What is intelligence?

People often talk about intelligence, but it is hard to say what it is. We measure IQ (Intelligence Quotient), but it isn’t entirely clear what that is measuring. This is illustrated by the Flynn Effect, which shows that IQ seems to be increasing over time. Some people have suggested that IQ is sensitive to culture, and I’m inclined to agree with that.

So what is intelligence? In this post, I shall give some of my own opinions. I don’t think there is a consensus answer to the question.

Biology and intelligence

I am inclined to think of intelligence as biological.

Take a pot plant on your window sill, and rotate it around. The plant will begin to change its growth patterns toward the new direction of light. The pot plant appears to have the ability to change its behavior so as to adapt to changes in the environment. Mechanical objects don’t do this.

What are those things we call “laws of nature”?

There was a recent post at Aeon by philosopher Marc Lang:

• What is a law of nature?

I want to discuss that, and to discuss some of my disagreements. My first disagreement, is that I don’t believe there are such things as laws of nature. But there are certainly things that people call “laws of nature”. I’m okay with calling them scientific laws. But I doubt that they come from nature. That is to say, I see these laws as human constructs. I do not see them as something that we can just read from nature itself.

In our science classes, we all learned some examples of what scientists currently believe (or once believed) to be laws of nature. Some of these putative laws are named after famous scientists (such as Robert Boyle and Isaac Newton). Some are generally called ‘laws’ (such as the laws of motion and gravity), while others are typically called ‘principles’ (such as Archimedes’ principle and Bernoulli’s principle), ‘rules’ (such as Born’s rule and Hund’s rule), ‘axioms’ (such as the axioms of quantum mechanics), or ‘equations’ (such as Maxwell’s equations).

It is interesting to note the expression “what scientists currently believe (or once believed) to be laws of nature” for that already suggests that scientists can change their minds as to what they take to be laws of nature. And this seems to agree with my point that these laws are actually human constructs.

On what exists

I follow the philosophy blog of Ian Wardell via my RSS reader. I disagree with some of what he posts. And I find myself not very interested in others of his posts. But at times he posts things that interest me.

Checking, this morning, I found his latest post:

• What physicists claim exists can be doubted

and that just happens to be right up my alley. It is a topic that I have posted about from time to time. So I suggest that you read his post.

As an example, physics describes the world in terms of mass, distance and time. Ian is arguing, in effect, that it is legitimate to doubt whether mass, distance and time actually exist. And I agree with him about that.

The way the world is

Ian asks “Do our theories in physics mirror how reality really is?”

I have been posting my ideas about this for some time. And my general view is that there isn’t a way that the world really is. There is a way that we describe the world. There are ways that we experience the world. But there is no human-independent way that the world is. No matter how we describe the world, we can only describe it in terms of our own interactions with the world.

Are analytic sentences tautologies?

An analytic sentence is one which can be seen to be true by virtue of the meanings of its terms. An example that is often given is:

• A bachelor is an unmarried man.

A widely held view, among academic philosophers, is that analytic sentences are tautologies. I disagree with that assessment. I am not saying that the philosophers are wrong. I am just expressing my disagreement. Maybe we don’t have the same idea as to what “tautology” means.

It is widely agreed that language is conventional. That is to say, there are social conventions that underlay language. That different societies have different languages points to this conventionality.

Among the various conventions, there can be syntactic conventions which set how words should be arranged in sentences. There can also be semantic conventions, which set the meanings of words. And, of course, there can be mixed convention that combine both syntactic and semantic aspects.

To my way of thinking, a tautology is a sentence that is true by virtue of syntactic conventions. But once we bring in dependency on semantic conventions, I don’t think we should use the term “tautology.”

Iowa and Illinois

Here’s an example.

Apparently there is an agreement between the states of Iowa and Illinois, setting the boundary between the two states as the Mississippi river (the center of the Mississippi river). According to that agreement, we can say “Iowa is to the west of the Mississippi.” From my perspective, that sentence looks analytic but I would not consider it to be a tautology.

Conventionalism

I skipped posting last week. I had planned to post about knowledge and belief, but decided to skip that post.

Conventionalism is interesting, in part because much of our life seems to depend on social conventions. And, in part, because philosophers seem to be strongly opposed.

According to Wikipedia, “Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicit or implicit) agreements in society, rather than on external reality.”

Convention

It is usually agreed that a social convention is an agreement, perhaps implicit rather than explicit.

The rule that we should drive on the right side of road is often mentioned as an example of a convention. In some parts of the world, including Australia (where I grew up), people instead drive on the left side of the road. That there was a choice between driving on the left, or driving on the right, illustrates why conventions are said to depend on arbitrary choices. But those two choices (left vs. right) are not the only options. For example, there could be a system where people drive on the left on even numbered days and on the right on odd numbered days. This would be more confusing, with probably more accidents. But it serves to illustrate that there is often a degree of pragmatism in our choice of convention. Saying that a convention is an arbitrary choice does not rule out the involvement of pragmatism in the making of that choice.

Poincare proposed conventionalism for geometry. In his view, the axioms of geometry derive from our measuring conventions. I agree with Poincare on that.

Hilary Putnam argued against conventionalism in “The Refutation of Conventionalism”. One of his arguments was that under conventionalism there could be no matters of fact. I just measured the height of my desk as 74 cm. That’s a matter of fact which depends on the measuring conventions which define the centimeter. From the way that I look at it, all facts are relative to the conventions that we follow when observing those facts.

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.