent when logicians tried to analyse definite descriptions
that do not refer to anything. Russell’s favourite example was: ‘The King of France is
bald’.
It has sometimes been thought that the meaning of a description is the object
represented, so ‘the square of 7’ means 49. Adopting that view makes it hard to deal with
descriptions that don’t apply to anything. For instance ‘The golden mountain is 3 miles
high’ seems perfectly intelligible even though there is no golden mountain. Indeed, if such
propositions are meaningless when they have no reference, we shall frequently not know
whether or not they have meaning. Not having checked the news recently I may not know
whether the King of Thailand is still alive but that does not mean that I don’t know whether
any proposition about him is meaningful.
Meinong (1853-1920) suggested that even if something did not exist it could subsist,
enjoying a sort of phantom twilight existence. He even postulated the subsistence of
referents for contradictory descriptions speculating that ‘the round square does not exist’
presupposed the subsistence of the round square, so that there was something to which
existence could be denied.
In Mathematics it often happens that someone refers to ‘the positive solution of
equation E’ when E has either no solutions, or has only negative solutions, or possibly
has several positive solutions. We could deal with that case by referring, not to individual
solutions of an equations, but to its solution set. An equation always has precisely one
solution set irrespective of how many solutions it has, or of whether it has any solutions at
all. However analysing all propositions involving definite descriptions as referring to sets
is implausible and would involve tortuous circumlocutions.
Frege had considered the question and suggested that we specify a special null
element to act as value in such a case. He suggested when a mathematical expression
purports to refer to one or more numbers, but fails to refer to any number, it could be
assigned the value zero. Unfortunately that would have risked confusing an equation with
solution zero, with an equation that has no solution, so if there is to be a null element it
would be better to invent some special element.
Russell proposed instead to give what he called a contextual definition which does
not ascribe any meaning to a definite description on its own, but does give meaning to
sentences of certain specified types containing definite descriptions. Sentences of the
specified form can then be meaningful even if there is no King of France, so that the
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descriptions have no reference. In that case the propositions purporting to give
information about the King of France are all false. Because there is no such King, both
‘The King of France is bald’ and ‘The King of France is not bald’ are false.
Russell argued that here are three contexts in which a definite description may
meaningfully appear.
(1) The G exists. ( for example ‘the sun exists’) That is interpreted as asserting that
one and only one individual is G. i.e. (x)(G(x)  (y)(G(y)  (x = y)) something is G and
everything that is G is identical to that something.
(2) F(The G) where F is some property, which is interpreted as asserting that there
is one and only one individual that is G and that individual is also F i.e. :
(x)(G(x)F(x)  (y)(G(y)  (x = y)))
So ‘The moon is lifeless’ is analysed as ‘there is something that is a moon and is
lifeless, and everything that is a moon is identical with that object.
(3) The G = K, where K is either a name, or another definite description, analysed
as: (x)(G(x)  (x = K)  (y)(G(y)  (x = y))). In a context where it is clear that K has a
reference that could be shortened to G(K)  (y)(G(y)  (y = K))
To use Russell’s own example: ‘The King of France is Bald’ means: There is an
entity KF such that all the following are true:
(R1) KF is the King of France
(R2) nothing else apart from KF is King of France
(R3) KF is bald
As (R1) is false the whole proposition is false (A French Royalist might consider
both (R1) and (R2) to be true, in which case the decisive matter would be the truth or
falsity of (R3))
Logical Analysis
Before the limitations of formalisation had become apparent Russell initiated and
inspired a philosophical movement called Logical Analysis, dedicated to elucidating
philosophical problems by using mathematical logic to explain difficult ideas. The best
and most often cited example of logical analysis was Russell’s theory of descriptions,
sometimes referred to as ’The paradigm of Philosophy’, (a phrase often quoted ironically
by John Wisdom in his lectures; it may have originated with by G. E. Moore). Some say
that the Theory of Descriptions was the only logical analysis ever completed successfully.
Russell’s programme was taken up enthusiastically by G. E. Moore (1873-1958) who
suggested, early in the twentieth century, that the purpose of philosophy is, or at least
should be, to provide an analysis of our concepts. Moore had been shocked into an
interest in Philosophy by meeting McTaggart, who scandalised Moore by denying the
reality of space, time and matter. Moore thought that such odd opinions must arise from a
misunderstanding of the concepts involved, misunderstandings that might be avoided if
we could obtain correct analyses of those concepts.
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Under Moore’s influence there developed a school of logical analysis that directed
attention to questions of meaning and language. Philosophy became much more self
conscious as Philosophers asked the same question I’m trying to answer in this essay:
‘what if anything is there left for Philosophers to discuss when so many of their traditional
questions are being answered by scientists’
An excellent example of Moore’s method is his famous attack on what he called the
‘Naturalistic Fallacy’ a term he applied to any attempt to settle the content of morality by
giving a definition of ‘good’. Suppose, for example, that someone proposed to define
‘good’ as meaning ‘promoting human happiness’. Presumably someone making that
proposal would want to make the moral judgement:
G: ‘Promoting human happiness is good’.
However if good = promoting human happiness G becomes the tautology:
G*: ‘Promoting human happiness is promoting human happiness’
which would be quite uncontroversial even to a misanthrope who considered the
promotion of human happiness a very bad thing.
Moore’s argument applies only to attempts to settle the matter by definition. It would
not apply to someone who held that human happiness is just as a matter of fact the only
ultimate good. It is not entirely certain that anyone has actually committed the naturalistic
fallacy so defined, though John Stuart Mill was the prime suspect. In chapter 8 I try to
prove him innocent.
The most conspicuous achievement of the school of logical analysis was to get
philosophers writing much more lucidly than had been the custom during much of the
nineteenth century and the early twentieth century, but it yielded few completed analyses.
Philosophical problems did not, as had been hoped, usually fade away under the
analyst’s scrutiny.
Moore may have thought that every proposition has a unique logical form that
could be made explicit by analysing the terms involved, but, as I pointed out in Chapter 2,
the assumption that a proposition has a unique logical form now seems untenable.
Philosophers have often sought definitions, not to specify the meaning of a word, but
to help their understanding of the concept expressed by the word. Such definitions seem
never to get it quite right. Definition is just not a good model for the explanation of tricky
terminology.
There are some terms that were originally introduced by a definition, that applies to
many scientific terms like ’force’ and ’specific heat’. For such a term, anyone who
doesn’t understand it can look up the definition. However, for a term that was not
originally introduced by definition, there is probably no unique, precise, correct definition,
although it may be useful to start an explanation with a rough definition ‘It’s roughly.... but
not quite’. As Moore feared, the alternatives are triviality or falsehood. (see the next
section)
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What is needed is not a definition but an explanation of when and how the term is
used, and that is what the generation of philosophers who came after Moore tried to
provide.
Sense and Reference
A problem that puzzled Moore till the end of his life was the status of identity
statements. Moore referred to this as ‘The paradox of Analysis’.
The object of analysis is some sort of identity. If P is the problem term philosophers
are trying to analyse, their target is something like: P = A, where A is the analysis of P.
However, if P = A is true it appears to be equivalent to the truism P = P, so that
apparently any analysis is either false or trivial: For instance
(1) A vixen is a female fox
is an accurate definition because ‘vixen’ is just an abbreviation of ‘female fox’ , and
whenever there is a completely accurate definition of a term, that term could be used as
an abbreviation for its definition.
Thus if a zoo has a vixen called ‘Celia’ we may reason:
(2) Celia is a vixen
Therefore, replacing ’vixen’ by ’female fox’
(3) Celia is a female fox.
However if we replacing ‘vixen’ by ’female fox’ in (1) we get
(4) A female fox’ is a female fox
Although that ought to be equivalent to (1), it differs from (1) in being quite
uninformative.
In general it appears that any correct analysis is reducible to ‘a = a’ which is vacuous
while any proposed analysis that is not reducible to that form must be false.
Frege had already discussed such problems and proposed to solve them by
making a distinction between sense of a word and its reference. Frege’s example was :
MS: ‘The morning star is the same as the evening star’
‘morning star’ and ‘evening star’ are both old popular names for the planet Venus
and could well have been used by people who didn’t realise that those were different
manifestations of the same planet. Once we realise that the morning star and the evening
star are both Venus we might reasonably hope to replace references to each by
references to Venus. MS then becomes
V: ‘Venus is the same as Venus’
However V does not appear to be equivalent to MS, since MS appears to be
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contingent, while V is analytic
Frege suggested we distinguish the sense (Sinn) of a phrase from its reference
(Bedeutung)
‘morning star’ and ‘evening star’ have the same reference, since they both refer to
Venus, but they have different senses, so that MS is true but contingent - it could
conceivably have been false. On the other hand V is necessarily true.
Replacing one word or phrase by another with the same reference usually
produces a new sentence with the same truth value as, but with a different meaning from,
the original, but there are exceptions. Consider:
JBMS: ‘John believes that the morning star is the same as the evening star’
JBV: ‘John believes that Venus is Venus’
These are not equivalent, because even though the morning star and the evening
star are both Venus, John may not know that.
Frege called propositions like MS and V, where substitution of terms with the same
reference leaves truth value unchanged, extensional contexts, and those like JBMS and
JBV intensional contexts. He suggested that in an intensional context the reference of a
term becomes its usual meaning and its new sense is what he called an ‘oblique’ sense.
Frege thought his theory could be extended from phrases identifying individuals to
complete sentences. The reference of a sentence was, he thought, its truth value and the
sense was what we usually call the meaning of the sentence.
In an intensional context such as ‘Amelia believes that King’s Lynn is the county
town of Norfolk’, ‘King’s Lynn is the county town of Norfolk’ will have as reference its
ordinary sense, and it will have an oblique sense. The multiplicity of oblique senses made
the full version of Frege’s theory unhelpfully complicated, but although many logicians
have reservations about Frege’s doctrine, the terms ‘intensional’ and ‘extensional’ are still
widely used as he suggested., and the basic distinction between sense and reference
seems to me correct. Beware of spell checkers that sometimes want to replace ‘intension’
by ‘intention’. John Stuart Mill’s terms ‘connotation’ for ‘intension’ and ‘denotation’ for
‘extension’ are also sometimes encountered.
I think it helps to compare a statement affirming an identity between two
grammatical subjects, with a statement attributing a quality to a single subject. Consider:
(1) Simon loves Phoebe
(2) Simon is Phoebe
In case (1) we can imagine going to the reality behind the words and make an
equivalent assertion by pointing to the two people in turn and saying ‘he loves her’
On the other hand there is no corresponding interpretation of (2); going up to he
person in question and saying ‘s/he is self identical’ definitely does not express the gist of
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(2).
We could say:
(3) This person sometimes assumes the persona of Phoebe and sometimes that of
Simon, so that many people think there are two people involved and not just one.
(3) is certainly not logically necessary, so, if (3) paraphrases (2), neither is (2)
Lewy (Meaning and Modality pp 88-89) suggested that the paradox of analysis
might be solved by developing Frege’s theory of sense and reference.
Consider the sentence:
X: ‘The concept of mother is the same as the concept of female parent’
In that sentence ‘concept of mother’ and ‘concept of female parent’ have the same
reference, namely that concept that may be referred to either as motherhood or female
parenthood. However the two phrases have different senses.
Therefore if in X we replace ‘female parent’ by ‘mother’ to give:
Y : X ‘The concept of mother is the same as the concept of mother’
we change the meaning of the sentence, though not its truth value.
That seems to me rather ad hoc. How does it explain the difference in meaning
between X and Y as opposed to simply asserting that the meanings are different ?
Saul Kripke (1941- )
An alternative view of sense and reference was provided by Saul Kripke, in the
context of a strikingly original approach to necessity. The infant prodigy among logicians,
Kripke wrote his first published paper on modal logic at the age of sixteen.
