Friday, November 18, 2011

Representation, truth, and infinite regress

I have argued (e.g. here and here that the notion of a ‘truthmaker’ leads to an infinite regress. If there is such a truthmaker, an entity that makes a proposition like ‘Socrates sits’ true - let it be A - then it comes into existence when Socrates sits down, and ceases to exist when he stands up. But then there would have to be a further truthmaker for A existing. I.e. the sentence “A exists” can be true or false, and so requires a further truthmaker B, that makes it true when B exists. But then “B exists” requires yet another truthmaker, and so on ad infinitum.

A similar problem attaches to the idea of representation (and at bottom, I believe, it is the same problem). Can the trueness or faithfulness of a representation – itself be represented? We say a picture is a true or faithful representation of what it represents. Aquinas says that truth is the adaequatio - literally the ‘equality’ or perhaps ‘adequacy’ – of thought to reality. This is like the modern concept of a ‘mapping’ or even ‘correspondence’ is similar – imagine the thought being like a picture or map that we could lay against the reality and match each element of the map against an equal and corresponding element of the reality that is mapped. But how do we represent the accuracy or ‘equality’ of the representation itself? The accuracy or trueness of the representation is itself an aspect of reality, and must be captured, but is not itself a feature of the representation. For accuracy is a relation, and the representation is only one term of the relation.

To represent the accuracy, we need a further representation – imagine a picture of both the represented object and the representation, with mapping lines drawn between the corresponding elements. But then this is also a representation. To represent its accuracy, we would have to represent it together with the two objects it represents, together with further lines joining both the mapped elements and the mapping lines. This is something too complicated to draw or even to imagine, but even that would not be enough, for we still have a representation. The accuracy of this must also be represented, and so on ad infinitum.

The problem is inescapable. If we buy the idea of a ‘truthbearer’ (a proposition, a thought, whatever), the idea of a ‘truthmaker’ comes with it. The truthbearer is one term of the relation, the truthmaker is the other. But the truthmaker can’t be the other term, because truth is a relation, and the truth includes the existence of the relation, as well as the existence of its two terms. Just as the accuracy of a representation cannot itself be represented, so the truth of a truthbearer cannot itself be expressed.


Anthony said...

Not buying the idea of a truthbearer requires not buying the idea of the laws of logic. To say that X is true, or that Y is false, is to admit that X or Y is a truthbearer.

This is not to say that such a truthbearer is a concrete, or that it is an existent. One need not admit that 5 or 7 or 13 are concretes and/or existents to say that 5+7=13. But to say that 5+7=13 is to admit that 5, 7, and 13 are numbers.

Edward Ockham said...

>>Not buying the idea of a truthbearer requires not buying the idea of the laws of logic. To say that X is true, or that Y is false, is to admit that X or Y is a truthbearer.

You clearly need to read up on the 'redundancy theory of truth'. The Wikipedia article is reasonable.

Anthony said...

Okay, I read the article.

Do you agree that the law of noncontradiction and the law of excluded middle hold? If so, hold for what? Whatever your answer is, that is what is meant by "truthbearer".

J said...

Representation is another issue--, per Hume, for a few nanoseconds...representation/
perception of phenomena might not be necessarily true==smoke does not always "mean" fire (say its an old car that burns oil and X perceives the oil smoke above the elm trees, etc). But if one perceives some sequence of events---smoke in the forest, etc. or what happens when dropping a chunk of K into H20 (not to say...gravity)--and it happens 995 out of 1000 times-- it's "true" for all ostensible purposes. One reason I contended the T-maker issue hinges on verificationism more or less.

And "Ant." is wrong. Logic --like mathematics--can be done without ...even getting into the problem of "truthmaking" or verification. As Lewis Carroll knew. Logical forms like integrals-- are not ...hanging on trees are they. The modus ponens shrub! Yeah.

David Brightly said...

The discussion at BV's seems to have reached the sand. I made one last comment referring to this post and effectively saying I couldn't make sense of the idea of a truth-maker. It strikes me that at least part of what makes the sentence 'Al is fat' true is that these are the right English words to use to assert that Al is fat. This Tarskian point Bill never mentions. Possibly because he starts with propositions, not sentences. All the interesting linguistic issues have already been abstracted away. He is left with a vanishingly narrow gap with which to prise apart the facts that obtain from the true propositions. It's hardly surprising that he finds that facts must have proposition-like structure! It seems topsy-turvy to me to start with a true sentence and ask what in the world makes it true. Better to start with the world and ask what in the sentence makes it true. But this appears to be a difference of method.

Your remarks here put me in mind of the idea of 'indefinite extensibility' in the analysis of how some predicates do not form sets. Sethood, for example: given some sets we can always find another set not amongst the givens, so no set of all sets. To discuss the accuracy of first-level statements about the world we need second level statements about the world and first-level statements. To discuss the accuracy of second-level statements we need third-level statements about the world and second-level statements, etc, etc, ad nauseam.

J said...

Russell's paradox as evidence contra Truthmakers?? Creative. Do sets exist? Surely not as say..mammals exist.

we can agree to a certain empirical realism without agreeing to...Vallicella's odd pseudo-platonism, IMO (or anyone's). The truth of "Jaguars are vertebrates" may depend on...syntactical givens in a sense (ie, knowing the language) but that's how the game is played--the particular (jaguar) being included in the universal /class of mammals (ergo, vertebrates, warm blooded, hair, etc). Ie, one learns what castling is in chess (and the openings, etc) without a metaphysical justification of the rules themselves.

Anthony said...

>> It strikes me that at least part of what makes the sentence 'Al is fat' true is that these are the right English words to use to assert that Al is fat.

Well, they're a set of English words that can be used to assert that. Another set would be "that guy is fat", or "yeah, he is", or "the fat guy who owns the pizza shop is fat".

Personally I think it's incorrect to say that the sentence itself is true, though. Maybe you could say that the particular usage of the sentence is true, but not the sentence itself. The sentence itself can be used in ways that are true, and ways that are false, and ways that are neither true nor false.

That's why there's the switch to propositions as truthbearers. Sentences don't make good truthbearers.