| 1. | ‘Sentence (1) is not true’ is true |
| 2. | Sentence (1) = ‘Sentence (1) is not true’. |
| C1. | Sentence (1) is true |
| C2. | Sentence (1) is true and sentence (1) is not true. |
In order to understand the importance of Tarski’s definition of truth, it’s important to see the reasons why the notion of truth was somewhat in disrepute at the time that Tarski wrote. To this end, we’ll briefly discuss three kinds of reasons for being skeptical about the idea that there is such a property as being true.
The first of these is due to Frege, who discussed truth in “Thought,” which we read earlier. Frege presented an argument that truth was indefinable. He presented the argument in the context of his claim that truth cannot be defined in terms of correspondence to facts:
“Grammaticallly, the word ‘true’ looks like a name for a property. ...It might be supposed ...that truth consists in a correspondence of a picture to what it depicts. ...But could we ...maintain that there is truth when there is correspondence in a certain respect? BUt which respect? For in that case what ought we to do so as to decide whether something is true? We should have to inquire whether it is true that an idea and a reality, say, correspond in the specified respect. And then we should be confronted by a question of the same kind, and the game could begin again. So the attempted explanation of truth as correspondence breaks down. And any other attempt to define truth also breaks down. For in a definition certain characteristics would have to be specified. And in application to any particular case the question would always arise whether it were true that the characteristics were present. So we should be going round in a circle. So it seems likely that the content of the word ‘true’ is sui generis and indefinable.” (326-7)
Later, Frege expresses the worry that his argument suggests to him:
“The Bedeutung of the word ‘true’ seems to be altogether sui generis. May we not be dealing here with something which cannot be called a property in the ordinary sense at all?” (328)
In general, you might think that we could reply to Frege’s argument by granting that truth is indefinable, but resisting skepticism about truth -- surely some things are both genuinely real and indefinable. Some empiricist reasons for thinking that the indefinability of truth gives good cause for skepticism about it. Skepticism about truth as a ‘metaphysical notion.’
A criticism of Frege’s argument, construed as an argument for the claim that any definition of truth will be circular. Two ways in which it might be true that establishing p involves establishing q: (i) once one has established p, q follows as a trivial consequence; (ii) to determine whether p is the case, one must first determine whether q is the case. A reading of Frege’s argument as conflating (i) and (ii).
A residual skepticism about truth in the absence of a definition of truth.
Another source of skepticism about truth is that we can never be absolutely certain of any proposition about the external world; and, for this reason, to use the concept of truth rather than, for example, the concept of having a certain probability, is always to go beyond the evidence. So, for all serious scientific or philosophical uses, the concept of truth is useless.
Soames (Understanding Truth, ch. 2) formalizes the implicit argument here as follows. (For a possible expression of such an argument, see Hans Reichenbach’s 1938 book, Experience and Prediction.) Consider first the following two sentences:
(a) It is true that p.
(b) It is highly probable that p.
Using these as examples, we can then argue as follows:
| 1. | When one asserts (a), one is committed to something stronger than what one is committed to by virtue of asserting (b). If it turns out that p is not the case, then one who utters (a) has made a mistake, whereas this is often not true of one who utters (b). |
| 2. | So, the proposition expressed by (a) must be logically stronger than the proposition expressed by (b). (1) |
| 3. | The strongest statement one can ever make about a proposition is that it is highly probable or well-confirmed by evidence. |
| C1. | One is never justified in making statements about truth, like (a). (2,3) |
| C2. | For scientific or other serious purposes, we should dispense with the concept of truth. (C1) |
A reductio of this argument based on the fact that we know a priori that p is true iff p. Why this is enough to show that, if the argument is sound, no statements are ever justified.
A flaw in the argument: step (2).
The most serious source of skepticism about the concept of truth is not that it is indefinable, or that it is not empirically useful, but that it leads to contradiction. The most famous argument for this paradoxical conclusion is the ‘Liar paradox.’ The paradox can be generated by a ‘Liar sentence’, and example of which is the following:
The first example sentence on the third page of the handout about truth skepticism for PHIL 415 at McGill University in the Winter Term of 2005 is not true.
or, more simply,
1. Sentence (1) is not true.
A way to derive a contradiction from this sentence:
| 1. | ‘Sentence (1) is not true’ is true |
| 2. | Sentence (1) = ‘Sentence (1) is not true’. |
| C1. | Sentence (1) is true |
| C2. | Sentence (1) is true and sentence (1) is not true. |
The idea that truth is a defective concept. ‘Tonk.’
(For more detail on various other kinds of skepticism about truth, see Soames, Understanding Truth, ch. 2.)
