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.

September 5, 2018

## On my philosophy of science

I haven’t posted for a few weeks.  Some of the ideas that I have been discussing and want to discuss, are difficult to present.

In the meantime, I posted something at an online forum that seems to have been received well.  And it does have to do with my philosophy of science.

So I’ll start by quoting that post.  For reference and context, the original post is here:

## So here’s that post:

Eddie: Would the same physicists all say that “the standard model is a true, or approximately true, depiction of nature?”

I don’t know about physicists.

As I see it, the standard model is neither true nor false as a depiction of nature. Our concept of “true” does not allow us to make such a judgment of the standard model.

Here’s the problem:

There is nothing at all that can be said directly about nature. In order to say something, we need words and we need a standard way of attaching those words to nature. Until we have the words and the standards, there is no basis for saying anything.

The role of the standard model is to provide us with those words and standards which would allow us to say things about nature. So the standard model, or some suitable replacement, is a prerequisite to being able to have true or approximately true depictions of nature.

I look at the cosmology of Genesis 1 in about the same way. In its time, it provided a vocabulary and a set of standards on how to have true depictions of nature. So I tend to see that cosmology as neither true nor false, but as setting the stage to be able to make true depictions. But, of course, it has been superseded by newer and better cosmologies.

July 18, 2018

## On ontology and materialism

Recently Dan Kaufman and Massimo Pigliucci had a discussion about ontology, materialism and related topics.

Here’s Massimo’s blog post, where he introduces the video.  And you can find the discussion video on that page:

Ontology is part of metaphysics.  And I have never seriously studied metaphysics.  So I watched the video all of the way through to see what I could make of it.

Generally speaking, I’m a skeptic of metaphysics and of ontology.  After watching the video, I am still a skeptic.  But I did enjoy the discussion.

I’ll add some of my own comments on what was discussed in the video.  I’m calling them comments, because this is not an attempt to review the video or to make serious arguments about what is discussed there.  It is just comments or reactions to what I am seeing and hearing.

July 16, 2018

## Alternative math

Jerry Coyne posted this video at his blog:

Presumably Coyne was making a point about alternative truths.  The video clip is quite exaggerated.  I don’t expect anything like that to actually happen.   But, of course, exaggeration is often a good way of making a point.

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July 11, 2018

## Patterns and lumps

Many people, both philosophers and AI proponents, talk about patterns.  They typically suggest that we start by finding patterns in the world.  We then build up perception and knowledge based on the patterns that we find.

Sometimes people talk of “regularities” rather than of “patterns”.  The term “regularity” implies some sort of rule following.  And that fits with our ordinary idea of pattern.

So let’s examine the idea of starting with patterns or regularities

### Patterns

What’s a pattern?