March 11, 2018

## Odds and ends about truth

In my previous post, I proposed a somewhat limited theory of truth.  Here I’ll discuss some of the issues that might arise out of that theory.

### What if there are no relevant standards?

According to my theory, we assess the truth of a statement based on accepted standards for evaluating that truth.  So what will happen if there are no applicable standards?

The simple answer, is that we cannot assess the truth of that statement.

This is not really a new situation.  When Gödel proved his incompleteness theorem, he showed that there are mathematical statements (arithmetic statements) cannot be proved true or false.  Such statements are often said to be undecidable.  If you use my suggested theory of truth, then there will  be undecidable statements in ordinary life, and not just in mathematics.

The existence of undecidable statement has not been any kind of calamity in mathematics.  And it is unlikely to pose a serious problem in ordinary life.

### What about the law of the excluded middle?

According the the law of the excluded middle (or LEM), a statement is either true or false.  However, LEM is usually considered a law or reasoning, rather than part of a theory of truth.  Mathematicians still use LEM in their reasoning, following Gödel’s incompleteness theorem.  And it does appear to cause any problems.  I would expect the same to be true in ordinary life.  If you use my suggested theory of truth, you will not have to give up LEM as part of your reasoning strategy.

### Changing standards

What happens if we change standards?