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What should we make of Wittgenstein’s paradoxical claim at the end of
the Tractatus that the propositions contained therein are nonsensical
According to the very theory it advocates much of the Tractatus is nonsense. The paradox
consists in how Wittgenstein argues that despite this we can still draw something meaningful from
the book. In this essay I will consider the resolute and irresolute reading of this paradox and argue
we should adopt the former.
In the Tractatus, Wittgenstein presents a metaphysical view that there exist in the world
simple, irreducible objects, henceforth known as simples. Contained within these simples is the
possibility of them combining with other simples to form states of affairs. The objects Jeremy
Corbyn, Number 10 Downing Street and the relation 'being inside' contain within them the
possibility of the state of affairs in which Corbyn is inside 10 Downing Street (assuming for the
sake of argument that all these objects are simple).
Not all possible states of affairs are actualised. Corbyn, for example, is not currently within
10 Downing Street. Those states of affairs that are actualised, i.e. those that exist, Wittgenstein calls
facts. Note, I have taken the translation of the German word sachverhalten to be 'states of affairs'.
The other standard translation, 'atomic facts', captures the elementary nature of sachverhalten - they
consist only of simples - but it is difficult to interpret propositions such as 2.05, where Wittgenstein
talks of existent v.s. non-existent sachverhalten, if we call them all “facts”.
Wittgenstein distinguishes thought, language and the world. His view of how these relate in
the Tractatus is known as “the picture theory”. Thoughts are psychological entities. Language is
how we express or communicate those thoughts using sensibly perceptible signs (e.g. ink marks on
a page), which Wittgenstein calls propositional signs. Lines in the Tractatus such as 3.11-3.12
suggest that Wittgenstein in some way takes propositions to be propositional signs that have a sense.
This sense is what allows someone to use a sign to communicate a thought. “The table penholders
the book” is a propositional sign but not a proposition as it communicates no thought. The
relationship between language and the world is pictorial or representational. When we express
propositions we form pictures of the existence of certain states of affairs. The elements of a
proposition correspond to the elements of the state of affairs being represented and both sets of
elements stand in the same definite relation to one another. It is in this sense that propositions are
pictures, although the exact nature of this relation is unclear (and not relevant to the purposes of this
Traditionally we think of propositions as the meaning of declarative sentences. However, we
can see that this is not how they are being used in the picture theory. Rather they seem to be a
particular subset of sentences capable of expressing a sense (TLP: 3.11-3.12). What is this sense?
To understand a proposition, to know its sense, is to know what would be the case were the
proposition true. Thus its sense is the state of affairs it represents. However, herein lies the paradox.
On this theory any sentence that does not represent a state of affairs is not a proposition and has no
meaning. The theories of philosophy do not express contingent relations between objects. A
philosophical “proposition” like the following must be considered nonsense:
A caused B iff there is a necessary connection between A and B.
The fact that such propositions express no state of affairs might not be immediately obvious. One
could construe, for example, (1) as expressing the state of affairs in which causation consists in the
necessary connection between two events. However, is it really fit to call this a state of affairs? The
philosophical theory does not assert that there is a necessary connection between two events - this
may be a contingent fact. Rather it asserts that the nature of causation is that there is a necessary
connection. It is by no means clear what simples would form the building blocks of such a state of
affairs. Furthermore if it were true it would presumably be true in all possible worlds (and likewise
if false) and so non-contingent. A genuine state of affairs cannot be non-contingent (Child 2011,
63). Which states of affairs exist must be accidental according to the picture theory and so the
existence of a state of affairs in one possible world should say nothing of the existence of another in
another possible world. By having the same truth value in all possible worlds (1) lends itself a
certain necessity but the only necessity allowed by the picture theory is that of logical necessity
(TLP: 6.37) and so we cannot regard (1) as expressing a state of affairs or having a sense.
Wittgenstein argues that the only propositions that can truly have a sense are those that belong to
the natural sciences (TLP: 6.53). The picture theory itself does not belong to the natural sciences, it
is a body of philosophy. By its own admission, the picture theory (and the propositions from which
it is built, such as “the sense of a proposition is the state of affairs it represents”) are nonsense.
In 6.54 Wittgenstein makes it clear that he is aware of this contradiction and yet he does not
see it as a problem. He argues that the Tractatus can still help one “see the world rightly”. 6.53
suggests he still thinks the theories of philosophy are meaningless and that instead philosophy
should be viewed as an activity whose purpose is to ensure that when people speak they only use
genuine propositions that have a sense.
