June 21, 2021

## 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.

May 31, 2021

## 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.

May 24, 2021

## 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.

May 17, 2021

## 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”.

May 9, 2021

## 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.

May 3, 2021

## 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 $2+2=4$ 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 $2+2=4$ 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.

February 26, 2021

## Induction is absurd

The term “induction” is used in a variety of ways. For example, it is sometime applied to statistical inference. I do not find anything absurd with statistical inference, if it is done properly.

The absurdity that I am posting about, is with respect to what is sometimes called “philosophical induction.” Here’s an example of that kind of induction:

All the many crows that I have seen are black. Therefore all crows are black.

That’s the example that David Stove used in his book “The Rationality of Induction.”

We are born into a world where there are no crows. As a child grows, she eventually learns to carve that world up into parts and to name the parts. What we call “crows” comes from that carving up operation (or that categorizing operation). For that matter, we are born into a world without black. We later learn to categorize into colors such as black, green, red, blue, yellow. That we have black things depends on our categorizing into colors. That we see crows depends on our categorizing into things.

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February 23, 2021

## Are there laws of nature?

This post is partly a reaction to a recent post that I saw at Erraticus.

That blog post is mostly a discussion (or disagreement) between two people, David and Margaret, about whether there are laws of nature. David thinks that there are, while Margaret is a skeptic.

As best I can tell, both David and Margaret are fictional. The author, Eleni Angelou, is using them to bring out some of the controversy involved with that topic.

I’ll start with my answer. No, there aren’t laws of nature. There are laws of physics, but those are not laws of nature. The distinction here is that I see laws of physics as human constructs, while I understand “laws of nature” to refer to things that are said to be independent of humans.

That puts me on the side of the skeptic. If anything, I am even more skeptical than Margaret.

May 31, 2019

## Knowledge of nuomena

A comment to my previous post asked an interesting question:

Do you yourself think that the noumenal world (The world “in itself”) is unknowable to humans?

This brings up issues which deserve a full post responding to the question.  In particular, it brings up questions such as:

• what do we mean by knowledge?
• what is the relation between the nuomenal world and the wolrd of our experience (the phenomenal world)?

### Some background

Let me state, at the outset, that I am not a professional philosopher.  My background is primarily in mathematics and computer science.  So you should take this post as mostly reflecting my personal opinion.  I like to think that opinion is informed by my study of cognition and consciousness.  As best I can tell, nobody else is studying consciousness in quite the same way.

For background on the meaning of “nuomena”, I suggest the Wikipedia article.  Apparently, Plato used the term to refer to his ideal forms.  But, more recently, the term has been used for what Kant described as the thing in itself.  I take that to be a reference to the world undistorted by human ideas and concepts.  I should note that “nuomena” is plural, with “nuomenon” as the corresponding singular.  And I shall use the expression “nuomenal world” for the world of nuomena.

May 8, 2019

## Nuomena and phenomena

Kant made a distinction between the world in itself (the nuomenal world) and the world of our experience (the phenomenal world).  This was the topic of discussion between Dan Kaufman (or “DK”) and Crispin Sartwell (or “CS”) in a video presented at Electric Agora.  I found it an interesting discussion.  In this post, I plan to comment on a small portion of what was discussed.

DK and CS disagree, in a friendly way, throughout the discussion.  That’s good, because it brings different viewpoints to our attention.

In earlier posts here, I have argued that there isn’t a way that the world is.  From the linked discussion, DK seems to agree while CS seems to disagree.  My own views don’t coincide with either, though perhaps they are a bit closer to DK.

At around 16:45 in the video, DK says “We shouldn’t think of the object of investigation as the world independent of anyone’s experience.”  I’m inclined to disagree with DK on that point.  It seems to me that we do investigate the nuomenal world.  And, yes, we investigate it by means of our experience.  But we create that experience by means of the ways that we interact with the world.  It doesn’t quite seem right to say that we only investigate the world of our experience, when we generate our own experience in order to investigate the unknown nuomenal world.

In some sense, the goal of our investigation is to find ways of satisfying our biological needs and urges.  But, to achieve that, we investigate the world looking for opportunities to meet those needs and urges.  And our investigation is unavoidably biased by our biology and perhaps by our culture.

## Objects

DK goes on to suggest that trees are not nuomenal objects.  And CS disagrees, saying that they are nuomenal objects.  My view is somewhere between the two.  That is to say, I see trees as part of the nuomenal world, but not as nuomenal objects.  I don’t think there is anything in the nuomenal world to decide what is an object.  It is up to us to decide what to count as an object.