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It seems fairly obvious. Even a five year old could probably come up with it. Its obvious that if something is the case, it is true (literally synonyms).

So, am I missing something? Is there a gulf between something being the case and it being true? What is the difference between "p" and "p is true". It seems trivially the same thing. Appending "is true" doesn't make any difference???

Paul Ross
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HelpMePlease
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  • One problem (see the SEP entry on deflationism for this) occurs when we take the left-hand side of an instance of the schema for a sentence. "Vixens are foxes," is true iff vixens are foxes, sure, except if, "Vixens are foxes," is a *sentence* rather than an abstract proposition, then the "iff" makes the existence of a fully interpreted sentence equivalent to the right-hand fact, but it could be a fact that vixens are foxes even if there were no fully interpreted sentence using those *words*. Generally, one can find reasons to question the T-scheme throughout the SEP. – Kristian Berry Aug 15 '23 at 01:30
  • Isn't this exactly the same question as your earlier one? – g s Aug 15 '23 at 03:53
  • T-schema is motivated by the correspondence theory of truth, the idea of truth as a "match" to reality. This is what makes it "obvious". However, the correspondence theory, despite its intuitive appeal, has a lot of problems. And the T-schema itself is not logically innocent. Adding it to a formal theory allows to derive statements that are not derivable without it, even those that do not mention truth. The contradiction in the Liar paradox is the most famous example. So it is not as "obvious" as it looks. The 'correct' theory of truth may be such where the T-schema is not universally valid. – Conifold Aug 15 '23 at 09:10
  • @Conifold What is the fundamental difference between "Snow is white" and "Snow is white is true"? Are they not synonymous? How can one possible accept "Snow is white" and reject "Snow is white is true" and vice versa? – HelpMePlease Aug 15 '23 at 09:40
  • No, they are not necessarily synonymous. One can have a lower standard for asserting "snow is white" than for claiming it true. That was already addressed in the comments to your [previous question](https://philosophy.stackexchange.com/q/101668/9148). – Conifold Aug 15 '23 at 10:16
  • @Conifold Can you just give one example in plain English (My brain is currently tried of reading all this philosophical gibberish to understand something that should be common sense). – HelpMePlease Aug 15 '23 at 10:19
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    Well, common sense has limited uses and won't be of much help here, so you should get some rest and then parse the gibberish. The only alternative is to keep running in circles, as you've been doing so far. I already gave you examples, one can look at the snow and assert "snow is white", but not claim it true until others agree and verify it with a spectrometer. Or ever. – Conifold Aug 15 '23 at 11:13
  • I think it parallels some stuff going on in mathematics at the time - an object and meta languages, truth. Analytic philosophy might look very strange from other views; it has mathematics as a bedfellow. It comes from beginning to see propositions (essentially statements which are either true or false) everywhere, and wanting to know how to formally demonstrate their truth/falsity. – J Kusin Aug 15 '23 at 17:11

1 Answers1

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To explain it further requires some jargon. There is a difference between an object language - a language we use to make statements - and a metalanguage - a language we use to talk about statements in the object language.

Tarski's T-schema are perhaps easier to see as being non-trivial if we use a different language for the object language. For example,

"La neige est blanche" is true in French if and only if snow is white.

Note that the left part is in quotes and the right part is not. The quoted part is a sentence in the object language; the rest is a sentence in the metalanguage. The sentence as a whole is stating (in English) under what conditions "La neige est blanche" is true (in French).

But even if we use English in the object language, it is not trivial.

"Snow is white" is true in English if and only if snow is white.

This sentence is stating in the metalanguage under what conditons "snow is white" is true.

Snow is white

is a statement about snow.

"Snow is white" is true

is a statement about the truth value of the sentence "snow is white".

If this still seems rather trivial, the payoff is that a language with a truth predicate, i.e. a way of saying "X is true", is stronger than without. In fact, if a (first order) language is strong enough to express arithmetic, Tarski showed that truth is undefinable within that language. This can be stated formally by saying that no consistent theory can contain all instances of the scheme:

True(⌜φ⌝) ↔ φ

Where φ is some sentence in the language, ⌜φ⌝ is the quoted sentence, and ↔ is the material biconditional. Informally, this means that the concept of truth within a first-order language cannot be defined by a formula within that language.

Bumble
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