I have been going back over some of my PhD research and have discovered an interesting example I didn’t consider. It shows up some odd consequences of the way we understand truth predicates. Consider the following:
B: Sentence A in this post is true.
There is no A in this post so intuitively we can rule out B being true. That means that whatever else we might say about it B is not true. However this leads to an odd argument:
1. B is not true.
2. B iff B is true. (T Schema)
3. A is true iff B is true. (Spelling out B)
4. A is not true iff B is not true. (Consequence of 3)
5. A is not true. (From 1 and 4)
However, it is somewhat ridiculous to conclude that A is not true since there is no A.
So where does this argument go wrong? It can only be in the initial argument that B is not true, or in the assumption of the T Schema.
The only way I can see that we could argue that it is not the case that B is not true is to argue that as there is no A, we can’t say anything about the truth of B. However, that means that it is not the case that “B is true” – which is equivalent to saying that “B is not true”.
So something odd is going on here with the assumption of the T-Schema.