He took the opposite approach to Quine‘s, arguing not only that the distinction
between the necessary and the contingent is a difference of kind, not of degree, but that
there are even more distinct types of proposition than had ever previously been claimed.
Kripke thought logicians have traditionally confused two quite different distinctions:
(1) an epistemological distinction between a priori truths which can be known
independently of experience and a posteriori truths that cannot and (2) a metaphysical
distinction between necessary propositions, that are true in all possible worlds, and
contingent propositions that are true in some possible worlds but not in others. Kripke
therefore denied both a priori = necessary and a posteriori = contingent
He pointed out that we can know a priori truths by experience if our knowledge is
derived from the result of running a computer program. There are no truths that cannot
be known by experience, so that it would be foolish so to define a priori that it has no
application.
However, as I remarked earlier, when we do learn of a necessary truth by
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experience, that experience points to an a priori justification that would be available if we
looked for it. The computer’s verdict gives reasonable grounds for thinking a number
prime, but there is a proof hidden in the operations of the computer, and it is because we
believe in the possibility of constructing such a proof that we believe the computer’s
conclusions. Someone who is familiar with the details of the computer program and
knows the form of proof it implements has stronger grounds for belief than someone who
does not, because the former is nearer than the latter to producing a priori grounds for the
belief.
Another point Kripke made was that a priori does not imply certainty. Some people
have supposed that it does; it is quite common to hear the claim that only a priori
knowledge can be certain, because it alone is supported by proof. But as Kripke pointed
out, even if we have a proof, we can never completely rule out the possibility that it
contains a mistake. Granting him that point, I observe that where it is possible to prove a
proposition, someone familiar with a proof has stronger grounds for believing that
proposition than someone who just relies on the testimony of another person or the
output of a computer program.
Knowledge of an a priori proposition on the basis of experience is open to two sorts
of doubt, both to doubts about the validity of the proof used (for the computer program
contains all the steps of a logical proof), but also doubts about the reliability of the
computer. Another way of putting it is that the doubts about the accuracy of any proof are
greater in the case are when we do not have access to the proof to check it, and have to
trust not only the proof, but also the computer and its operator. Someone who has seen
and understood a proof will always be better placed than someone who hasn’t seen a
proof but relies on the testimony of others to assure him that it is valid.
Kripke has another reason for saying that necessary propositions need not be a
priori, for, he says, some necessary propositions may not be provable. For example
Goldbach’s conjecture that every even number greater than 2 is the sum of two primes, is
necessary if it is true, since it is either true in all possible worlds, or false in all possible
worlds. Its falsehood would present no problem, for if false it could easily be proved false
by giving a counter example. However, if true it might not be provable. Kripke must be
thinking of incompleteness, and the possibility that Goldbach’s conjecture is not provable
from ZF. However any mathematical truth can be proved in some consistent system. I
think the example of Goldbach’s conjecture shows something quite different, that, as I’ve
already suggested, the a priori/a posteriori distinction should be analysed in terms of
falsification, not of verification.
Kripke’s arguments point to the conclusion that ‘a priori’ should either be reserved
for the way we know particular propositions, or not used at all. I suspect the reason he
doesn’t put it like that is that he wants to make another point too, that a proposition may
be necessary without there being any way of knowing it a priori, so that some
propositions are both necessary and a posteriori. However, there could hardly be a
clearly defined set of a posteriori necessary propositions.
There are two ways in which a necessary proposition may not be known to us a
priori. (1) We may not know it a priori just because we do not know it at all; that reflects
just the present state of knowledge. Not being known is not an intrinsic property of any
proposition. (2) We may know the proposition a posteriori.
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Neither (1) nor (2) justifies asserting that the proposition in question cannot be
known a priori, because the available examples of a posteriori knowledge of necessary
propositions all show how we might have a posteriori knowledge of the possibility of
proving the proposition in question. In other words, our a posteriori knowledge is
knowledge that it is possible to know the proposition a priori. Furthermore there can be no
justification for claiming that there are any necessary propositions that cannot be proved
at all, since provability is relative to some formal system, and any necessary truth can be
proved in some formal system, trivially in a system in which it is an axiom.
Consider the connection of a priori propositions to any evidence that might be put
forward in their support. When I discuss science it will emerge that basing theories on
experimental evidence centres on creating situations in which the theories are tested by
exposure to the possibility of refutation. But a proposition that can be known a priori must
be necessary, that is true in all possible worlds, otherwise we could not establish its truth
without calling on some information about our world to show that it is one of the possible
worlds in which the proposition is true. If a proposition is necessary there is no possible
observation that could contradict it, so it cannot be tested by exposure to the possibility of
falsification, for there is no such possibility. The a posteriori justification of a proposition
that could be known a priori is therefore rather a sham, since if P is necessary Q  P for
any proposition Q so that any proposition at all could be said to confirm P. On the other
hand, if confirmation is interpreted as surviving a test that might have falsified it, no
necessary proposition can be confirmed. To describe a possible observation that would
falsify some proposition suffices to show that proposition is neither necessary nor capable
of being known a priori.
In recent times a necessary proposition has usually been regarded as one that
encapsulates an implicit inference, so that ‘Any human is a mammal’ is a necessary truth
because any proposition of the form ‘A is human’ entails the proposition of the form ‘A is a
mammal’, so that ‘Harold is a mammal’ would not usually be considered necessary,
though it is a necessary consequence of ‘Harold is human’ Only if ‘Harold’ is defined to
be the name of a human could ‘Harold is a mammal’ be presented as necessary. So if
Harold is defined as ‘The man who lives next door’ ‘Harold is a mammal’ would be
necessary, but if ‘Harold’ were defined as ‘The subject of your next novel’ the proposition
would not be necessary.
Logicians like Kripke who want to follow Aristotle in attributing necessity to the
application of predicates to individuals, as opposed to deductions from descriptions of
individuals, have to explain necessity not in terms of deduction, but in terms of possible
worlds. A proposition is necessary iff (= if and only if) it would be true in every possible
world, yet that definition conceals a circularity.
Suppose Harold actually is human and that Quine said he could imagine the
possibility that Harold might not have been human, but might have been someone’s pet
snake, while Kripke says that the imagined snake is not a possible variant of Harold (I
think Kripke would have said that though I’m not sure whether Quine would have argued
as I suggested). How do we decide whether or not the snake called ‘Harold’ that Quine
says he can imagine, would be a genuine variant of human Harold, rather than just an
imagined alternative being that just happens to have the same name? Assuming the
discussion is not to degenerate into ‘Oh yes he is!’/’Oh no he isn’t!!’ the only answer I can
think of is for Kripke to say that a genuine alternative Harold must have all the necessary
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properties of Harold. Thus, while possible worlds are called on to define necessity, it is
only by recognising necessity that we can decide what flights of the imagination constitute
possible worlds, rather than unrealisable speculations. Truth in every possible world is not
an alternative definition of necessity, it is an alternative way of looking at whatever other
definition we have.
Kripke on Identity statements
Kripke held that all identity statements are necessary, on the grounds that if ‘a = b’
asserts ‘x = x’ for some x, it can be deduced from (x)(x = x). He also held the
‘indiscernibility of identicals’, a = b  [F(a)  F(b)] for all F. The universal closure of that
was used as a definition of equality in the proof in modal logic that x = y (x= y)
So for Kripke MS = ‘The Morning Star is the same as the Evening Star’ is
necessary. Yet it would have been quite possible for there to be two different celestial
bodies, one of which often shone brightly shortly after sunrise, while the other shone
shortly before dusk, so Kripke cannot have been asserting that it is logically necessary
that the two descriptions apply to the same object. He seems to have meant that MS
asserts, of the object that is in fact both the morning start and the evening star, that it is
identical with itself. One could interpret MS like that, but I doubt if people asserting it
usually meant to do so, because in hat sense of the words there would be no point in
saying it unless one is a logician constructing an example.
Kripke claimed that MS is ‘contingently necessary’, presumably meaning that it is
necessary but might not have been. If by that he means that it is contingent that the
English sentence ‘The Morning Star is the same as the Evening Star’ expresses a
necessary proposition, then that is true, but much the same could truly be said of any
sentence expressing a necessary proposition and all would be contingently necessary
because the English Language might have been different. If, on the other hand, he is
claiming that what is contingently necessary is not the truth of the sentence, but the
proposition expressed by the sentence, it is not clear where he locates the contingency.
For the contingency arises from the fact that in certain languages there are two different
terms that both refer to different the planet Venus, but refer to it viewed in different
circumstances, and that because of the difference in the circumstances those terms might
not have referred to the same planet. Translated into a language that had only one term
to refer to Venus MS would be something like V= ‘Venus is the same as Venus’ If we
make MS contingent by attributing to it assertions about language - namely that the
phrases ‘morning star’ and ‘evening star’ both refer to Venus, then we make it contingent,
but only by depriving it of any claim to necessity.
Kripke seems to be interpreting MS as
MSK: ‘the particular object, referred to sometimes as the ‘Morning Star’ and
sometimes as the ‘Evening Star’ is the same as itself.’
MSK is indeed necessary, but that just shows that MSK is not equivalent to MS
Part of the problem is that MS is often used to convey information that it doesn’t
directly assert. Such assertions are often puzzling.
The point of asserting MS is likely to be to acquaint the hearer with the fact that:
MSL: ‘The English phrases ‘Morning Star’ and ‘Evening Star’ are different names for
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the same object’
Some logicians have suggested that MS is equivalent to MSL, but that is clearly
false as MS is about heavenly bodies, not the English Language, and the same
proposition could be expressed in other languages.
However someone who hears MS asserted in English by a trustworthy informant is
likely to draw the conclusion:
‘ ‘The morning star is the same as the evening star’ expresses a true statement in
the English language’
and from that they can draw the further conclusion MSL, so although MS makes no
claim about the English language, its assertion in English in circumstances in which it is
clearly intended to be believed, will lead hearers to infer something about language, and
provoking them to make that inference may be the point of asserting MS in the first place.
Returning to the question of identity, (x)(x=x) does not convey information about
every individual; it states a property of equality. Propositions of the form a = a are special
cases of (x)(x=x) and so convey if anything even less information.
9 = 7+2 is not a roundabout way of telling us that 9 = 9; it is a direct way of telling us
that the application of the addition algorithm to 7 and 2 produces the answer 9.
Names
By ‘names’ logicians don’t just mean personal names like ‘Richard Thompson’ but
any phrase intended to identify a certain particular. ‘this toothbrush’, ‘that car’ will do
equally well.
I’ve already discussed Frege’s distinction between sense and reference, but didn’t
then say anything about names. Frege thought that the reference of a name was, of
course, whatever is named. Quite what he considered the sense to be is less clear,
though he thought proper names did have senses as well as references, and the sense of
a particular proper name must in some way encapsulate whatever criteria are used to
decide to that the name should be applied.
One alternative view is that ‘proper names’ like personal names in English have no
sense but just denote a referent. If that analysis is correct the best case for it would be
the failure of all other accounts of names, so I shall discuss those first, before saying any
more about the ‘no sense’ theory.
One proposal is that the sense of a name is a description of its reference. Quine
suggested that all names be treated as definite descriptions so that ‘Quine’ becomes ‘the
unique x such that Q(x)’ where the predicate Q is sufficiently detailed to apply only to
Quine, to whom others have therefore sometimes jokingly referred as ‘the unique
quinizer’.