This is a troublesome claim. How could Wittgenstein hold the view that the propositions of
philosophy are meaningless when this can only be justified through a theory of meaning (like the
picture theory) which itself would belong to philosophy? The traditional response (known as “the
irresolute reading”) to this problem posits the existence of some realm of ineffable truths. Although
strictly speaking the propositions of the Tractatus are meaningless, the irresolutist argues that still
they are able to communicate truths to us, it is just that it is impossible to express those truths using
language. If you try you will only generate nonsense. At first glance this response looks
contradictory: it simultaneously says the propositions of the Tractatus do and do not express
Irresolutists typically use a distinction between saying and showing to explain this apparent
contradiction, a distinction developed within the Tractatus. A proposition represents a state of
affairs. Wittgenstein defines the form of this proposition as the possibility of the simples within this
state of affairs being arranged in the way they are (TLP: 2.032-2.033). Its logical form is thus the
logical possibility of this arrangement and is shared between both the picture and that which it
pictures. However, on the picture theory all propositions about this logical form will be
meaningless. A statement of the form “the logical form of p is...” will suffer from the same
problems as (1): it is non-contingent and so has no sense. However, it feels right to say that we can
know the logical form of propositions. If we were unaware of which arrangements of simples are
possible and impossible surely we would be unable to form propositions? Thus Wittgenstein
introduces the idea that although one cannot say what a proposition's logical form is, this logical
form is nevertheless shown by the proposition. Irresolutists interpret this as meaning we can
determine the logical form of a proposition just by inspecting it but are unable to express this
knowledge using language. It is an ineffable truth. Philosophers such as Anscombe (1971, 162)
argue we should use the saying/showing distinction to interpret 6.54. The propositions of the
Tractatus are meaningless in the sense that they say nothing. Nevertheless they can be used to show
ineffable truths about meaning and language and it is these truths that justify 6.53.
To what extent is this idea of ineffable truths a coherent one? I think the idea can be
sketched out using the following example. Squirrels have a basic language they use to communicate
with each other. For example, they use a “kuk” noise to signal the approach of a predator (McRae &
Green 2014). However, they also know facts such as the location of the nuts they buried the
previous autumn. This is despite the fact that their language is too primitive to express such
knowledge. To them this knowledge is thus an ineffable truth. And yet it would still be possible for
them to show this knowledge to other squirrels by guiding them to the burial sight. Similarly an
irresolutist might argue that human language is too primitive to express the truths which justify 6.53
(and so allow us to make sense of 6.54) and yet still these truths can be shown to us.
This interpretation of the saying/showing distinction rests on an unjustified equivocation
(Kremer 2013, 18-9). We have to distinguish different uses of the word ‘show’: ‘to show how’ and
‘to show that’. Consider the following sentences:
Corbyn showed Cameron how to hang glide.
Corbyn showed Cameron that austerity is counter-productive.
It is only in (3) that what is being shown is a proposition. In (2) Cameron is learning what practical
actions must be taken in order to successfully hang glide. There is nothing of a propositional type
involved. He could form propositions about what he learnt should he wish, but this is not essential
to him having been shown how to hang glide. When Wittgenstein says that the proposition shows its
logical form we should see this as an example of ‘to show how’. To show the logical possibility of a
state of affairs is to show how to construct it from simples. Irresolutists confuse themselves into
thinking that what is being shown is a proposition-like entity - an ineffable truth - but this does not
follow. We can see a similar confusion within our squirrel example above. Squirrels know how to
find their buried nuts but not that their nuts are buried in a given location: there is no need to say
they know some ineffable truth. So we cannot use the saying/showing distinction to make sense of
the paradox.
Michael Kremer provides a more convincing reading of 6.54. On this reading (the “resolute”
reading) the preface and a select few propositions within the Tractatus, such as 6.54, 4.112 or 3.323
(but not 6.53 or 7!), should be treated as a frame to the book (Kremer 2001, 41). This frame tells us
that all other propositions within the Tractatus are genuine nonsense. It is not a textbook
expounding a philosophical theory but rather an exercise we go through that helps us “see the world
rightly” (TLP: 6.54). How could a set of nonsensical pseudo-propositions achieve such a feat? The
analogies Kremer uses to bring out his explanation are rather obscure. Let us instead use the
following example. Suppose, just before he goes onstage to perform a solo piece, an anxious
musician called Ian asks his friend, “Should I be nervous?” Ian’s friend responds:
The only thing you have to fear is fear itself.
At first sight Ian might find this answer rather puzzling. He might question if his friend is telling
him he should be fearful (of being afraid) or that he should not fear anything. However, what Ian’s
friend is really trying to communicate with this seemingly paradoxical statement is that to ask,
“what should I fear?” is to ask the wrong question. Rather, so long as Ian manages his emotions he
will be able to deal with any problems that arise.
