## 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?

Andy Tanenbaum famously said “The nice thing about standards is that you have so many to choose from.”  So if you don’t like one standard, you can change to another.  Tanenbaum was talking about network standards, but it applies more generally.

Is this a recipe for relativism?  Can the truth of a statement change if we switch standards?

This might at first seem a problem.  But I don’t think it is.

Consider an example:

• It is 35 miles to Chicago;
• It is a 90-minute drive to Chicago.

Those two statements use different standards for expressing something about the distance to Chicago.  But they don’t contradict.  And they don’t raise the prospects of relativism.  The words used in each statement tell us what standard is appropriate for that statement.  And, generally speaking, we know what standard to use either from the wording of the statement or from the context of the discussion where the statement arose.

Thomas Kuhn, in his “The Structure of Scientific Revolutions”, used the term “paradigm shift” for the change from one scientific theory to another.  A change in standards is very similar.  We can think of a scientific theory as a set of standards for doing science in a particular area.

Kuhn’s thesis has been used to argue for relativism of truth.  An example would be that some folk took geocentrism to be true, while others took heliocentrism to be true.

My own modest theory of truth cannot be applied to argue for relativism in this case.  There is no standard for evaluating whether a scientific theory is true.  We generally accept scientific theories on pragmatic grounds, so we do not need to assess whether the proposed theory is true.  We only need to know how well it works.  And if we cannot assess the truth of theories, then there isn’t any truth conflict between competing theories.  So such paradigm shifts do not present a case for relativism if you limit yourself to my modest theory of truth.

### Incommensurability

Kuhn argued that a paradigm shift can lead to an incommensurability of meanings.  If you look at the examples I gave above, the two statements “It is 35 miles to Chicago” and “It is a 90-minute drive to Chicago” do appear incommensurable, in the sense that there is no simple logical transformation from one to the other.  But this kind of incommensurability does not seem to pose the kind of threat that some people have seen in Kuhn’s thesis.