How detailed should such a description be? Making the sense of a name a
complete description of the particular referred to has two drawbacks. All true propositions
about the particular become logically necessary, and if we make the smallest mistake in
describing the particular, the name will fail to refer. Since I was born in 1938, we should
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have to say that it would be impossible for anyone to believe that I was born in 1939 for
the sense in which they would be using ‘Richard Thompson’ would include having been
born in 1939 and in their sense of the words they would therefore not refer to me. Yet
people often are either entirely ignorant of other people’s birthdays, or mistaken about the
precise date, yet we do not usually regard such ignorance or error as a failure to refer to
the person they are trying to talk about. Recently one of my cousins who has been tracing
his family tree revealed that one of my grandmothers was born a year later than we had
all believed. That mistake did not prevent our successfully referring to her.
Perhaps instead of using a full description we could select just some particularly
important properties of a particular as the sense of its name. However there will usually
be many different partial descriptions, each sufficient to pick out a particular. Whichever
one we choose will introduce a distinction between necessary and contingent properties
of the particular in question, the necessary properties being the ones that follow from the
definition, and the contingent properties those that don’t. Different people might then use
the name in different senses, for each might know and want to incorporate in the set of
necessary properties, some property of the particular important to them but not known to
any of the other users of the name. What properties of a particular are necessary and
what are contingent would then vary from uses to user. Moses’ wife may have thought the
mole on his left buttock one of the necessary properties of Moses, but as that attribute is
not recorded in the Bible the rest of us can’t use ‘Moses’ in the same sense that she did.
Arguably it may not be logically necessary that an individual posses even the
properties referred to in a definition. Our way of referring to individuals, and to types of
individuals, works because the world can be divided into sets so that all the members of
the same have many common properties, and any two individuals belonging to different
sets differ from each other not just in one or two qualities, but in a fair number. For
instance all specimens of gold melt at 1063º C, boil at 2660º C, have specific gravity
19.3, do not dissolve in concentrated hydrochloric, sulphuric or nitric acids, but do
dissolve in aqua regia, have latent heat of fusion 63 KJ/Kg, and so on, through thermal
and electrical conductivity, specific heat, magnetic properties, and elasticity. If we select
as a definition, DG, of ‘gold’ a selection of properties that includes the melting point of
1063º C then it will indeed be analytic that anything satisfying that definition melts at
1063º C, but I do not think that that need be quite the same as asserting that it is analytic
that gold melts at 1063º C, for ‘gold’ need not mean ‘what satisfies definition DG’,
because DG is just one of many possible criteria, any one of which might have been used
to pick out the same collection of objects, and ‘gold melts at 1063º C’ tells us something
about the objects in that collection, not about the particular criterion used to identify the
collection.
I think that that is what John Searle was thinking of when he proposed that a name is
what has subsequently come to be known as a ‘cluster concept’ . He suggested that the
sense of a name should be of the form: ‘a reasonable selection of the following.....’ with a
list of the known properties. It is then possible to say we have been mistaken about any
particular attribute of a particular without having to deny that it was that particular we were
talking about. I think such an analysis would be improved if the properties in the list were
weighted, so that we took a particularly serious view of errors in matters such as place,
time and (for people) gender. Thus if someone discovered that the Biblical stories about
Moses all referred to someone called Jacob, we might so ‘Oh, so he was really called
Jacob’, but the discovery of someone having Moses like adventures at a time when the
relevant books of the Bible were already in existence would make us say ‘Similar
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adventures, but not the same man’, even if the historical figure we discovered were
actually called ‘Moses’.
Kripke proposed what at first glance looks like a version of the ‘no sense’ theory,
saying that names are ‘rigid designators’ that are given to particulars in some sort of
ceremony. The criterion for applying a name so given is spatio-temporal continuity with
the particular originally given the name. That is correct for particulars that have been
ceremonially (even if informally) named, like people, pets, plots of land (official registries)
antiques and works of art (insurance schedules), but it is of no use for ‘Moses’ where we
have no record of the naming ceremony. ‘Moses really did exist’ should be analysed as
Searle suggests.
Careful analysis of Kripke’s theory shows that his account of meaning is more
problematic than it first appears. Far from adopting the ‘no sense’ theory he seems to be
treating names as a special sort of definite description according to which ‘John Richard
Thompson’ would mean:
JRTDEF: ‘The human being spatio-temporally continuous with the baby born in 5,
th
Barbara Avenue Leicester on 15 September 1938 and shortly afterwards named “John
Richard Thompson”’
Note that I don’t know precisely when I received my name; it probably wasn’t
immediately after my birth, and now my parents are both dead it is possible that no-one
now does know, but that doesn’t seem to undermine the credentials of my name.
However it is hard to be sure precisely what Kripke intended, because he follows his
claim that names are ‘rigid designators’ with the statement that some of the properties of
an individual are necessary, because there is no possible world in which it would not have
those properties. He said for instance that ‘Nixon is a human being’ is necessary because
there is no possible world in which Nixon was not human - an odd thing to say for might
not the very same Nixon who was twice elected President of the United States just
possibly have been not human but an alien in disguise?
Consider now:
JRTM: ‘John Richard Thompson is male’,
If that is equivalent to ‘JRTDEF is male’, in which my name is replaced by the
definition JRTDEF I offered above, the sentence is not necessary, because the baby born
then and there could well have been female. Kripke would, I think, say that JRTM is
necessary, because it means not that whatever baby was born then and there was male,
but that the particular baby that was actually born was male. The specification of my birth
details is merely a way of pointing to me, not a definition of me. In that case it is hard to
pick any property that I possessed at the time I was born that is not necessary, and
Kripke seems committed to the view that everything true of me at the time of my birth is
necessarily true.
However my state at birth must have been affected by events before I was born - my
mother’s food intake and so on, and these could easily have been otherwise, so birth may
be a poor choice for the crucial time. The body after birth is a continuation of the foetus
before birth, and that can be traced back to a fertilised ovum. We could take someone’s
essential properties as their genetically determined properties, and if he wished Kripke
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could make those necessary, by using the Genome as a definition of the person. My
having brown straight hair and blue eyes would then both be necessary properties.
Although that is a possible usage, I do not think we actually use words like that,
because it would be thought reasonable to say ‘you might have been a girl’ For instance
my mother once said that had I been a girl I should have been called Barbara, for not
knowing in advance what sex I should be, my parents had decided in advance on Richard
for a boy and Barbara for a girl. I do not think my mother was imagining something
logically impossible when she said that.
While Kripke has a defensible, if implausible, distinction between necessary and
contingent properties for a person, I see no such possibility for many inanimate objects. A
person, in common with many though not all living things, has a definite starting point. It is
quite different with a mountain, a forest or a river. Difficulties in applying Kripke’s theory to
inanimate objects reflect on its application to people, because propositions about people
cannot be treated in isolation from propositions about the other components of the world.
Consider:
(1) ‘Dr. Samuel Johnson was born in Lichfield.’, and
(2) ‘Lichfield is Dr. Johnson’s birthplace.’
For Kripke (1) is a necessary truth about Dr. Johnson, but (1) and (2) are equivalent
so that if (1) is necessary, so is (2). Yet it is most implausible to maintain that being Dr.
Johnson’s birthplace is a necessary property of Lichfield. Lichfield existed long before Dr.
Johnson’s birth, and one could hardly maintain that it wouldn’t have been Lichfield had it
not been destined eventually to become the birthplace of Dr. Johnson.
There will often be difficulties with artefacts. Suppose a joiner makes two tables X
and Y, of the same size, for an old aristocratic family. On the top of each table is inlaid a
scene depicting some event in the family’s past, a different scene for each table. On each
of the legs is carved the coat of alms of one of the other families into which our family has
married, so there are eight different coats of arms, one for each leg (eight legs for the two
tables). Suppose table X had legs A, B, C, and D and table Y has legs E, F, G, and H. Is
the fact that table X has leg A and not leg F necessary or contingent? It is certainly
possible that the joiner should have attached legs B, C, F, and G to the top that in fact
became part of table X. Would that have constituted the same table having different legs,
or should we say that the joiner would in that case have made a different table? Searle’s
analysis seem the most appropriate here. Of course we could take the table as being
‘born’ when the legs are screwed on. Would a scratch made at the same time become a
necessary property too? Would it make a difference to the answer to that question if the
making of the scratch affected the selection of which legs were attached to which top?
Perhaps when he saw the scratch the joiner went off to find some plastic wood to conceal
it, leaving his assistant free to fit legs ABCD to X, while the joiner himself, had he been
present at the time would have chosen A, D, F, G. Whether a particular property is
necessary or contingent now seems a matter of what we want to call it.
I think Kripke is muddling the logical problem about meanings with the practical
problem of re-identifying objects. Supposing we have formally bestowed the name ‘Harry’
on a puppy, which is then lost. Years later we encounter a dog, and wonder if it might be
Harry. The question we ask in not ‘has this dog the essential properties of Harry’ but is
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this dog spatio-temporally continuous with Harry. The answer will be definitely ‘no’ if we
find something about the dog that shows it couldn’t have grown out of the little puppy we
originally named. The relevant sense of ‘couldn’t’ is physical or biological impossibility,
not logical impossibility. Of course DNA evidence would be excellent, though not because
we decide to use that as a definition of a creatures essence, but because of the
contingent fact that an organism’s DNA does not change as it ages, and no two creatures
that are not clones have the same DNA. Logical necessity is becoming confused with
physical necessity.
Kripke’s theory does not actually license us to classify as necessary any propositions
we are likely to be in a position to make about the bearer of a name. Even if it is a
th
necessary property of myself that I was born on 15 September 1938, someone who
says of me ‘Richard was born on...’ would not be asserting a logically necessary
proposition because he will be thinking of me as the man satisfying a certain description
such as ‘bearded webmaster of the Leicester U3A’ and his assertion about my birthday is
an assertion that the bearer of that description was born on the day in question. Often we
know someone as ‘this person just here’ and even if ‘Z is necessarily left handed’ and ‘Z
is the person just here’ are both true, it does not follow that ‘the person just here is left
handed’ is necessary. Even if someone who was present at my birth met me some years
later, his assertion ‘Richard was born on...’ would not be necessary, for it might be false if
the Richard he was meeting turned out not to be the same Richard whose birth he had
attended.
Taking Russell’s example ‘Scott was the author of Waverley’, Kripke would not
accept the argument that that is not necessary because there could well have been
someone otherwise just like Scott, except that he did not write the Waverley novels. So
Kripke would have included the authorship of Waverley among the necessary properties
of Scott. What he would then be asserting to be necessary would be the proposition:
‘Scott, who among other things was the author of the Waverley novels, wrote the
Waverley novels’
That is indeed necessary, but the claim is far less exciting than someone would
expect on hearing for the first time the claim that Scott was necessarily the author of
Waverley, and it is quite different from saying that the baby Scott necessarily grew up to
write the Waverley novels; that would be exciting, but is not true.
Truth
John Austin (1911-1960) wrote “ ‘in vino veritas’, but in sober discourse ‘verum’ ” He
meant that the noun ‘TRUTH’ is dispensable; what we need to say can be said with the
adjective, ‘true’. Once we notice that, we are likely to conclude that little need be said
about ‘true’ at all, and most of that little is to combat confusing comments made by people
who prefer the noun to the adjective.
In simple cases we don’t even need ‘true’ To say that a proposition is true is just to
assert it. What we are asserting when we say something is true is that it correctly
describes things as they are.
The words ‘true’ and ‘truth’ are linked etymologically to ‘trust’, which has been
derived from the Indo-European root deru meaning tree with the associated meaning of
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something that can be relied upon.
Plato discussed an existence theory of truth - that true propositions are directed to
what is, and false propositions to what is not, but rejected that in favour of the
correspondence theory of truth, summarised by Aristotle as ‘To say of what is that it is
not, or of what is not that it is, is false; while to say of what is that it is, and of what is not
that it is not, is true’
Applied to a particular sentence ‘true’ is just a device for removing the quotation
marks, so ‘fish are vertebrates’ is true = fish are vertebrates, but the word ‘true’ can’t
always be eliminated like that.
