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Fallacies: asymmetry thesis
“A fallacious argument, as almost every account from Aristotle onwards tells
you, is one that seems to be valid but is not so” (C. Hamblin Fallacies, p. 12)
Is a theory of fallacies an account of ‘seeming valid’ and ‘being not so’?
Can we come up with an account of when something seems valid? To
whom?
Can there be a theory of invalidity?
There is no theory of fallacies whatsoever!
(G. Massey “The Fallacy behind Fallacies” Midwest Studies in Phil. 6
(1981): 489-500)
Treatments of fallacy exhibit aimless thinking, shoddy reasoning and lack of
theoretical rigor for the simple reason that there is no theory behind it.
Objection: we have at least a theoretical account of formal fallacies, i.e.
arguments that can be classified as formally invalid.
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Fallacies: asymmetry thesis
(1)
If p, then q. q. Therefore p.
How do we identify this as invalid? Naïve account: argument form (1) is
invalid, so any argument exhibiting this form is invalid. Hence, any such
argument commits the fallacy of affirming the consequent.
(2)
If Philadelphia is the capital of Pennsylvania, then Pittsburgh is not.
Pittsburgh is not the capital of Pennsylvania. Therefore, Philadelphia
is the capital of Pennsylvania.
However:
(3)
If something has been created by God, then everything has been
created by God. Everything has been created by God. Therefore,
something has been created by God.
The naïve account must be wrong.
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Fallacies: asymmetry thesis
Why the naïve account?
We accept:
(4)
Arguments that instantiate valid argument forms are valid. (Principle
of logical form)
(5)
Translations of valid arguments are valid and translations of invalid
arguments are invalid. (Translation Principle)
We translate arguments from natural language under these principles and
then assume that the inspected translation tells us what is valid. If the
argument instantiates a valid form, we deem it valid. But proof of invalidity
cannot be done the same way. For example, truth-tables provide decision
procedure for argument-form validity, not for argument validity.
We further assume:
(6)
Valid arguments instantiate valid argument forms. (Converse
Principle of Logical Form)
We seem to assume that the same would hold for invalid arguments.
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Fallacies: asymmetry thesis
We should also note that the method of counter-example, what Massey calls
‘the trivial logic-indifferent method’, is independent of logical theory, just as it
is irrelevant to physical theory. (Physics is at times is relevant to establishing
the truth of premises, but the trivial method is indifferent to physical theory).
(7)
John took a walk by the river.
John took a walk.
(8)
Tom, Dick and Harry are partners.
Tom and Harry are partners.
Both of these inferences were invalid by logical theory, until Davidson (1968)
showed (7) to be valid and Goodman and Leonard (1940) showed (8) to be
valid.
Bona fide theory of invalidity would show how (2) and (3) differ, beyond a
mere reference to intuition (which is okay as such but it is not theory!)
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Fallacies: asymmetry thesis
Even if you could show that some translation has no valid form in the existing
logical systems, how could you prove that it has no valid form in any possible
system?
If we find that our argument instantiates an invalid form, we abandon the
argument for now. We do not need a theory (which does not exist) to do this.
If we want to identify a fallacy, we can reasonably assume, via some extra
moves, that the person at times uses inference rules (e.g. affirming the
consequent) that he or she does not accept.
But this is not logical theory. Fallacy theory belongs to psychology or
psychiatry, not to philosophy!
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Fallacies: criticism of asymmetry thesis
First, let us give a tentative definitions of fallacy:
A fallacy is a mistake in reasoning, a mistake which occurs with
some frequency in real arguments and which is characteristically
deceptive.
Offered by Trudy Govier (Problems in Argument Analysis and Evaluation,
Dordrecht: Foris, 1987) but similar ones can be found across the texts.
Next, a reconstruction of some of Massey’s argument:
(1) Whatever else fallacies are, they are invalid arguments.
(2) Hence, to show that an argument is a fallacy, we must first show that it is
invalid.
