To: Pat F.
From: Geoffrey Klempner
Subject: The redundancy theory of truth
Date: 16 October 2007 12:04
Thank you for your email of 7 October, with your University of London essay in response to the question, 'Is the Predicate '...is true' redundant?'
You offer an argument by Grayling against the redundancy theory, and back it up with an argument of your own. However, I wasn't convinced by your argument; either your argument is unsound or I have misunderstood it, either way you need to say more in order to put a convincing case (at least, a case that convinces me: it is possible that I am just being dense, although I don't think I am).
First, Grayling's argument. It could be argued that the problem stems from the fact that propositional quantification is a lot more difficult to understand than truth, because of the problem of giving criteria of identity for propositions.
If propositions don't have clear criteria of identity, then objectual quantification is ruled out. There is no entity without identity. While substitutional quantification is either purely syntactic -- which gives meaningless results -- or we are identifying particular syntactic sequences as having a meaning, in which case we are back with seeking identity conditions for propositions.
However, suppose that propositions did have clear criteria of identity (or at least, that we had an account which worked 'for practical purposes'). Then I don't see why, from what you have given of Grayling's argument, we need to regard the third 'p' in (p)(hAp, p) as elliptical for 'p' is true. A third possibility would be that propositions are not 'objects', either in the sense of objective inhabitants of Frege's world of thought, or in the sense of syntactic strings with a meaning. Propositions are propositions, not objects. Quantification over propositions is therefore sui generis.
When I say, 'Smith said something true,' I am doing two things. I am asserting that Smith asserted something, and I am also asserting -- at one remove -- what Smith asserted. My assertion is 'at one remove' because I haven't actually told you what it is, in Smith's long speech, that I agree with. However, you have the right to challenge my right to make this claim, and, if necessary you could reel off the entire speech sentence by sentence, and challenge me, to back up what Smith asserted in at least 'one' case (note here, the relevance of criteria of identity: the number of 'things that Smith said' is not necessarily the same as the number of sentences that he spoke).
The crucial difference between propositional quantification (supposing there could be such a thing) and ordinary quantification lies in the fact that we assert propositions, whereas we do not 'assert' objects.
This brings me to your argument. Firstly, it looks like your argument in 2. is just a straightforward modal fallacy. It is necessarily true that if all gods are immortal and Socrates is a god then Socrates is immortal. It does not follow that 'Socrates is immortal' expresses a necessary truth. It makes absolutely no difference whether we formulate the argument as in 1. or as in 2. Either way, the necessity is the necessity of an 'if...then...' statement. The argument in does not establish the conclusion that 'Socrates is immortal' is a necessary truth.
There seems also to be some confusion over the notion of 'what can be asserted'. I 'can' assert that the moon is made of green cheese. All I have to do is open my mouth and say the words. For the very same reason, I can also assert, 'It is true that the moon is made of green cheese.' However, if I do make either of these assertions, you have the right to challenge my right to make the assertion. To make an assertion implies that one has adequate grounds for that assertion.
(When the weatherman says, 'It will rain tomorrow,' it is understood that this is elliptical for something to the effect that, 'There is a sufficiently high probability of rain'. Normally, if you only know that p is probable, then you have no right to assert that p, but only that p is probable. This is consistent with the observation that a weatherman would never say, 'It is true that it will rain tomorrow' because this does, effectively, remove the possibility that the assertion is elliptical for 'There is a sufficiently high probability of rain.')
In general, the truth predicate is a handy way to remove quotes from a proposition. It also serves as equivalent to what we would express by means of propositional quantification, were it not for the fact that it is difficult to give a coherent account of the rules for propositional quantification. So, in this sense, it is not redundant. It would be difficult to do without this notational device.
Most importantly, having this notational tool allows us to raise deep metaphysical questions about the relation between language and reality. The most prominent is the debate between realist and anti-realist theories of truth. As before, the predicate, '...is true' serves as a notational device which it would be difficult, if not impossible, to do without. Both realism and anti-realism offer 'accounts' of truth, but not in the sense of traditional theories of truth, i.e. attempts to define the truth predicate, e.g. in terms of 'correspondence' or 'coherence'. Both the realist and anti-realist can accept that truth cannot be defined, yet each clearly gives a different account of the 'nature of truth'.
All the best,