Suppose the personnel director of a company says ‘We check everything job
applicants say on their CV’s and would never employ anyone unless everything they say
is true.’ That can’t be replaced by the conjunction of the statements people actually make
on their application forms, because many of those forms haven’t yet been filled in.
Tarski argued that we can’t give a ‘general’ definition of truth, but only a specific
definition for any particular language. He proposed that for any language L we construct a
semantic definition of truth that specifies, for each sentence S of L the conditions under
which S is true. The often quoted example is:
‘snow is white’ is true if and only if snow is white.
Tarski was interested in giving truth conditions for formalised languages, specifying
when simple sentences like ‘snow is white’ are true by saying how the world must be to
satisfy them, and specifying when complicated sentences are true by referring to the truth
conditions for their simpler components, so that a truth table gives the truth conditions for
a truth function of simpler sentences.
He noticed that contradictions can arise if we try to specify the truth conditions for a
language in that same language, so he specified that the truth conditions for the
sentences of some language L can be specified only in a metalanguage L1 so if
‘snow is white’ is in language L
“ ‘snow is white’ is true if and only if snow is white.” is in the metalanguage L1
The last sentence, which contains a reference to L1, is in metalanguage L2
Pragmatists think we can at best obtain only a series of approximations to the truth.
If we go further and say that there is no truth independent of our beliefs, we have a
pragmatist theory of truth, that the truth is the set of propositions to which our belief
system converges as we test it and refine it. That raises the questions
(1) might the eventual point of convergence depend on the starting point of the
process, so that there might be alternative truths? , and
(2) are our beliefs converging at all?.
Rudy Rucker
In Infinity and the Mind, Rucker combined a number of interesting observations
about infinite sets and the foundations of Mathematics, with obscure references to a
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mystical vision that all reality in One. He seems to have been influenced by several
interviews with Gödel who had a quasi Platonic view of mathematics as describing a
world of timeless entities somehow existing beyond the phenomenal world of physical
objects and sensory experience, and incapable of being adequately described by any
formal system
Rucker wanted to establish that no formal system or machine can fully capture the
potential of human thought, citing in his support Gödel’s incompleteness theorems and
also various of the semantic paradoxes. In this section I want to discuss his references to
the latter.
I shall concentrate on his discussion of paradoxes about the definition of numbers,
and especially Berry’s Paradox. In Chapter 4 I presented that in the following form:
Let us define the number N so that
N = the smallest number that is too large to be defined in fewer than sixteen words.
Now consider the length of that definition; it contains only fifteen words which is less
than 16, contradicting the terms of the definition.
Russell and Whitehead introduced a ramified theory of types to avoid such
paradoxes, but I think paradoxes about the definability of numbers can be avoided by
distinguishing different senses of ‘define’.
The mathematicians' ideal is:
(1) A constructive definition, that enables us to produce the value of the number in
some approved notation.
but where no constructive definition is available many might accept as a second
best:
(2) A non-constructive definition that is sufficient to enable us to recognise the
number in question should anyone ever manage to construct it in any context.
The definition proposed in Berry’s Paradox does not satisfy even 2. For suppose
someone defined some number in 18 words, it would not follow from the length of that
definition that the same number could not be redefined in only 16, apparently leaving
open the possibility it actually is the Berry number. Indeed, once some number has been
defined we can easily give it a short definitions. A school Maths club might each day
select some number to be the ‘number of the day’ A number initially defined at great
length might then be referred to as ‘Tuesday’s number’
To make it worth examining any further the paradox must be restated.
First of all we must replace ‘word’. Ordinary language is fluid. In it we are free to
define new words and there is no maximum length for a word. We could therefore define
any number we wished in one word, just by counting as one word the sequence of digits
that express the number in the scale of 10. ‘Word’ had better be replaced by ‘character’.
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Yet it is still not clear what would count as a definition of a number in a certain
number of characters, for whatever can be defined in a language, at whatever length,
could used as a definition for some other sequence of characters that could be as short
as we like. For instance certain infinite series are of such great interest to mathematicians
that there are represented by the single characters  and e.
We could not produce definition of word sufficiently precise to allow a clear
statement of Berry's paradox without somehow including the explanatory power of the
whole language in the length of any proposed definition. We should therefore have to
settle on some formal system, and on a certain type of definition within such a system.
Yet in a formal system it would probably be impossible to state Berry’s Paradox.
Another style of argument used by Rucker was to cite our apparent ability to reach
an intuitive understanding of proper classes, even though they represent totalities too
large to be incorporated in a consistent formal system. Examples are the class of all sets,
the class of all ordinal numbers, and the greatest ordinal (considered a class according to
the definition of an ordinal as the set of all smaller ordinals). It seems to me doubtful that
we do have an intuitive grasp of such concepts. The mathematically aware do think of
sets and ordinal numbers in general, but that does not imply that we think of the totalities
of all sets or of all ordinals as distinct entities. Meditating successively on ‘set’ and
‘totality’ does not constitute thinking about a totality of sets.
Jacques Derrida (1930-2004)) and Deconstruction
Derrida believed that almost all contemporary thought depends on unsupported
assumptions common to both sides in any debate, and he launched a programme for
identifying such assumptions. Derrida described his programme as ‘Deconstruction’, a
word he is said to have borrowed the from Heidegger.
Deconstruction seems to be a sort of substitute for literary criticism, though it has
some philosophical pretensions. While it is clear that Derrida advocated a critical
re-examination of all aspects of intellectual life, it is not at all clear that that examination
was guided by any unifying idea, because his use of the word ‘deconstruction’, which is
clearly supposed to stand for such an idea, is impenetrably obscure.
In the local library I found Acts of Literature, various writings of Derrida, edited by
Derek Attridge (a US academic), who contributed an introduction and an interview that
Derrida had given him. Although there are many references to deconstruction, I found no
direct statement of what it is, nor any stated examples of deconstruction in action.
For Derrida Literature was an institution, seen as inseparable from philosophy. We
are told of the need to determine the essence of literature. There is talk of reading "in a
transcendent fashion" (that seems to be a Bad Thing). Most of what I read made little
sense to me so I cannot paraphrase it. I quote a few sentences to illustrate my difficulty.
"Deconstruction is indeed contradictory. [It is also impossible, Derrida likes to say-and
it doesn't exist]. It is both careful and irreverent, it does both acknowledge and traverse borders, it
is both very old - older than philosophy, Derrida claims - and very new, not yet born perhaps."
(Attridge)
"The Literary character of the text is inscribed on the side of the intensional object in its
noematic structure, one could say, and not only on the side of the noetic act" (Derrida)
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‘noematic’ does not appear in my copy of the Shorter Oxford English Dictionary; the
free online dictionary says ‘pertains to the understanding‘. In the SOED ‘noetic’ is stated
to mean ‘intellectual’, possible purely intellectual. I suspect that the choice of obscure
words was a ploy by Derrida to make his writing appear more recondite than it was.
Substitution of the dictionaries’ suggested meaning in Derrida’s sentence produces only
nonsense.
A common theme in self styled ‘deconstructive’ argument is a criticism of contrasting
pairs of ideas, such as mind and body, speech and writing, especially when one of the
pair is considered to be in some sense prior to the other. Derrida was especially
concerned to combat the assumption that writing is secondary to speech. Yet in the
obvious sense of the words that is clearly true, for spoken language preceded written,
children learn to speak before they learn to write, and most written languages have a
substantial phonetic component. Written language is indeed in some circumstances
superior to spoken; it is better for the careful examination of difficult ideas, especially
when supplemented by special symbolism and by diagrams, but to make that point is at
only to remind us of something that only enthusiastic educationists sometimes overlook;
it does not amount to the exposure of a deep rooted misconception.
Derrida was influenced by Ferdinand de Saussure who had developed an extreme
nominalist theory according to which the concepts we apply to the world depend on the
way we use language and are culturally determined, having no other basis in reality, and
Derrida seemed to develop this argument almost to the point of saying that there is no
truth independent of culture and language.
It seems to me that Derrida is one of those people who write obscurely in the hope
of being thought profound, but the general drift of deconstruction seems to be to insinuate
a denial that any general or abstract theory has any greater validity than any other,
without actually being prepared to assert that explicitly so that it can be challenged.
Derrida’s appeal was mainly to academics teaching literature, especially in American
universities.
Local Truth, Alternative Truths
People sometimes reject criticism of their beliefs by saying ‘It’s true for me’ and
sometimes comment on other people’s beliefs ‘That’s just your local truth’. They rarely
explain whether they consider that claim just part of their own local truth, in which case
there is little point in their saying it to people outside their own circle, or whether they
consider it a truth that holds for everyone, in which case they have admitted truths that
are not local.
Such talk may often be just a misleading way of distinguishing established
knowledge from tentative belief, but sometimes it may be the expression of a radical
scepticism that denies there is any objective knowledge. Even from the point of view of
that stronger skepticism, it is still misleading to talk of different ‘truths’. For truth is
whatever we try to make our beliefs agree with, whether or not we are successful, so that
talk of different truths would make sense only if it meant not just that individual people
sometimes have mutually inconsistent beliefs, but that different groups of people aim their
belief systems at different targets.
It is conceivable that there might be different species of intelligent creatures with
systems of belief so different from each others' that there is no correspondence between
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one system and the other, but for there to be no correspondence at all the two species
would have to avoid any interaction. For suppose there were some interaction; species
A’s spaceship lands on species B’s planet. That would be an event of which both would
have to take account, and even if they described it in very different ways, each of those
descriptions would have to take account of something happening at a certain place and
time, so the two belief systems would not be entirely independent.
However the people whom we sometimes hear talking about alternative truths are
not members of other species which never interact with humanity, they are other human
beings speaking to us in languages we and they both understand, sharing beliefs in the
existence of the chairs we sit on when we communicate face to face and of the
computers or telephones we use to communicate at a distance. Where our opinions differ
we can tell each other what the differences are, and show each other how we reach our
conclusions. In those circumstances there can be no reason-proof barrier between one
system of belief and the other. At most there can only be a refusal on the part of one
group to pay attention to the opinions of the other.
I conclude that there are no local or alternative truths in the sense of alternative
objectives, any one of which a belief system could pursue with at least some hope of
success. So far as they have any cogency, arguments in favour of a system of local truths
go no further than to suggest that there is no definite truth at all, in which case it would be
best not to talk about ‘truth’ of any kind. However, anyone wanting to establish such a
position would need to explain how the various truth systems work, and how they are
related so that people subscribing to different truth systems can still to some extent
communicate with each other. In practice what purport to be arguments for local truth are
usually arguments for a general scepticism, dishonestly deployed by someone who does
not actually believe in scepticism but just wants to avoid criticism of their own beliefs.
Logical Positivism
Difficulties in handling the meanings of individual words led to the suggestion that
the primary unit of meaning is the sentence. Concentrating on sentences that can be said
to be either true or false (not all sentences can be true or false ‘Let’s play Bridge’ may be
sensible or silly depending on the circumstances, but it can’t be true or false) the meaning
of a sentence seems to be what it purports to tell us about the world, in other words the
state of affairs, or set of states of affairs, that would apply were the sentence true. We can
explain the meaning of a sentence by saying what things would be like if it were true.
Logical Positivists, who flourished from the early 1930’s till about 1950, assumed
that nothing could be meaningful unless it could be either true or false. They summed up
their programme in the slogan
D: the meaning of a sentence is the method of its verification.
Taken literally that is false. We can understand a sentence without being aware of
precisely how it is verified; we can understand what is meant by saying that cut flowers
last longer if a little sugar is added to their water without receiving detailed explanation of
the statistical techniques used to show that the sugar makes a significant difference.
