The reasonable effectiveness of mathematics in the natural sciences

In 1969, Eugene Wigner wrote what has become a famous paper, titled “The unreasonable effectiveness of mathematics in the natural sciences.”  There’s a pretty good summary of the related issues in the Wikipedia article of the same  name.

As you might guess from the title of this blog post, I disagree with Wigner.  In my view, the effectiveness of mathematics is entirely reasonable.  And it has long seemed reasonable to me.  I thought about it either in high school or as a graduate student in mathematics (I’m not sure which), and came up with what I found to be a satisfactory explanation.

Perspective on mathematics

I’ll start with my broad perspective, which I have probably mentioned before on this blog.  I often say that mathematics is not about reality.  The mathematician Kronecker famously said “God gave us the natural numbers.  All else is the work of man.”  I almost agree, except that I think Kronecker gave God too much credit.  As I see it, the natural numbers are also the work of man.  That’s part of why I am a mathematical fictionalist.

Convention (1) — introduction

I am starting a series of posts on the idea of conventions, as in social conventions.  It has long been clear to me that conventions are important.  This, however, seems to be controversial.  As best I can tell, philosophers are deeply suspicious of convention.

As a self-declared heretic about philosophy, I am not troubled by opposing what seems to be the conventional view of convention among conventional philosophers.

Here’s some background reading:

• Convention – Stanford Encyclopedia of Philosophy
• Convention (norm) – a relevant Wikipedia page

HSW – Kepler’s laws are false

While my title line might seem dramatic, I want to be clear that this post is not intended as a criticism of Kepler, or of Kepler’s laws.  Rather, it is critical of the view that scientific laws are true descriptions of the world.  This post is intended as part of my series on how science works.  My aim is to describe my own understanding of Kepler’s laws.

The basis of Kepler’s laws

In case some of my readers are not familiar with them, Kepler’s laws are an attempt to account for the motion of the planets in our solar system.  Kepler’s laws were preceded by the Ptolemaic idea that the planets moved in cycles and epicycles.  Galileo argued, instead for the idea of Copernicus, that the planets traveled in circular paths around the sun.  I presume that Kepler was looking for something a little more precise than the Copernican circles.

HSW – Against induction

In this post, I shall argue against induction.  Specifically, I shall argue against what I referred to as “philosophic induction” in a recent post.  My earlier post — “All emeralds are green” — was intended to illustrate the view that I shall be presenting here.  I suggest you read that now, if you have not already done so.  Throughout this post, I shall assume familiarity with that story.

That emeralds are green has sometimes been used to illustrate the idea of induction.  Presumably, the argument would be:

• All the many emeralds that I have seen were green;
• Therefore all emeralds are green.

Interestingly, emeralds were also used by Nelson Goodman in his skeptical “grue” argument.

HSW – about induction

I have long been a critic of induction.  The trouble with the word “induction” is that it is used in many different ways.  As part of my continuing series on how science works, I want to explain here what I am criticizing, and what I am not criticizing.

Baconian induction

Sir Francis Bacon suggested used the term “induction” in his recommendations on investigating the natural world.  As described by Wikipedia, his method called for:

procedures for isolating and further investigating the form nature, or cause, of a phenomenon, including the method of agreement, method of difference, and method of concomitant variation.

HSW2 – How I see Newton’s mechanics

This continues my discussion of how science works, a topic that I introduced in a recent post.  The “HSW” in the title of this post is intended to indicate that.  My plan, for this post, is to describe how I look at Newton’s laws.  I won’t be discussing his law of gravity here, mostly to keep this post reasonably short.  I might post on that at a future time.

A note on history

I am not an historian.  My primary concern is with how the science works, rather than with how it was discovered.  If you think that I have said something about history, then you have misunderstood.  Some of what I am discussing here might actually be due to Galileo or to other scientists.

Answering V.J. Torley’s questions

Over at the Uncommon Descent blog, poster vjtorley has posed “Ten Questions for Professor Coyne.”  I am not a spokesman for Jerry Coyne, and I disagree with some of what he writes.  But I thought I would try giving my own answers to those questions.  I’m pretty sure that Jerry Coyne would disagree with me on some of the answers.

Question 1 – Is science the only road to knowledge?

I’ll note that there is some ambiguity on what is meant by “knowledge.”  For myself, I would never claim that science is the only way to all knowledge, though it is an excellent way to knowledge about the natural world.  In any case, vjtorley breaks this question into several parts.

On metaphysics

In an earlier post, I hinted that I would discuss the two essays by Massimo Pigliucci on naturalized metaphysics.  So that will be the goal of this post.  For convenience, I shall refer to those two essays as NM1 and NM2.

• NM1: Surprise! Naturalistic metaphysics undermines naive determinism, part I
• NM2: Surprise! Naturalistic metaphysics undermines naive determinism, part II

The goal

It is not my aim here to argue that Pigliucci is wrong.  Rather, the aim is to present how I look at the questions he is discussing.  Partly, this is because I have rather non-typical views, and am sometimes asked to explain them.  Partly, it is because I have indicated my dislike for metaphysics, and some have suggested that we cannot actually do without metaphysics.  So perhaps the discussion here will help my readers better understand my viewpoint.

The Neil deGrasse Tyson discussions

There have been several recent posts at Jerry Coyne’s site, related to the views of Neil deGrasse Tyson.  They began with “Neil deGrasse Tyson goes all militant“, and there are followup posts here and here.

My personal take on the first of those posts was that I did not see Tyson as going all militant.  In fact, I did not see his comments on religion as much different from what I have seen in other video talks, though he does raise some interesting questions.

In any case, those posts and the featured videos are worth reading and watching.

Yes, Newton was the greatest scientist ever

According to Larry Moran, Darwin was the greatest scientist ever.

Most of us know that Charles Darwin was the greatest scientist who ever lived but one still finds the occasional misguided physicist/mathematician who thinks that the honor should go to an eighteenth century Englishman named Isaac Newton (1642-1727).

I agree that Darwin was a great scientist.  But I will stick with Newton as the greatest ever, even though Larry thinks that misguided.

Yes, Newton had some weird religious ideas.  And parts of Newton’s science have since been displaced by relativity and QM.  But it is not Newton’s laws themselves that make him great.  Rather, it is his involvement in the transformation of how we do science.

For sure, that transformation was the work of a number of people.  Copernicus was important, and Galileo was very important.  Others, such as Boyle and Hooke were important.  But the greatest credit must go to Newton, for why science today is so different from what it was at, say, the time of Aristotle.