[FOM] Slater on the Liar (and other issues)

Arnon Avron aa at tau.ac.il
Tue Oct 3 18:20:05 EDT 2006

Personally, it seems to me that almost everything Slater
is saying below (whether these are sentences or something 
else which supposed to have the property of truth)
is neither true nor false. The reason may be that being
a machine (while Slater is not), I cannot attach any meaning 
to this sequence of sentences...

Arnon Avron

>On Tue, Oct 03, 2006 at 10:08:26AM +0800, Hartley Slater wrote:
> The point is that it is *not* the sentence which has the property of
> truth; at the very least it is the sentence when interpreted a given
> way.  But the problem with that is that standard twentieth century
> logic has had no way to write the sentence when interpreted a given
> way as a referential phrase referring to an object which might be the
> subject of a truth predication. What is true, in the Goedel case, for
> instance, is not '(x)Fx' but that all natural numbers are F.  Humans
> certainly can, like machines, utter sentences like '(x)Fx' -
> sentences which are then put in quotes - but they also do something a
> machine cannot, namely use sentences like '(x)Fx' to state things
> about models (in this case the standard model) - the sentences are
> then not in quotes. In terms of the operation of a machine it would
> have to not only utter a sentence, but *mean by it* one thing rather
> than another.  But it lacks any capacity to mean anything.
> Forgetting this is exactly why, for instance, people get into such a
> tangle with The Liar Paradox. They think that the Liar sentence
> (let's call it 't'), on the self-referential interpretation is
> paradoxically both true and false.  But what one is involved with, if
> one chooses the self-referential interpretation is not a syntactic
> identity in direct speech,
> t = 't is not true',
> but a statement about content in indirect speech, namely
> t says that t is not true.
> This is clearly true only on a certain semantic interpretation, and
> so it is not just an extensional remark about the syntactic object 't
> is not true'.  The distinction makes it plain that what is true or
> false is not the bare sentence 't is not true', but the statement
> made when it is used a certain way, namely to say that t is not true.
> The inability of the logical tradition to represent such a
> propositional referring phrase as 'that t is not true' has made it
> seem that what is true or false on the given interpretation is still
> the (mentioned) sentence, but only the sentence in use, preceded by
> 'that', refers to the item that has the truth value.
> As a result sentences, in themselves, are neither true nor false, so
> that t is not true is definitely true, in this case.  In fact the
> full truth is that t is neither true nor false.  It follows that
> there is no longer any problem with Strengthened Liars, either.
> Certainly the question naturally arises about what to say in
> 'strengthened' cases, where, for instance, one has
> s = 's is neither true nor false'.
> But first of all there is no need to take the sentence thus defined
> to speak about it itself being neither true nor false.  For
> sentences, by themselves, have no voice, and the 's' in quotes could
> be interpreted differently.  If anyone chooses to interpret this
> sentence self-referentially that is therefore an additional
> (intensional) matter beyond the extensional, direct-speech identity.
> And what is true in that self-referential case is simply that s is
> neither true nor false, which is not paradoxical in any way, since to
> say that is not to say that what is true is s, i.e. 's is neither
> true nor false'. It is to say that what is true is what s says on the
> self-referential interpretation.
> -- 
> Barry Hartley Slater
> Honorary Senior Research Fellow
> Philosophy, M207 School of Humanities
> University of Western Australia
> 35 Stirling Highway
> Crawley WA 6009, Australia
> Ph: (08) 6488 1246 (W), 9386 4812 (H)
> Fax: (08) 6488 1057
> Url: http://www.philosophy.uwa.edu.au/staff/slater
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