I think that what the Logical Positivists meant was that the meaning of a sentence is
what the world would have to be like for the sentence to be true, so that it can‘t be
meaningful unless there is some way of checking it against the world to see if the actual
state of affairs is what the statement says it is. However such checking need not involve
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verification. Testing would suffice and the Logical Positivist program would be easier to
defend if ‘verifiable’ were replaced by ‘falsifiable’. In some cases it might have been
possible to dispense with any sort of checking and just ask for examples to show what it
would be like if a problem statement were true.
The Logical Positivists held there were only two ways of verifying a sentence.
Logically true sentences may be verified by proving them, and contingent sentences may
be verified by presenting confirming observations.
A lively and concise account of Logical Positivism may be found in A. J. Ayer
Language Truth and Logic
Confronted by any sentence that appeared incapable of taking a truth value Logical
Positivists either dismissed it as meaningless, or else tried to interpret it so that it could
have a truth value. For instance ‘This picture is beautiful’ might be interpreted as meaning
‘I like this picture very much’ or as ‘Most people experienced in viewing pictures would
like this picture very much’ Such analyses are not plausible, as the original sentence is
about the picture, and neither about the feelings of the speaker, nor about the feelings of
people in general.
Some Logical Positivists interpreted sentences that cannot be true or false as
expressions of emotion, so that ‘this picture is beautiful’ was equivalent to ‘Cor, yum,
yum, yum, what a smasher!!!’ While an excellent paraphrase of much aesthetic criticism,
that hardly does justice to all of it. Probably most aesthetic judgements do convey the
feelings or preferences of the speaker but there is often something else too - at least an
indication of which aspects of the admired or denigrated object inspire the admiration or
disapproval.
Logical Positivists thought that logical truths were linguistic ‘A vixen is a female fox’
was interpreted as ‘vixen’ means ‘female fox’, or possibly ‘vixen’ means female fox.
However neither of these is equivalent to the original, as the first makes no claim about
the English language, while both the proposed analyses do.
Speculative metaphysics, or at least the part of it that has not been converted into
science, cannot be verified in either of the ways they recognised, so Logical Positivists
condemned it as nonsense. More than a century earlier Hume had taken a similar
position, in a passage Ayer quoted with approval in Language Truth and Logic.
“If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask
Does it contain any abstract reasoning concerning quantity of number? No. Does it contain any
experimental reasoning, concerning matter of fact or existence? No. Commit it then to the flames: for
it can contain nothing but sophistry and illusion.” (Enquiry section 12 part III)
‘School’ refers to the scholastics, the medieval Aristotelians.
Opponents of Logical Positivism countered that the verification principle was in that
case itself self condemned as meaningless, because there appeared to be no way of
verifying it. I’m not sure why Logical Positivists didn’t say that the principle was logically
necessary, but I don’t know of any instance of their doing so. Perhaps the other difficulties
of their position persuaded them to give up rather than fight a rearguard action. Language
Truth And Logic was first published in 1936. In his introduction to the second edition of
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1946 Ayer qualified the verification principle into almost unintelligible complexity. In the
following ten years successive qualifications gradually converted Logical Positivism into
the truisms that: (1) beliefs need some justification (2) what a sentence means
determines how it may be justified and (3) how we justify a sentence sheds a good deal
of light on what that sentence means.
As the wordy metaphysical wool-gathering that had provoked it went out of fashion
under the Logical Positivists’ attack, Logical Positivism itself faded away as fewer and
fewer felt prepared to maintain its counter intuitive classification of much discourse as
either meaningless or really about something quite different from what people had always
supposed it to be about.
It’s demise was accelerated by Popper’s attack on the idea of verification, which I
discuss in the next chapter. If it was not possible to verify the sentences of theoretical
science, which were for Logical Positivists (many of them with a background in the
physical sciences) the paradigm of theoretical knowledge, their programme had failed.
Popper’s emphasis on falsifiability as a criterion of factual content provided a neater way
of weeding out empty verbalising masquerading as theory, while the recognition that the
power of language is not confined to describing the world persuaded those had been
Logical Positivists that the factual/non-factual distinction was not the same as that
between the meaningful and the meaningless. Certainly by the mid 1950’s it was rare for
anyone to declare himself to be a Logical Positivist.
Wittgenstein
Under the influence of the teaching and posthumously published writings of
Wittgenstein (1889-1951) Logical Positivism developed into Linguistic Philosophy.
In his lifetime Wittgenstein published one book, the Tractatus Logico Philosophicus
and one paper, on logical form. The Tractatus is an exercise in logical analysis in the
style of More and Russell. It was written on the assumption that mathematics can be
reduced to logic and that logic can be reduced to the study of tautologies. It was refuted
by the discovery that there is no decision procedure for the general predicate logic,
followed by Gödel’s incompleteness theorem.
Towards the end of his life Wittgenstein started to write another book. He was
profoundly dissatisfied with what he had produced and asked that after his death all his
writings should be burnt, but a good deal of material was nevertheless published, most
notably Philosophical Investigations composed of drafts of parts of the intended book. In
his later work Wittgenstein rejected any attempt to introduce formal precision into
philosophical discussions. He seemed at pains to avoid committing himself to any definite
conclusion, apart from the conclusion that other philosophers were generally confused.
The general drift of his discussions was that philosophers, and many other thinkers
too, have been misled by language, often because they looked to language for a
precision that it cannot provide. He often emphasized how, in unfamiliar contexts, the
quirks of language can mislead us into misunderstanding problems, or into seeing
problems where there are really none. The style and content of his later work is so
different from that of the Tractatus, which was based on a grossly oversimplified view of
logic and mathematics, that it would be easy to imagine they were written by different
men. The Tractatus is now regarded as of only historical interest; One academic
philosopher once remarked to me that the only significance of the Tractatus is that it was
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the only philosophical work that Wittgenstein had read before writing Philosophical
Investigations. Henceforth I shall discuss only Wittgenstein’s later work.
Because he published so little, Wittgenstein’s influence arose mainly from his impact
on those who attended his lectures and seminars. Some of those whom he taught seem
to have been intellectually crippled for life by the experience, spending the rest of their
lives editing their lecture notes. I find The Blue and Brown Books his most accessible
later work. That consists of notes on lecture courses delivered in the academic years
1933-4 and 1934-35, duplicated by some of Wittgenstein’s students, initially secretly, but
eventually with his knowledge and grudging consent. It seems to be an earlier draft of
much of the material in the Investigations.
The published material does not form a coherent whole. In places a line of argument
is sustained for a dozen pages or even more, but such passages are interspersed with
aphorisms, and short passages relating anecdotes and examples whose precise import is
often obscure. I find that dipping into Wittgenstein can be a stimulus to thought, though
whether the thoughts it stimulates are those Wittgenstein hoped to convey is quite
another matter. There are intriguing stories and striking aphorisms there. Wittgenstein’s
writings are a rich source of puzzles and illustrative examples, but offer few answers.
Wittgenstein famously discussed the possible definition of ‘game’ Someone might
say “A game is an activity undertaken for amusement or entertainment in which people
compete to see who can achieve some goal and thus ‘win’ the game”. However in a
game of patience there is only one player, in ring ‘a ring ‘a roses there is no competition
and no winner, and if all games were fun there would be no need to have compulsory
games in schools. On the other hand a typical game will meet the description given. All
activities we call games will resemble others in some respects, and will be linked to the
central cases by a chain of resemblances. In the Philosophical Investigations he wrote,
(the numbers give the sections, not the pages)
66. [discussing the concept of a game] We see a complicated network of similarities
overlapping and criss-crossing; sometimes overall similarities, sometimes similarities of detail.
67. I can think of no better expression to characterize these similarities than “family
resemblances”; for the various resemblances between members of a family: build, features, colour
of eyes, gait, temperament etc. etc. overlap and criss-cross in the same way, and I shall say:
’games’ form a family....[he then switched to the example of what constitutes a number]
..And we extend our concept of number as in spinning a thread we twist fibre on fibre. And the
strength of the thread does not reside in the fact that some one fibre runs through its whole length,
but in the overlapping of many fibres.
But if someone wished to say “There is something in common to all these constructions namely the disjunction of all their common properties” - I should reply: Now you are only playing
with words. One might as well say “Something runs through the whole thread - namely the
continuous overlapping of those fibres”
Wittgenstein was wrong about the various concepts of number; there is a common
factor. Each of the classes of entities we call ‘number’ contains as a subset the natural
numbers, and is closed under addition and multiplication.
Wittgenstein thought that many concepts are like ‘game‘, but it is probably no
accident that he chose ‘game’ as his example, for he often likened our intellectual
activities to ‘language games’ and described several simple language games to illustrate
the various functions of language.
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I quote a few more short passages from Philosophical Investigations. Some of the
passages quoted have a bearing on some of the problems discussed in this chapter, such
as universals, identity, and the attempts to distinguish between necessary and the
contingent properties of individuals. All quotations except the last are taken from part I
76. If someone were to draw a sharp boundary I could not acknowledge it as the one that I too
wanted to draw, or had drawn in my mind. For I did not want to draw one at all. His concept can
then be said to be not the same as mine, but akin to it. The kinship is that of two pictures, one of
which consists of colour patches with vague contours, and the other of patches similarly shaped
and distributed, but with clear contours. The kinship is just as undeniable as the difference.
115. A picture held us captive. And we could not get outside it, for it lay in our language and
language seemed to repeat it to us inexorably.
119. The results of philosophy are the uncovering of one or another piece of plain nonsense
and of bumps that the understanding has got by running its head against the limits of language.
These bumps make us see the value of the discovery.
123 A philosophical problem has the form “I don’t know my way about”
124 Philosophy may in no way interfere with the actual use of language; it can in the end only
describe it. For it cannot give it any foundations either.
It leaves everything as it is.
It also leaves mathematics as it is and no mathematical discovery can advance it. A “leading
problem of mathematical logic” is for us a problem of mathematics like any other.
203 Language is a labyrinth of paths. You approach from one side and know your way about;
you approach the same place from another side and no longer know your way about.
204 As things are I can, for example, invent a game that is never played by anyone. - But
would the following be possible too: mankind has never played any games; once, however,
someone invented a game - which no one ever played ?
216 “A thing is identical with itself.” - There is no finer example of a useless proposition, which
is yet connected with a certain play of the imagination. It is as if in imagination we put a thing into
its own shape and saw that it fitted.
We might also say: “Everything fits into itself.” Or again: “Everything fits into its own shape.” At
the same time we look at a thing and imagine that there was a blank left for it, and that now it fits
into it exactly......
255 The philosopher’s treatment of a question is like the treatment of an illness.
309 What is your aim in philosophy? - To shew the fly the way out of the fly-bottle.
414 You think that after all you must be weaving a piece of cloth: because you are sitting at a
loom - even if it is empty - and going through the motions of weaving.
593 A main cause of philosophical disease - a one-sided diet: one nourishes one’s thinking
with only one kind of example.
Part II, iv The Human body is the best picture of the human soul.
Wittgenstein devoted much effort to problems about the interpretation of sense
experience and of propositions about mental events. Philosophers, especially but not only
Cartesians and Phenomenalists, had discussed the matter as if we started with
propositions about sensations and, after due deliberation, derived from them propositions
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about material objects. Suppose I see a rose in the garden. What actually happens, a
Phenomenalism would say, is that I see a red patch in the centre of my visual field, with a
pinnate green patch to its left, accompanied by a sweet smell. This is of course a gross
oversimplification; there would actually be much more than that, but the Phenomenalist
would say it would be much more of the same, though quite how the smell would be
described without saying ‘like a rose’ or ‘like tea’ was never clear.