The seeming paradox of the Tractatus plays a similar role. Kremer argues we are attracted to
philosophical theories out of a desire to justify our beliefs (2001, 51). For example, a system of
ethics might attempt to justify our belief in giving to the homeless, and a philosophical solution to
the problem of induction will attempt to justify our belief in the scientific method. Similarly, a
theory of meaning such as the picture theory can be seen as an attempt to justify our belief that
language can be used to make statements about the world. The paradoxical nature of the Tractatus is
meant to help us see that to ask “How can I justify such and such a belief?” is to ask the wrong
question. In the previous example, Ian is trying to think of all the possible sources of worry and
hopes not to find any but, through the paradoxical statement in (4), his friend points out that to do
so is to fight a losing battle: worry itself is a source of worry. Similarly, to attempt to find
justifications for our belief in the meaningfulness of language is to fight a losing battle because such
justifications will inevitably be meaningless. The solution in both cases is to adopt a change in
attitude and outlook. We are to realise that the search for justification is futile and in fact we have
no need of it. The Tractatus is an exercise and not a textbook in the sense that it is not meant to help
us understand any truths. Rather, it is meant to help us to adopt this spiritual change in attitude.
Hence “the point of the book is an ethical one” (Wittgenstein 1979, 94). It does this by presenting
what at first seems like a coherent and complete philosophical theory and then showing how in
actual fact this theory says nothing at all.
We can explore the resolute reading further by considering two objections raised by Michael
Morris. The first is that the claim that
All philosophical theories are meaningless
is itself a philosophical theory and so self-refuting (Morris 2008, 343). However, Kremer is not
committed to (5). He argues that philosophical theories are meaningless in so far as they are
attempts at justifications of our beliefs. Thus (5) should be translated into the claim
All justificatory talk is in the end meaningless nonsense.
The fact that Kremer is committed to (6) is evidenced by it being a direct quote (2001, 51).
However, (6) is only self-refuting if it itself is an attempted justification of a belief. I can see no
belief which it is attempting to justify; it is just simply a belief. Morris’s second objection is that “to
claim that sentences which seem perfectly meaningful” are in actual fact nonsensical requires a
“substantial metaphysical view” (2008, 344). When viewed through the lense of the resolute
reading, which refuses to provide any theories of meaning, Morris is asking in what sense are these
justifications meaningless? They do not appear overtly meaningless like sentences such as “the table
penholders the book”. Kremer counters that we can use our everyday, pre-theoretic understanding
of meaning to see why justifications are ultimately nonsense (2001, 51). A word or sentence has no
meaning if it fails to have a purpose or use within our language.
Philosophical justifications cannot serve the purpose for which they were intended: they
themselves (and our belief in them) will also need justification. Attempting to find a justification
plunges us into regress. So, for example, Bertrand Russell’s theory of the meaning of propositions
says that they are built from the things they are about, but he had to question his own theory
because of the problem of the unity of the proposition. He attempted to solve this problem by
appealing to the notion of relating relations. He then had to question this solution because it suffers
from Bradley’s regress, and so on. Whatever justification a philosopher provides another can always
question. Note, the same also applies to the picture theory.
According to the irresolute reading the propositions of the Tractatus simultaneously
communicate nothing and something. To make sense of this view a mechanism needs to given to
explain how exactly this is achieved. We have seen that the most plausible mechanism offered by
irresolutists is founded on an unjustified equivocation. On the superior resolute reading the preface
and a few select propositions within the Tractatus are meaningful and the rest are genuine nonsense.
However, the process of at first taking the seriously the propositions of the Tractatus only to see
them collapse to nonsense is meant to help us adopt a change in attitude. We are to abandon our
desire for justifications for our beliefs because we now see it as a losing battle. The book's purpose
is not to communicate truths but to “change our relationship to nonsense” (Kremer 2001, 57).
Word Count: 2746
Anscombe, G. 1965. An Introduction to Wittgenstein's Tractatus. New York: Harper & Row
Child, W. 2011. Wittgenstein. Oxon: Routledge
Kremer, M. 2001. 'The Purpose of Tractarian Nonsense', Nous, 35: 39-73
Kremer, M. 2013. 'The Whole Meaning of Book of Nonsense', in M. Beaney (ed.), The Oxford
Handbook of the History of Analytic Philosophy. Oxford: Oxford University Press
McRae, T. & Green, S. 2014. 'Joint tail and vocal alarm signals of gray squirrels', Behaviour, 151:
Morris, M. 2008. Wittgenstein and the Tractatus. Oxon: Routledge
Wittgenstein, L. 1979. ‘Letters to Ludwig von Ficker’, trans. B. Gillette & A. Janik, in C. Luckhardt
(ed.), Wittgenstein: Sources and Perspectives. Ithaca: Cornell University Press, 82–98
Wittgenstein, L. 2005. Tractatus Logico-Philosophicus, trans. C. Ogden. Oxon: Routledge
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