Recent posts on “truth”

Today I want to give an overview of what I have been pointing to in recent posts. That is to say, I want to put them in perspective.

Truth is important. If you think I have been arguing against the idea of truth, then you have misunderstood my intentions. When I read various arguments, I see many misconceptions about truth. I have been attempting to clear up those misconceptions.

Why and how?

I have been studying human cognition. And one of the things that we humans do, is make assessments of truth. In order to understand cognition, we need to understand how we make those decisions.

My approach has been to attempt understand human behavior in how we use “true”.

Truth is a human artifact

Perhaps the most common misconception is the idea that truth is human independent. We see this, for example, when people talk of “the way the world is” rather than “the way that we see the world” or “the way that the world is to us”. When they talk of “the way the world is,” they typically are talking of true statements that can be made about the world and they are taking it that this is human independent.

Truth, information, science

Philosophers of science tend to want to see scientific theories as true. I sometimes point out that Boyle’s law is false. Some time ago, I wrote an earlier post saying that Kepler’s laws are false. In this post, I want to paint a picture of where truth and information fit into science.

The stopped clock

You have probably heard the saying, “a stopped clock is right twice per day”. And, along the same lines, we can say that a clock which is 1 minute slow is always wrong. However, you would probably prefer to have a clock that is 1 minute slow, than to have a stopped clock.

“Right” and “wrong” here are references to truth. The example of the stopped clock suggests that there is more to science than truth.

We can, instead, look at it in terms of information. The clock that is 1 minute slow is actually giving pretty good information about time. It isn’t perfect information, but it is good enough to be useful for many purposes. The stopped clock, by contrast, does not provide any useful information. Yes, twice per day it has the correct information. But that stopped clock cannot tell us whether this happens to be the time of day when it is correct. Since it does not tell us that, we cannot trust the time as reported by the stopped clock. It is, at best, useless information.

Truth and correspondence

The title is a reference to the correspondence theory of truth. This is not a post about letter writing.

When asked what they mean by “true” people often mention the correspondence theory. However, I find the common descriptions of the correspondence theory to be unsatisfactory. So this post will be an attempt to make sense of the idea of correspondence.

The correspondence theory is sometime said to say that a sentence is true if it corresponds to the facts. I always saw this as puzzling, because to me the term “fact” was just another name for a true statement. Described that way, the correspondence theory of truth seemed to just say that true statements are true and false statements are false. Of course, I did not disagree with that, except that it did not say anything at all.

It is sometimes suggested that facts are metaphysical things, and that correspondence to facts means correspondence to these metaphysical entities. I have trouble trying to understand what a metaphysical fact might be. Several hundred years ago, it would have been taken to be a metaphysical fact that the earth is fixed and the sun goes around the earth. Today, we instead say that the earth goes around the the sun.

Another way of presenting it, that I sometime see, is to say that a sentence is true if it expresses what is the case. But, once again, “what is the case” just seems to be another word for “true”, so we are again left with the correspondence theory saying that true statements are true and false statements are false.

Truth as a property of syntactic expression

There’s an intuitive idea, that a statement is true if it corresponds to reality. But it usually isn’t defined that way because of the difficulty of explaining “corresponds to reality”.

Truth in ordinary life

Last week, I posted about truth in mathematics. So now I want to move to discussing our use of “true” in every day life.

Ordinary statements

As with mathematics, there are many statements on which people can agree as to their truth. These are typically simple descriptive statements such as “it is raining” or “the grass need mowing” or “there’s a pothole down the street.” These are the kinds of statements that we can check for ourselves by looking around. There are others that we cannot quite check for ourselves, such as “the Yankees won today’s baseball game”, but we generally accept the rulings of the umpires or other officials. The statement “Biden won the presidential election” should be of this type, though there is surprising disagreement this time around.

For these types of statements, we judge their truth based on our ordinary language use, including the meanings of the words. We can perhaps say that they are true because they follow to implicit rules of language use, or the implicit conventions of language use. For such statements, truth is usually not controversial because of the shared agreement about these implicit rules.

Heliocentrism

There are other statements which have generated disagreement. A traditional example is the question of whether heliocentrism is true. Galileo got into an argument with the church because of his insistence on heliocentrism. Today, most people accept heliocentrism without much disagreement. Clearly this is a different kind of question from those I considered to be ordinary statements.

Truth in mathematics

I’m tentatively planning several posts on “truth”, and mathematics seems a good place to start — partly because I’m a mathematician, and partly because some of the distinctions seem clearer in mathematics than in other areas.

I can think of at least two different ways that we use “true” in mathematics. The most basic of these is with ordinary statements such as or the Pythagorean theorem. Both are generally recognized as true. The other way that some people use “true” is when they talk about whether the axioms are true. That could refer to the Peano axioms for arithmetic, the Zermelo-Fraenkel or about whether the axiom of choice is true or about whether the continuum hypothesis is true. As we shall discuss below, the way we think about the truth of axioms is different from the way that we think about the truth or ordinary mathematical statements.

Ordinary statements

When I talk of “ordinary statements” in mathematics, I am talking about statements such as in arithmetic or the Pythagorean theorem in geometry. We normally have a system of axioms that we use in our mathematics. For ordinary arithmetic, these are the Peano axioms. For geometric questions, we normally use Euclid’s axioms, supplemented by some version of the parallel postulate. For set theory, we most commonly use the Zermelo-Fraenkel axioms, possibly supplemented by the axiom of choice.