Wittgenstein considered such stories absurd. He argued that we can’t start with
just ‘sense data’ because there could not be a language that just describes sensations
independently of physical objects. Of course we can and do describe our sensations, but
only by referring to material objects as in ‘I saw a black shape moving across the sky - it
looked like a swallow, but it moved so quickly that I wasn’t sure, and afterwards I
wondered if I’d imagined it’. As I understand Wittgenstein, he thought that language is a
social phenomenon in which members of a linguistic community discuss the world around
them. One can use language to soliloquise, or to write notes in a secret diary, but the
soliloquy could be overheard and understood by a concealed audience, the notes could
later be published if one changed one mind about the secrecy. However the description of
sensations envisaged by the phenomenalist is intrinsically private. There is no way of
checking whether today’s red patch is the same colour and shape as yesterday’s. In the
public world of gardens and roses I can record a description, and look the flower up in a
flora, but that assumes material objects. Without them I can’t talk sense even about my
sensations.
That is usually called the ‘Private Language Argument’ and has been generally
accepted, though not without dissent. A. J. Ayer, for instance, argued that the ability to
compare one sensation with another is presupposed by our ability to recognise anything
at all, since when we recognise a physical object we are comparing the present
sensations induced by it with our memories of previous sensations. Even if we look up the
rose in a flora we are comparing our perception of the rose with our perception of the
picture in the flora. If we can’t compare our sensations with one another we can’t
compare them with anything else either. (Can There be a Private Language pp 41-43, in
The Concept of a Person)
I occurs to me that Wittgenstein’s argument might not be conclusive against a
pragmatist who started with a conventional belief in material objects but then questioned
how securely it was supported by sensory evidence. The pragmatist could use the
language of material objects to describe sensations because he wouldn’t be trying to
construct material objects out of sensations, he’d rather be starting with assumption that
there are material objects and reviewing that assumption critically.
In the course of discussing a suggestion of Strawson’s, Peter Winch (The Idea Of A
Social Science pp 33-39) seemed to favour a stronger interpretation of Wittgenstein’s
thesis. Strawson had suggested that someone who had grown up in solitude with no
contact with any human society might still develop a language that might even eventually
be learnt by others, should the isolated man ever be discovered by other people. Winch
thought that impossible, on the grounds that any description of linguistic activities involves
the use of concepts like following a rule, interpreting the rule in the same way today as we
did yesterday, making and correcting a mistake. Winch therefore seems to have adopted
a strong thesis:
(1) language cannot be devised or used except in the course of the interaction
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between members of a society.
Thesis (1) is clearly false since someone who has learnt a language in a society may
then use that language in non-social context, such as soliloquy, and could go on to
devise some other language, like Esperanto - a language they could admittedly later
teach to others if they desired, but which would be no less a language if they chose not
to. Those solitary uses of language by a socialised person would be permitted by:
(2) A weak thesis: Language cannot be devised or used by someone who has never
previously used a language in the course of social interaction with other language users,
and there cannot be a language private to a particular person in the sense that it would
be impossible for that person to teach it to anyone else.
Thesis (2) escapes the objections I raised to thesis (1), but it is not strong enough to
rule out the supposed private language of sense data in which Idealists and
Phenomenalists sought to describe sense experience. While it does rule out the
possibility of someone who has never used a language socially, communicating with
themselves in some inner language, that does not undermine the position of the idealist
or phenomenalist, for he has learnt to use language socially, and could say that he is
applying those socially learnt language skills to his inner experience.
If we are to show that that supposed use is bogus we must appeal to the special
problems of describing inner experience, not to the social functions of language. Of
course Wittgenstein himself did consider those special problems, and it is his followers
who have been most concerned to develop those specific arguments into a more general
argument for a comprehensive social theory of language. In so far as some of
Wittgenstein’s own remarks may seem to support such a generalisation, we have to bear
in mind that his detailed arguments applied mainly to the more limited thesis that there
can be no inner language, and also that the text of the Investigations never reached a
stage Wittgenstein himself considered fit for publication - his own preference was that it
should be burnt.
Someone arguing that language is intrinsically social must in any case say what
constitutes a society. Must it be a society of human beings, or would a man and a dog
suffice? Arguably the dog might not understand the various gestures and calls the man
uses to control it, but if it usually obeys them that might suffice for the man’s use of them
to qualify as language. The core of Wittgenstein’s argument against a private language is
that we have no way of checking that the sign we are using today is the same as the
sign we used yesterday, and that seems to be true in the case of a supposed language
applying exclusively to our inner experience. However for the man with a dog such a test
is provided by the reactions of the dog. If he whistles to it to come to him and it does, that
is an indication that he got the whistle right. The dog might be replaced by a computer
running a speech recognition system,
Indeed, any external reference for a symbol seems sufficient to establish a checking
procedure for a language. Consider this possibility. A solitary man, M, invents a system of
signs to record the places where various useful materials may be mined or harvested,
and also to record the quantities of already harvested materials in his storage cave. If, for
instance, he needs a flint, he removes one from the flint store, and decrements the stock
record. When stocks of any item fall to what he considers a dangerously low level, he
consults the list of sources, goes to the appropriate place, and collects some more. The
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test that his symbolism is being applied correctly is that whenever he goes to the storage
cave, he returns with some useful object, that no item is ever out of stock, and that
whenever he goes foraging he returns with materials that replenish his stocks of materials
that were previously in short supply.
One form of the private language argument concerns the thesis that two people who
both see a red object and call it ‘red’ may yet have different perceptions. Provided that
they both learn to associate the word red with the correct objects that would not matter.
Followers of Wittgenstein consider that his argument against the possibility of a private
language commits them to rejecting that possibility as absurd. I am not sure.
Consider an intelligent talking robot that has red, green and blue colour receptors,
and learns the names of colours as humans do by being shown examples. Suppose there
are two robots of the same make, but that in one robot the red receptor is wired to the
part of the artificial brain that usually deals with input from the blue receptor, and the blue
receptor is wired to the part of the brain that usually processes input from the red
receptor. Both robots learn to use colour words correctly, but when we take them to
pieces for maintenance and notice the difference in their wiring we might say that when
they both said ‘red’ they were experiencing different brain events.
Suppose a human eye were analogously connected to the brain in an irregular
manner, might we not say the same then? Suppose that someone has normal
connections for one eye, but irregular ones for the other eye, so that when he looks at a
rainbow and compare what he sees though his two eyes, each eye sees the same
colours as the other, but arranged in the opposite order, so the right eye’s sensation of
red was the same as the left eye’s sensation of blue. Considering the normal case of
people to whom colours look the same through both eyes, such a person could ask ‘do
they see what I see through my right eye, or what I see through my left eye? Do the
people who see the same with both eyes all see in the same way, or are there some
people who see my left eye colours with both of their eyes, and others who see my right
eye colours?’
Even if such an irregular connection never occurs naturally, irregular eye/brain
connections are likely to be created in the future as surgeons create artificial eyes for the
blind. Possibly people with their two eyes wired differently would say that colours looked
the same through either eye. Those who deny the possibility of a private language might
expect them to say that. However, if true, that is a contingent matter. Even if it is in fact
wrong to suppose that such people would have two different perceptions of colours, the
supposition is not absurd.
My own experience gives additional ground for thinking that these speculations are
not entirely fanciful. There is one hue in the yellow/orange region that to me looks slightly
different depending on which eye views it. One eye sees it more orange than the other.
The principal target of the private language argument, possibly its only target, was
the theory of ‘sense data’ as the building blocks of the universe. It is therefore worth
remarking that the theory of sense data is suspect on other grounds and may be rejected
without any need to appeal to Wittgenstein’s argument.
During the first half of the twentieth century it became customary to talk of sense
data as if they were independent atoms of reality from which our perceived world may be
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created. It was even speculated that some sense data might be identical with the
surfaces of the objects sensed. Yet ‘sense datum’ must, if it refers to anything at all, refer
to an event in which a person either senses some physical object, or seems to do so.
Sense data can rarely even be described without referring to the objects that appear to be
sensed in them. It therefore seems absurd to suppose that such events could have any
existence independently of the objects perceived and the person perceiving them, still
less that sense data could not only have an independent existence, but could in a sense
be the only objects with an independent existence and form the basic building blocks of
the universe.
The supposition that sense data might form a basis for knowledge probably rests on
their apparent incorrigibility; they are not open to doubt. At the time we have a sensory
experience, it is indeed not open to doubt that we are having an experience, but as soon
as any interpretation is placed on an experience, that interpretation is open to doubt.
Experience is basic in the sense that it is a reference point against which our beliefs may
be checked, but it is not a foundation from which knowledge can be built.
John Austin(1911 - 1960)
Austin was prominent in the school of Linguistic Analysis that developed in Oxford in
the late 1940’s and 1950’s. Although strongly influenced by Wittgenstein, Austin
eschewed his oracular style and emphasised ordinary usage. ‘What should we say in this
situation, or that?’ was his approach.
He thought that philosophical puzzles often resulted from the use in one context of
forms of words appropriate to another. Supposedly philosophical problems were to be
dismembered, some components referred to the scientists, some to the lexicographer,
some to the logician, and any residue recognised as just empty. The following passage is
an excellent example of Austin’s style:
“...Certainly ordinary language has no claim to be the last word, if there is such a thing. It
embodies, indeed, something better than the metaphysics of the Stone Age, namely, as was said,
the inherited experience and acumen of many generations of men. But then, that acumen has been
concentrated primarily upon the practical business of life. If a distinction works well for practical
purposes in ordinary life (no mean feat), then there is sure to be something in it, it will not mark
nothing: yet this is likely enough not to be the best way of arranging things if our interests are more
extensive or intellectual than the ordinary. And again, that experience has been derived only from
the sources available to ordinary men throughout most of civilised history: it has not been fed from
the resources of the microscope and its successors. And it must be added too, that superstition
and error and fantasy of all kinds do become incorporated in ordinary language and even
sometimes stand up to the survival test (only, when they do, why should we not detect it?).
Certainly then ordinary language is not the last word: in principle it can everywhere be
supplemented and improved upon and superseded. Only remember it is the first word” (A plea for
Excuses, p. 133 in his Philosophical Papers)
In a footnote on the same page Austin provided an often quoted distinction between
an accident and a mistake.
“You have a donkey, so have I, and they graze in the same field. The day comes when I
conceive a dislike for mine. I go to shoot it, draw a bead on it, fire: the brute falls in its tracks. I
inspect the victim, and find to my horror that is it your donkey. I appear on your doorstep with the
remains and say - what? ‘I say old sport, I’m awfully sorry etc., I’ve shot your donkey by accident?
Or ‘by mistake’ ? Then again I go to shoot my donkey as before, draw a bead on it, fire - but as I do
so the beasts move and to my horror yours falls. Again the scene on the doorstep - what do I say
‘By mistake’ ? Or ‘by accident’ ?” (Philosophical Papers p 133)
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Austin coined the term ‘performative utterance’ for a speech act that does not just
describe or evaluate the way things are, but actually changes things. For instance when
the priest says ‘I declare you to be man and wife’ his saying it actually creates the
marriage.
Strawson’s criticisms of mathematical logic, discussed in chapter 2, provide another
example of the approach of the ‘ordinary language’ philosophers.
Existence of Abstract objects
E1 ‘Vampires don’t exist, but vampire bats do’ tells us that vampire bats are among
the contents of the universe, but vampires are not. It is less clear what is meant if
someone makes an existence claim for an abstract object.
E2 A friend once said that his virus scanner had produced the message:
"This scan cannot be started because it already does not exist."
E3 ‘blue exists, but octarine3 doesn’t’ is more problematical.
Does it assert that some objects are blue, but none are octarine? It is possible to
imagine circumstances in which there were no blue objects, yet we still experienced blue.
