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.

April 25, 2021

## The garbage thief

It’s been a while since I last posted, and a reader is encouraging me to post some more. The truth is that, as I get older, my enthusiasm for posting dwindles. But let’s give it a try.

I’m starting with a story that happens to be true.

In our town, we are expected to separate recyclables from regular garbage. We are required to purchase a sticker to attach to the regular garbage, but the separated recyclable items are taken for free. This is intended to give us an incentive to recycle, though I would have done it even without that incentive.

We only put out the recycling bin every 3-4 weeks. And our regular garbage is usually fairly small in quantity. The best way we can help the environment is to live our lives so as to produce very little waste.

So on Friday, we put out the regular garbage. The wasn’t enough in the recycling bin to put that out. We put the garbage in a black garbage bag, attached a sticker, and left it on the driveway near the curb. This was at around 8:30 am.

When we looked at 9 am, the garbage bag was gone. We know it was not collected the usual way. The contractors who collect it make a lot of noise, and usually collect it around 2-3 pm. So it had just disappeared.

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.

January 22, 2021

## America is really, really back

I guess I was a little premature in my earlier post (“America is back“). I knew that Trump could still cause problems, but I was not expecting an attempted coup — or whatever we call what happened on Jan 06.

Biden has now been in office for two days. And already, things seem to be moving in a good direction. It’s not that Biden has great expertise that Trump lacked. Rather, the difference is the Biden has the good sense to seek advice from experts who understand the problems. Trump was never willing to take advice, and that was the real cause of his downfall.

## The deep state

The Trumpians, and other right wing reactionaries, have long complained that there is a “deep state” that actually decides what happens. They are right about that. The deep state is just us, the American people. And the deep state — that is, we — defeated Trump’s attempts to change the nature of America.

November 8, 2020

## America is back

It’s been a while since I last posted. And I rarely post on politics. But it was good to see the election of Biden/Harris.

For the last four years, it has somehow seemed as if I were living in The Banana Republic of America. And it may continue to feel that way until inauguration day in January. But the old USA will be back as Joe Biden attempts to re-unite the nation.

I guess I’ll keep this short and sweet. And this is my first post with the wordpress Block editor — which greatly dislike.

July 31, 2020

## My views on science and relativism

When I posted a review of “Science and Relativism” last week, I indicated that I would follow up with my own views on that topic.  So here it is.

When Kuhn’s “The Structure of Scientific Revolutions” came out, I thought it painted a somewhat better picture of science than what has been traditionally presented.  I didn’t agree with everything that Kuhn said, but I did like that he was challenging the traditional picture.

When, many years later, I read Feyerabend’s “Against Method”, I thought it a pretty good read.  I took Feyerabend to be poking fun at traditional philosophy of science, and I saw that as a good thing.  When he suggested that voodoo might work as well as science, I was not sure whether he was serious — and I’m still not sure.  In any case, I did not see him as a threat to science.

## Where philosophy goes wrong

In my opinion, much of what people see as criticisms of science are really a reaction to the idea (from epistemology) that knowledge is justified true belief.  As best I can tell, most scientists and most mathematicians see knowledge as distinct from belief.

July 23, 2020

## Science and Relativism

I have been procrastinating on posting this.  I want to say more about truth and how it is actually used.  So I’ll start with a review of the book “Science and Relativism” by Larry Laudan.

I’ll note that the book was published in 1990.  I purchased it, maybe 15 or more years ago.  I recently returned to it for a second reading.

The author, Larry Laudan, is a philosopher of science.  I assume that he is semi-retired by now, but that’s just a guess.

In this post, I shall mainly refrain from expressing my view of the issues.  I plan a followup post where I present that.

## What is relativism?

Broadly, relativism if the position that something is relative to something else.  And cultural relativism is that something is relative to culture and cultural traditions.  Most commonly, we hear of moral relativism.  However, when discussing science the issue typically has to do with scientific conclusions and scientific truth.

I’ll quote Laudan from his preface:

But it can be defined, to a first order of approximation, as the thesis that the natural world and such evidence as we have about that world do little or nothing to constrain our beliefs.  In a phrase, the relativists’ slogan is “The way we take things to be is quite independent of the way things are.”

April 29, 2020

## The scientific and manifest images

As a followup to my previous post, I’ll note that Dan Kaufman has posted a second round in his proposals for metaphysics:

As background, I’ll note that I am sitting at my desk.  According to the manifest image, my desktop is solid wood.  According to the scientific image, my desktop is mostly empty space surrounding a sparse array of atoms.

The scientific image is how physics sees the world.  The manifest image is closer to how we see the world.  But sciences vary.  Biologists are concerned about individual organisms.  And those belong in the manifest image, rather than in the scientific image.  Likewise, most of the concerns of psychology fit better with the manifest image.

In my view, philosophy (by which I mean academic philosophy) is mainly oriented toward the scientific image.  And, in my opinion, it should be more oriented toward the manifest image.  I think that’s also how Dan Kaufman sees it, but perhaps I am misreading him.  Please go read his post to see what he says.

## Where I come in

A little background about myself.  I started studying learning (or how humans learn) in the 1980s.  And I quickly found myself disagreeing with philosophers.  I imagined myself to be a solitary animal or organism on some planet, with little or know innate knowledge of the planet.  And I had to work out ways of learning about that planet.