(3) There is no formally adequate method of showing that an argument is
invalid.
(4) Hence, we cannot show that an argument is invalid in any theoretically
adequate way.
(5) Hence, there is no adequate theory of fallacies.
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Fallacies: criticism of asymmetry thesis
However, invalidity is not a necessary criterion of fallaciousness: begging the
question is the prime example. Straw man?
Invalidity is not sufficient for fallaciousness either: there are good inductive
arguments.
-
-
In fairness, Massey took the generic description of fallacy from Hamblin
(1970) and seemed to assume that he was attacking the tough case.
Govier also notes that Massey (and Hamblin) did not assume so: an
inductive arguments need not even seem valid, so they do not fit the
description.
Conceptions on validity:
(UV)
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An argument is valid if its premises are properly connected to its
conclusion and provide adequate reasons for it. It is invalid
otherwise (Umbrella validity)
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Fallacies: criticism of asymmetry thesis
Conceptions on validity:
(SV)
An argument is valid if its premises deductively entail its conclusion,
that is, given the truth of those premises, the falsity of the
conclusion is a logical impossibility. It is invalid otherwise. (Semantic
validity)
(FV)
An argument is valid if its conclusion is formally derivable from its
premises using the rules of a correct logical system. It is invalid
otherwise. (Formal validity)
A fallacy theorist should be interested in (UV). Hence, Massey’s premise (1) is
not true. (2) got its motivation from (1) and is hence unsupported.
(3) is acceptable, if by “formally adequate method” we mean a method that
“a method which is formal and does not require any significant preformal
judgments”. But if we grant (2) for the sake of argument, and (3) as
described, there is still a gap in the argument from (2) and (3) to (4).
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Fallacies: criticism of asymmetry thesis
Namely, it assumes that the move from ‘no formally adequate method’ to ‘no
theoretically adequate method’ is acceptable. If one holds that respectable
nonformal theories are possible, one will not need to accept the conclusion.
Yet, Massey’s argument is important and telling against insensitive
formalization:
we need to attend to how the argument actually works,
detect the intended linkage,
distinguish between features relevant to its logical appraisal and features
irrelevant.
So, we need a paraphrase which captures all of the logically relevant features.
Formal invalidity shows nothing, unless we are sure that the paraphrase has
accurately captured the original argument.
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Fallacies: criticism of asymmetry thesis
Consider argument (from Susan Haack Philosophy of Logics, p. 24-26):
Every natural number is either greater than or equal to zero, and every
natural number is either odd or even, so every natural number is either
greater than or equal to zero and either odd or even.
Sentence calculus:
P, hence Q.
invalid
Predicate calculus:
(x) Fx & (x) Gx.
Hence, (x) (Fx & Gx)
valid
But also:
(x) (Fx V Gx) & (x) (Hx V Ix)
(x) ((Fx V Gx) & (Hx V Ix)
valid
What is the “true” logical structure of the argument?
Haack quotes Quine’s maxim of shallow analysis: “where it doesn’t itch, don’t
scratch.”
Whether there is a “true” logical form can be debated. Russell and
Wittgenstein, during their atomist period, held there is.
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Fallacies: criticism of asymmetry thesis
G. Harman, based on the Chomsky’s work, has suggested that the logical
form could be identified with the deep grammatical structure.
This would have to be universal; there should be no cases where an argument
could be valid, for example, in Hebrew but invalid in Hindi.
Haack is not optimistic about this but sees no reason for dismay at the
interdependence between intuitive informal judgments and development of
formal systems.
It seems that we must not resort to pessimism, since:
There is no theory of validity for any argument of English!
(J. Woods: “Fearful Symmetry” in Fallacies: Classical and
Contemporary Readings, Pennsylvania: Pennsylvania University,
1995):
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Fallacies: symmetry thesis
Consider again the definitions:
Def. V: An argument is valid if it is not in any sense possible both that its
premises are true and its conclusion false.
Def. IV: An argument is invalid if it is in some sense possible both that its
premises are true and its conclusion false.
