[hist-analytic] Steve's and Roger's recent interchange

Danny Frederick danny.frederick at tiscali.co.uk
Wed Aug 26 09:18:42 EDT 2009

Hi Bruce,


Here is the promised criticism of your chapter 3. It is a bit hastily put
together because of practical demands on my time at the moment, so please
forgive any infelicities. As I understand it, you claim that:


(i)               there are a  priori truths;


(ii)            all a  priori truths are analytic;


(iii)          all analytic truths are true by convention;


(iv)          conventions may be either explicit (including explicit
'implicit definitions') or they may be implicit in the linguistic practices
of a community or cult.


I can accept (ii) and (iii), but only because I think the class of analytic
truths and the class of a priori truths are empty. I can accept (iv) as a
statement about kinds of conventions. But (i) is false. I will go straight
to the main point: it is impossible for any convention to guarantee a truth,
because truth depends on objective fact.


Let's take an explicit stipulative definition: by 'bachelor' I mean an
unmarried man. It might be thought that this guarantees the truth of 'all
bachelors are unmarried,' since 'all unmarried men are unmarried' is a
logical truth. But that thought would be mistaken. It assumes that
substitution of synonyms for synonyms can be made salva veritate. This has
been disputed by Kripke and others. More importantly, it assumes that the
so-called logical truth is guaranteed to be true. But it is not. There are
two prongs to this objection. First, if we understand the logical words in
'all unmarried men are unmarried' ('all' and 'are') in their ordinary
senses, then some people (Aristotelian types, for example) will maintain
that 'all' has existential import, making 'all unmarried men are unmarried'
contingent. Second, if we regard the logical words as having their meaning
specified in a particular formal logical system, the necessary truth of 'all
unmarried men are unmarried' will depend upon the logical system being
consistent. But we can never know that a logical system is consistent.
Apparent self-evidence is no guide: Russell's paradox showed that Frege's
'self-evident' fifth axiom was inconsistent. And consistency proofs are
question-begging. A proof of consistency of a logical system requires
logical principles (premises and rules of inference, or at least the
latter). These principle are either the same as (some of) those used in the
system, in which case the proof is circular, or they are different, in which
case the question of consistency arises for them.


Now let's look at an explicit 'implicit definition:' by '&' I mean whatever
makes inferences of the following forms valid

p&q, therefore p

p&q, therefore q

p, q, therefore p&q.


We cannot know whether '&,' so defined, picks out a coherent notion for the
reason already given: for all we can know, a logical system in which such
inferences can be made may be inconsistent. Indeed, advocates of connexive
logics do deny the validity of the rule of conjunction elimination. They
might be mistaken; but they might not be. We cannot make propositions true
or inferences valid by stipulation.


But it also, almost obviously, follows that we cannot make propositions true
or inferences valid by means of our practices either. The way we use words
may lead to inconsistency: our linguistic practices may be incoherent, even
demonstrably so (recall Frege's fifth axiom). If our 'linguistic behaviour'
involves the tacit assumption of a rule of inference, it may still be the
case that the rule is unsound. Indeed, this should be obvious. For millennia
our linguistic practices committed us to inferring 'A is simultaneous with
B' from 'B is simultaneous with A' whether or not the co-ordinate system
changed between the two utterances; but we nowadays reject such inferences
as invalid.


Let me illustrate. On p.62 you say: 'words, phrases, clauses and
constructions in existing dialects of natural languages have implications so
vital to the meaning of what they are used to say that any alert and
attentive speakers of a relevant dialect would find it odd, puzzling, or
paradoxical to question them. When this condition is satisfied by a word or
symbol, it seems to me that a sentence of the dialect clearly and
unambiguously expressing an appropriate implication can reasonably be
regarded as analytically true for those alert and attentive speakers.'


It does not seem so to me. I would guess that, even today, the vast majority
of people, whatever language they speak, would find it odd, puzzling, or
paradoxical to question absolute simultaneity or the axiom of parallels. Yet
Einstein questioned both; and negations of each have become a part of
accepted physical science. Far from the absoluteness of simultaneity or the
axiom of parallels being analytic truths, they are regarded by experts as
being factually false.


Let me comment on a different, though connected, point. You say: 'We
consider a determinate color A to be the same as a determinate color B just
when A and B are indistinguishable' (p.61).


Who is 'we'? I certainly do not consider that. The problem with it is that
it mixes up subjective and objective. Talk of determinate colours belongs to
the realm of objective fact. Distinguishability is relative to a subject.
This is obvious if we understand 'distinguishable' phenomenologically: our
powers of visual discrimination are limited, so different determinate
colours are often indistinguishable by us by sight. But it is also the case
if we understand 'distinguishable' conceptually. When we talk of different
determinate colours being indistinguishable by sight, we are probably
thinking of the colours as different wavelengths of light, in which case we
are distinguishing them conceptually. But, of course, it is possible that
our theories of light are mistaken and that our classification of light in
terms of wavelength fails to distinguish objectively different colours. What
we can distinguish depends on our limited and fallible powers, but how
things actually are does not.


Nothing I have said above is original. The sources are:


Whitehead and Russell, 'Principia Mathematica,' Vol 1, second edition, p.59.


A N Prior, 'The Runabout Inference-ticket,' and N D Belnap 'Tonk, Plonk and
Plink,' both in 'Philosophical Logic' ed. P F Strawson.


W W Bartley, 'The Retreat to Commitment,' second edition.


I Lakatos, 'Infinite Regress and Foundations of Mathematics,' and 'A
Renaissance of Empiricism in the Recent Philosophy of Mathematics?' both in
his 'Mathematics, Science and Epistemology,' ed. J. Worrall and G. Currie.


S Kripke, 'A Puzzle about Belief.'


Priest and Thomason, '60% Proof,' Australasian Journal of Logic, 2007,
available here



T Williamson, 'Conceptual Truth,' Proceedings of the Aristotelian Society,
Supplementary Volume 80 (2006), available here



Best wishes,



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