For a blue object is one that, exposed to white light, reflects more of the blue incident light
than it does light of other colours. Even if there were no such objects we could still
experience blue by looking at a spectrum. So better interpretations of ‘blue exists, but
octarine doesn’t’ are either that we sometimes sense ‘blue’ but never ‘octarine’, or that
‘blue’ is defined by range of wave lengths, but no such range has been assigned to
octarine.
So it appears that a property is thought to exist when there is a criterion for
deciding to what individuals it applies. The status of properties has attracted a good deal
of attention as part of the so called Problem of Universals. I discuss that in the next
section and shall therefore devote the remainder of this section to various observations
about existence in general
C.S. Peirce distinguished ‘real’ from ‘existent’, one remarking the he thought God
real, but hesitated to say that God existed.
C. D. Broad (in Mind and its Place in Nature around pp 18-19) divided reality into
what he called existents and abstracta. Although he held both to be real he denied that
abstracta exist. He restricted existence to what can appear in a proposition only as a
logical subject. He was unsure that that was a sufficient condition for something being an
existent, and supplemented it with the condition that existence must be in time, a claim
also made by Russell (in Problems of Philosophy p 57 of the 1967 paperback edition).
Broad neither defined ‘logical subject’ nor explained why he thought existence
must be in time so what follows is my speculative reconstruction of his thought.
3
octarine is the colour of magic in Terry Pratchett’s disc world series of phantasy
novels
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I think that by the ‘logical subject’ of a sentence Broad meant whatever it is about
which the sentence purports to give information, even though that may sometimes not be
the grammatical subject. For instance ‘Simon took Jennifer to Durham’ gives us
information about Simon, Jennifer and Durham, all of which are therefore logical subjects,
although only Simon is the grammatical subject. The distinction is linked to another
between two quite different ways in which a sentence might be false. It might be that the
existents referred to are not in whatever state the sentence claims they are, if, for
instance, Simon and Jennifer had stayed at home or she had taken him to Skegness, but
the sentence might also have been false because there is no such person as Simon or as
Jennifer, or no such place as Skegness.
A plausible reason for saying that existence must be in time is that ‘A exists’ asserts
that there is something in the world corresponding to our idea of A, so that the proposition
is contingent; even if there are A’s, there might not have been so that the question ‘when
were there A’s at least makes sense. If, on the other hand, some particular P can exist
out of time, it appears that ‘P exists’ must be logically determinate - logically true if true,
and logically false if false. Although plausible, that train of reasoning suggests that
abstract objects cannot properly be said to exist, and in particular that none of the
existence statements appearing in mathematics can be true.
Sometimes we can dodge ‘exist’
2
2
E3 ‘real solutions of x + 4 = 0 do not exist’ could be rephrased as ‘x + 4 = 0 entails
that x is not real’
but there’s no such easy move to avoid the existential claim in:
E4 ‘every cubic polynomial that has no repeated factor has three distinct (real or
complex) roots’
Might asserting the existence of a number be a way of saying there is something in
the world which that number could measure? If so the assertion seems to be vacuous.
What numbers we find in the world depends on how we describe the world.
One man is also {one body, one head and 4 limbs}, or several hundred bones, or
many billions of molecules, or rather more billions of atoms. If we allow sets of objects as
well as objects, we can produce examples involving much larger numbers. From n
n
objects we can form 2 sets, including the empty set. Taking sets of sets, sets of sets of
sets... we can produce natural numbers as large as may be required, even though we
may start from only a few elements, or even from just the empty set.
It is possible to define either negative numbers or rational numbers as ordered pairs
of natural numbers. In the sense of those definitions we could say that negative and
rational numbers exist if natural numbers do. Alternatively someone might say that
negative and rational numbers do not exist, because what appear to be negative or
rational numbers are really just pairs of natural numbers.
What about transcendental 4 numbers? Someone might say that , for instance,
4
The number system comprises: (1) The natural numbers {0,1,2...}(2) The Integers {0,
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2
exists if there is somewhere a perfect circle with area = r , or a perfect ellipse with area
ab, or two lines with lengths in the ratio :1.
There wouldn’t be much point in such a claim because no measurement is entirely
free from error. A measurement of some quantity Q gives a result of the form L<Q<U.
Even if that range included , it would also include infinitely many other real numbers, and
indeed infinitely many rational numbers. No physical measurement could commit us to
the existence of objects that cannot be measured without using irrational numbers,
though a physical theory could entail their existence.
Alternatively ‘ exists’ could be treated as asserting that there is some way of
calculating to any required degree of accuracy, but sometimes mathematicians assert
the existence of numbers even though they have no means of calculating them.
However the distinction I noted earlier between two ways that a proposition can be
false can be also made in Mathematics. ‘The greatest real root of equation E is less than
7’ would be false if equation E had a real root greater than or equal to 7, but would also
be false if the equation had no greatest real root. So, at least formally, an assertion of
existence in mathematics is similar to the assertion that a physical object exists. The
claim that a number exists may be established by exhibiting proofs of some propositions
about the number in question.
It is such a formal treatment of existence, as the assurance that our propositions
have a subject matter, that is embodied in a proposal of Quine’s, when he suggested that
we determine the ontological commitment of any theory by seeing what sort of objects
appear in the scope of quantifiers, summarising his position by the slogan ‘To be is to be
a value of a variable’.
Thus ‘my coat is blue’ does not commit me to the existence of colours but ‘there is a
colour brighter than navy blue, but duller than shocking pink’ does make such a
commitment. According to that criterion E3 does not entail the existence of any number,
but E4 does.
Two quite different ideas have become entangled in the philosophers’ abstract
discussions of existence. On the one hand there is a desire to specify what there is in the
world. That was Broad’s question; he wanted to know whether everything is made of
matter, or everything is made of mind, or whether the ultimate constituents of the universe
include both minds and matter. From that point of view we try to avoid double counting,
±1, ±2,...}(3) The rational numbers, comprising all the integers and fractions(3) The algebraic
numbers, namely all the solutions of polynomial equations with integer coefficients. A Polynomial
is an equation in which the unknown appears only in positive integer powers, as in5x 5- 7x3 + x2
+9x - 3 = 0(4) The real numbers, which space does not permit me to define here; think of a real
number as anything that can be expressed in the decimal notation, if an infinite sequence of
decimal places is permitted and the decimal need not recur (a recurring decimal represents a
rational number)(5) Real numbers that are not algebraic are called transcendental. It can be shown
that the algebraic numbers are denumerable, and we have already seen (in chapter 4) that the reals
are not, so the transcendental numbers are not denumerable. Speaking imprecisely we could say
that ‘most’ real numbers are transcendental. Perhaps the best known transcendental number is
(This note simplifies the matter by ignoring the complex numbers)
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so we don’t include both a set and its members, both society and the people who belong
to it. Realising that saying there is a flock of sheep in the garden says more than just that
there are sheep in the garden, it is easy to slip into assuming that that something extra
must be an extra dollop of existence. However, the extra information is not about
existence but behaviour. What makes the difference between a mere collection of sheep,
and a flock of sheep is their behaviour.
It is especially confusing if we allow ourselves to treat a set as the same sort of thing
as one of its members, for instance by treating ‘society’ as if it were a person, rather than
a collection of people behaving in certain ways.
One could rephrase any statement so that it appears to assert existence; e.g. 'David
is a proud grandfather' could be rendered 'A state of affairs exists in which David has
grandfatherly pride'. So it's best not to count as existential statements than can easily be
rephrased so as not to assert existence, and in particular not to interpret 'is' as asserting
existence except in contexts where it can bear no other interpretation.
I have some sympathy with both Materialism and Nominalism, so my list of existents
would include material objects, and not abstractions. I prefer to avoid asserting the
existence of an entity if the same information can be conveyed without making such an
assumption. For instance, instead of saying 'society exists' I’d prefer to say 'these people
exist and cooperate with each other in these sociable ways'. I shall return to the status of
states and societies in Chapter 9, where it becomes apparent that we cannot analyse all
references to them in terms of statements about the people who belong to them, but I still
think we can eliminate claims that societies exist in favour of claims that there exist
people behaving towards each other in the various ways we call ‘social‘.
As well as the question of the contents of our inventory of the world, there is Quine’s
question, what subject matter does a given proposition assume? He was thinking of
questions like: which parts of mathematics assume that there are sets, and which parts
go further and assume that there are infinite sets.
Whatever exists in Broad’s sense, also exists in Quine’s but the converse is not
true. Quine may need to assert that there are sets of numbers as well as numbers, but a
set and its members should not both appear in the same inventory. I think it may be worth
pursuing an analogy between assertions of existence in mathematics, and assertions that
a character exists in a fictional story. ‘There are inaccessible cardinals in so and so’s
extension of Zermelo set theory’ may be comparable with ‘Fagin is a character in David
Copperfield’ In such cases the less obtrusive ‘is’ seems preferably to the brasher ‘exists’.
The assertion of existence is now attenuated to little more than a grammatical
requirement that we can in some way make sense of the subject of a sentence that says
something about whatever is supposed to exist.
Sometimes an assertion that a mathematical object exists may amount to saying
that it is possible to carry out a certain process. ‘There is a multiple of 21 lying between
99 and l06’ means that it is possible to count in 21’s (21, 42, 63...) and get an answer
between 99 and 106.
Universals
I’ve already mentioned this problem when discussing Plato’s theory of Forms and
Aristotle’s criticism of it. Both Plato and Aristotle wanted to explain how different
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individuals can be in some respects the same - what it is we are recognising in both a
plum and a chocolate when we say both are sweet.
Plato, as I’ve already mentioned, thought that what similar things have in common is
that all are, more or less imperfect, copies of Forms, which are entities only accessible to
the human mind by the confused recollection of a knowledge we obtained in a earlier
state before we were trapped in the imperfect world of appearance. After a while he
noticed a difficulty. If the mutual similarity of all fish requires explanation to the effect that
all fish are copies of a Form of ideal fishiness, then the similarity of individual fish to that
form should also require an explanation of the same kind but this time involving a
super-form, of which both individual fish and also the form of fishiness, are copies, and so
on, leading to an infinite regress. That objection is usually called the ‘Third Man
Argument’
Aristotle endorsed the Third man Argument but also criticised the Theory of Forms
on many other grounds including: (1) it appears to involve the same thing, the form, being
simultaneously present in many different places. (2) it is not clear why the Form has to be
eternal in order perfectly to embody the relevant property. Is a white object that exists for
a long time on that account whiter than one that exists only for a short time? (3) When
applied to ethics the theory faces the additional problem that things can be good in many
different ways; what has a good dinner in common with a good pair of shoes?
Aristotle therefore denied the independent existence of forms. He said that things
can be classified together by virtue of some common component. All fish contain an
essential fishiness, and all birds a birdyness, common properties that we easily recognise
when we examine specimens of fish or birds.
Medieval thinkers referred to ‘sheepness’ ‘blueness’ and so on as ‘universals. They
called the Platonic doctrine universalia ante rem, and the Aristotelian universalia in
rebus.
Plato and Aristotle are both called realists on this question because both believed
that the possibility of classification reflected some truth about the world independent of
human language.
Throughout the middle ages most of those who discussed the problem tried to
elaborate Aristotelianism, or less often Platonism. But gradually more logicians were
attracted by a very different view - Nominalism, the claim that the only common feature of
a class of individuals that we distinguish by a common name, is just that we apply that
name to them all.
Although he was far from being the first prominent nominalist I shall introduce
Nominalism with a quotation from Hobbes :
“Of names, some are proper, and singular to one only thing, as Peter, John, this man, this tree,;
and some are common to many things, man, horse, tree; every one of which, though but one name,
is nevertheless the name of divers particular things; in respect of all which together, it is called a
universal; there being nothing in the world universal but names; for the things named are every one
of them individual and singular” (Leviathan, p. 75)
That passage is a remarkably succinct statement both of the problem, and of the
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Nominalist answer.