This a semantic criteria, and one without proof procedures. A theory of
validity and invalidity should not only define what it is for an argument to be
valid/invalid but also give proof procedures for what is to be valid, i.e. a
general method for demonstrating that the argument is valid/invalid.
Def V*: An argument is valid iff it has a valid logical form.
Def IV*: An argument is invalid iff it has an invalid logical form.
But arguments that we are interested in do not come in their logical forms.
They have to be ‘dressed up’ and reconstructed before we can examine their
validity.
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Fallacies: symmetry thesis
So we need:
BRP:
The rules of reconstruction have the backward reflection property
with respect to validity and invalidity; that is, and argument is valid
if its reconstruction under these rules is a valid logical form, and
similarly for argument’s invalidity.
Consider:
(R)
The thing is red.
The thing is colored.
(RPC)
p
q
Def IV* now gives us a an invalidity verdict that Def IV does not. But we must
retain Def IV*, because it has proof procedures.
SI:
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Sentences eligible for reconstruction must themselves be pairwise
semantically inert, if simple, or compounds of simple and
semantically inert otherwise.
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Fallacies: symmetry thesis
Now consider:
(M)
All men are mortal.
Socrates is a man.
Socrates is mortal.
(MPC)
r
s
t
(MQT)
(x)(Fx -> Gx)
Fa
Ga
But every logical form of PC is a form of QT. So, M is both valid (in PC) and
invalid (in QT). To resolve this, we hold:
(SSE)
A sentence is a simple sentence of English iff it contains neither any
sentence as a proper part nor any conjunction and it contains no
quantifiers.
Now, “All men are mortal” is complex and cannot be represented as ‘r’.
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Fallacies: symmetry thesis
But, “all men are mortal” has existential import but “For all x, if x is a man”
does not. So, we cannot really argue that they are synonymous (even if we
were to accept synonymy (contra Quine), we would be in trouble).
Further, is “All things are identical to themselves” complex?
Instead, we rule, along with Massey:
Def I’
An argument is invalid iff there is no valid logical form that it
possesses.
Now M is PC-invalid and QT-valid, hence valid. This is asymmetry:
reconstruction rules have no backward reflecting property with respect to
invalidity. (Note how the asymmetry is reversed between showing validity
and invalidity from the semantic definitions Def V and Def IV.) So there is no
formal theory of invalidity of arguments on the hoof.
One more time, why will no reconstruction principles have backward reflecting
property if Def I’ is true?
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Fallacies: symmetry thesis
Because arguments invalid by Def I’ have the property of having no form that
validates them, arguments having that property will not have it in virtue of
any form that they have. Why?
Suppose not. Then there will be arguments that are invalid by form, and any
reconstruction rule exposing that form, will reflect it backwards.
Now reflect back on argument (M). Even if we did understand what simplicity
is, we would also have to have a theory of when are two sentences pair-wise
semantically inert. So, our reconstruction principles would have to, for any
pair of sentences Φ, Ψ, give the truth conditions for ‘Φ implies Ψ’ and ‘Φ is
inconsistent with Ψ’
So, the reconstruction would have to, prior to defining the logical theory, use
logical forms, which are the output of reconstruction. But this cannot be had,
at least without some nonlogical axioms or axiom schemata.
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Fallacies: symmetry thesis
So:
1.
2.
3.
4.
5.
6.
7.
8.
9.
For any argument of English, A, having a logical form is, by Def V* a
condition of its validity.
Being dressed is a condition on A’s having a logical form.
Having a informal logic is a condition on a dressing theory for A (by the
pairwise semantic inertia condition).
No theory is a logic if it lacks proof procedures.
Informal logic, so called, lacks proof procedures.
Hence, informal logic does not exist.
Hence, there is no dressing theory for A.
Hence, there is no reconstruction theory for A.
Hence, there is no theory of validity for A.
So, logical theory remains wedded to informal judgments of invalidity and
validity.
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