Although attractively simple, nominalism is distinctly uninformative. Are horses really
similar only in being called ‘horses’ or are they called by the same name because they
are in some other way similar?
For a Nominalist words are human artefacts, so we can invent a term for any
collection of objects we please. I could, for instance, define ‘grundleplonk’ to apply to
every member of the set
{my sink plunger, the planet Mars, Leicester Clock Tower}
Nominalists conclude that because any word could be given such a definition, every
general term actually is so defined. General terms may sometimes seem to be defined in
that way, when people just give a series of examples, but the appearance can be
deceptive. We don’t need to list all the fish there are to define ‘fish’, and even if we could
and did list all the fish alive now and in the past, we shouldn’t have listed all the fish that
will come to be in the future. When explaining the word to someone who lacks the
concept ‘fish’ it should suffice to give our pupil a moderately small sample - all the fish in
an aquarium perhaps, while drawing attention to some of the important common
properties of fish, such as being egg laying aquatic vertebrates that breathe through gills,
and conclude our explanation with words to the effect ‘and anything else like that’
Compare that case with ‘a grundleplonk is my sink plunger, the planet Mars,
Leicester Clock Tower or anything else like that’ Imaginative people might be able to
suggest other candidates for grundleplonkhood, but I’d be very surprised if there were
much agreement between the respective suggestions of different people.
Underlying the use of a general term is the possibility of teaching people to apply the
term to cases they have not yet encountered, so that different people will independently
apply the term to the same objects. General terms that apply to common everyday
objects can usually be taught by giving a set of examples, preferably combined with a list
of salient features. More recondite terms like ‘allowable business expenses’ may require
an explicit definition, but however the term is learnt, learning it involves being able to
apply it successfully to cases that were not used to teach its use.
Locke is usually classed as a conceptualist. Conceptualism is the thesis that
universals may be defined in terms of similarity. In assuming that general ideas can be so
defined conceptualists make a non trivial assumption about the way the world is
constituted. Conceptualism is equivalent to saying that there is really only one universal,
namely similarity, and that other apparent universals can all be defined in terms of that.
Locke probably did not realise that he was making such an assumption, and thought he
was denying that there are any universals at all.
“Words become general by being made the signs of general ideas; and ideas become general
by separating from them the circumstances of time and place and any other ideas that may
determine them to this or that particular existence. By this way of abstraction they are made
capable of representing more individuals than one......” (An Essay concerning Human
Understanding Bk III ChIII, 6.)
Later he says that children first learn words as applying to just one particular object,
such as ‘mother’ ‘father’ ‘cup’, but later, as they encounter many objects that ‘in some
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common agreements of shape and several other qualities, resemble their father and
mother...they frame an idea which they find those many particulars partake in’ having
thus constructed a general idea ‘they make nothing new, but only leave out of the
complex idea....that which is peculiar to each and retain what is common to all’ (Bk III Ch
III 7) That such a process must work is not self evident, so Locke hasn’t explained
universals away, as he seems to assume, but there still seems to be a lot in what he
says.
Is there one general notion of similarity that we can somehow detect in many
different circumstances, or does each class of things have its own sort of similarity?
Locke seems to have thought that all similarities are examples of the same relation,
because similarity always consists of having common properties. However any set of
things will have some common properties. All fish have at least the common property
conceded by the Nominalist, that someone who has been taught the word ‘fish’ with a
wide selection of samples, will call them ’fish’. If we are interested enough in fish to have
a special word for them, we’ll be interested enough to coin other words for various
aspects of fishiness, breaking down their common fishiness into what we’d call more
specific common properties. Purely formally, if all members of set A have the property F,
so they satisfy F(a), then they will all have the property ‘F G’ so that they all satisfy ‘F(a)
G(a)’ they will also all have the property ‘F G’ so that they all satisfy ‘F(a) G(a)’ .
However F(a)  (F(a)  G(a))&(F(a)  G(a)), so that F can be analysed into the
conjunction of the two properties and (F G) and (F G).
Berkeley denied that there are any abstract ideas at all:
“a word becomes general by being made the sign, not of an abstract general idea, but of
several particular ideas, anyone of which it indifferently suggests to the mind. For example, when it
is said "the change of motion is proportional to the impressed force," or that "whatever has
extension is divisible," these propositions are to be understood of motion and extension in general;
and nevertheless it will not follow that they suggest to my thoughts an idea of motion without a
body moved, or any determinate direction and velocity, or that I must conceive an abstract general
idea of extension, which is neither line, surface, nor solid, neither great nor small, black, white, nor
red, nor of any other determinate colour. It is only implied that whatever particular motion I
consider, whether it be swift or slow, perpendicular, horizontal, or oblique, or in whatever object,
the axiom concerning it holds equally true. (The Principles of Human Knowledge p. 52)
but his position may not have been as far removed from Locke’s as he supposed
since Berkley too relied on similarity.
“Now, if we will annex a meaning to our words, and speak only of what we can conceive, I
believe we shall acknowledge that an idea which, considered in itself, is particular, becomes
general by being made to represent or stand for all other particular ideas of the same sort ” (op. cit.
p. 52)
‘ideas of the same sort’ sounds rather like ‘similar ideas’; Berkeley may have been
less of a Nominalist and nearer to conceptualism than he realised.
Part of the difficulty people have had in accounting for abstract ideas has been the
search for a picture. Examples from geometry are common. How can we have a general
idea of a triangle? Any triangle we draw will be in some way special - having two angles
o
o
equal, having one side twice the length of another, having its angles equal to 73 , 51 ,
o
and 56 . Geometers usually illustrate their proofs with diagrams, so that whatever
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diagram they use will illustrate a special case; the triangle they draw will have many
properties not common to all triangles.
However ‘triangle’ has a definition. ‘ABC is a triangle’ is equivalent to ‘A, B and C are
three distinct coplanar but non collinear points’. Geometers try to make their proofs
depend upon such definitions, not on diagrams. Given the definition, they can generate a
wide variety of diagrams to illustrate various possibilities, but however many diagrams
they draw, geometers look for proofs that follow from definitions and axioms.
Psychologically most people find it easier to use a diagram while trying to guess
geometrical relationships and strategies for proving them, but once a proof has been
constructed we can check its validity without reference to any diagram.
Central to the problem of universals is the question of what sets of things or events
count as similar, requiring the selection of a privileged set of qualities to pick out those
sets. That links the problem of universals to the problem of induction, since induction also
involves the identification of a special set of qualities, the projectable properties. The
properties we pick out instinctively are colours, shapes, facial features, tones of voice,
smells, which are the properties projectable in the sort of everyday situations in which our
ancestors probably evolved, situations where they needed to identify members of the
family, things that are good to eat and things that aren’t, things that bite, things that sting,
and things that run quicker than men can run. Hence we readily recognise kinds of
creature in the natural world, so that Aristotle, a keen natural historian, didn’t realise there
was a problem of induction - you only had to look at a mouse to see the essential
properties that made it a mouse and not a hedgehog, and as, he supposed, those were
its essential properties, other mice would obviously have them too, unless they’d been
injured.
Once humans began to make artefacts and develop technology, they started to
encounter situations unlike those that guided our evolution, and intuition was no longer
always a reliable guide to projectability. It has taken most of the life of the human race to
identify momentum, kinetic energy, potential difference and entropy as quantities worth
studying. That a property is projectable is an important scientific discovery, and cannot in
general be answered by intuition. The same applies to ‘similarity’
‘Why is it useful to classify these things together as F’s ’ has the same general
answer in all cases ‘Because F is a projectable property’ In many simple everyday cases
it also has a subsidiary answer ‘because people can learn the predicate ‘F’ by
experiencing a relatively small number of samples’ There is nothing wrong with the
subsidiary answer provided that we recognise it for what it is, a reference to an instinctive
ability to pick out some projectable properties, those that would have been important to
primitive man.
So in a way the conceptualist is right; there really is only one story to be told about
general terms, although Locke didn’t get that story quite right. Aristotle, who thought there
was a different story for every predicate, was wrong, though not as wrong as Plato who
looked for the answer outside the natural world.
Grice on meaning something by what we say
To say ‘please pass the salt’ meaning that the person addressed (P say) should
pass us the salt involves not only uttering those words, but at the same time thinking that
that’s what we want him to do, but on its own that isn’t a complete explanation..
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Suppose we know that K knows no English but responds to any remark addressed
to him by passing the salt, and suppose that X who does not know that, but who,
coincidentally, does want the salt, turns to K and says ‘what do you think of the weather?’
whereupon K passes the salt. That’s not a case of meaning ‘Please pass the salt’ though
it does get someone to pass the salt in accordance with the speaker’s wishes.
Now suppose that Y who is aware of K’s linguistic eccentricity induces K to pass the
salt by asking ‘what do you think of the weather?’ That still seems to fall short of meaning
‘please pass the salt’ even though the passage of the salt was what Y sought to bring
about by saying what he did. Even if Y says to K ‘Please pass the salt’ it is arguable that
the meaning of the words is irrelevant, though if X, who is unaware of K’s problem utters
the same words to K, that seems to be a straightforward use of language, at least from
X’s point of view.
Grice suggested that to mean something by what we say we must (1) intend that P
shall understand what we say, in the sense that P should be aware of our intention and
(2) that P shall respond because of that understanding.
If we say something to an audience - A - meaning to assert proposition P then:
(1) We intend that A should come to believe P
(2) We intend that A shall realise (1)
(3) We intend that (2) shall be part of A’s reason for believing P
According to that analysis someone who seriously overestimated the intellectual
capacities of animals could address quite recondite remarks to his pets and still mean
what he says. In my example, when X speaks to K he means whatever he says to K,
while everything Y says to K means ‘Please pass the salt’. However that would be the
case only so far as Y considered only the effect his remarks would have on K. If Y was
also thinking of the impact his interaction with K might have on others present, what he
said would not have meant ‘Please pass the salt’ unless those were the words he uttered.
Grice proposed a similar analysis for our asking someone to do something.
The meaning of Life
We often meet people who expect Philosophy to tell them the Meaning of life. That
puzzles me because I have never wondered what the meaning of life might be, or even
supposed that there should be any such thing.
‘What is the meaning of life?’ seems to be used to ask one or another of several
different questions.
(1) ‘What is the purpose of Life’ (or possibly ‘What is the purpose of human life?)
(2) What is the purpose of the universe?
(3) How did Life/The Universe come into being?’
All those questions are usually asked on the assumption that someone or something
made the universe, or at least life, for some purpose. I see no evidence of that, so in that
sense there seems to be no answer to the question in any of its forms.
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On the other someone could ask (1) wondering what purpose there might be in his
own life. In that case the answer is ‘whatever purpose you choose’
When people try to find evidence that we have some special purpose, they seem to
hope that nature will point out some prestigious role for themselves such as: Trustee of
the Natural World: Master of the Beasts: Thinker; but our part in the natural order appears
quite different. We are recyclers. Plants build elaborate structures from mainly inorganic
matter, other creatures eat plants, and some like ourselves eat both plants and animals.
We turn them into carbon dioxide, urine and dung, ready for the plants to have another
go. A provocative oversimplification in the spirit of much environmentalist moralising
would be to say that our purpose is to provide food for the dung beetle, but that we’ve
multiplied far beyond necessity, so it would be a good thing if a goodly number of us were
to die and turn into nourishing carrion or compost.
Of course, even if we accept that that is, in a sense, the function of our species in
the natural world, we don’t have to adopt that purpose as our own. As rational beings we
can perfectly well choose another, but it is sobering to note what we find if we look into
nature in the hope of reading in it a ready made purpose for ourselves.
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