Why I don’t like philosophy of mathematics

I recently posted a link to an explanation of the philosophy of mathematics.  While I thought that Balaguer’s explanation was very good, I also remarked that I don’t find the philosophy of mathematics to be useful.  In this post, I’ll say why I don’t find it useful.

Toward the end of his explanation, Balaguer presents the following argument for platonism:

1. Semantic platonism is true–i.e., ordinary mathematical sentences like ‘2 + 2 = 4’ and ‘3 is prime’ are straightforward claims about abstract objects (or at any rate, they purport to be about abstract objects). Therefore,
2. Mathematical sentences like ‘2 + 2 = 4’ and ‘3 is prime’ could be true only if platonism were true–i.e., only if abstract objects existed. But
3. Mathematical sentences like ‘2 + 2 = 4’ and ‘3 is prime’ are true. Therefore,
4. Platonism is true.

Balaguer, who says he is a fictionalist and not a platonist, questions step 3 in that argument.  However, it seems to me that step 2 is already mistaken.  People simply do not use “true” in the way that step 2 supposes.

What philosophy of mathematics is about

Found via a reference at the M-Phi blog, here a pretty clear statement on what the philosophy of mathematics is all about:

• A Guide for the Perplexed: What Mathematicians Need to Know to Understand Philosophers of Mathematics (Mark Balaguer)

This does, indeed, seem to capture much of what philosophers of mathematics are studying.  However, it fails to persuade me that such study is useful to mathematicians.

Obese legislation

Richard Posner, in a post about the proposed immigration reform, writes:

It is an unreadable 880 pages in length (legislation has become obese in tandem with the increasing obesity of the population).

Emphasis added, to highlight the part that I found both amusing and true.

Why the hard problem is hard

In short, the hard problem is hard because it is bogus.

The “hard problem” here refers, of course, to what David Chalmers has referred to as “the hard problem of consciousness.”  There was a recent post about this at the Rationally Speaking blog.

• Why the problem of consciousness won’t go away (Guest post by Michael Lopresto)

Lopresto starts by talking about location problems, and the “problem” of locating consciousness in the physical world:

My project here is to ask whether it’s possible to locate consciousness in the physical world. That is, can we locate phenomenal properties in the physical world? My thesis is that given our conception of the physical world, it is in fact extremely difficult to locate phenomenal properties within it.

Talk of “phenomenal properties” already sounds dubious to me.  For sure, philosophers have long used the word “phenomena” to refer to sensory experience.  But what is it that is supposed to make sensory experience a kind of property?

The intelligibility of the world

As I recently mentioned, I intend taking some quotes from Nagel and presenting my position.  I’ll start with a comment on intelligibility:

The intelligibility of the world is no accident. Mind, in this view, is doubly related to the natural order. Nature is such as to give rise to conscious beings with minds; and it is such as to be comprehensible to such beings. Ultimately, therefore, such beings should be comprehensible to themselves. And these are fundamental features of the universe, not byproducts of contingent developments whose true explanation is given in terms that do not make reference to mind. (p. 17 of “Mind and Cosmos”).

When I look at that quote in my Kindle software, I see a note that 94 readers have highlighted that particular text.  So this is not merely Nagel’s opinion.  It is a view that is enthusiastically shared by a number of readers.

Nagel’s “Mind and Cosmos” – not quite a review

I have been reading Nagel’s book, “Mind and Cosmos:Why the Materialist Neo-Darwinian Conception of Nature Is Almost Certainly False“, so naturally I want to say something about it.  However, this won’t be the usual kind of review.  There’s no need for that.  There are already plenty of reviews available for this book, some of them scathing critiques and some of them offering high praise.

For myself, I disagree with much of what Nagel writes.  But I find it interesting nonetheless.  Readers of this blog will have noticed that I disagree with a lot of traditional philosophy.  And Nagel particularly emphasizes some of those parts where I disagree.  So, in a way, this highlights my disagreement.  If I were to suggest an alternative title for Nagel’s book, it might be:

• “What’s wrong with philosophy” on steroids

A theory of everything

As I mentioned in my previous post, I am currently reading Thomas Nagel’s book, “Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature Is Almost Certainly False.” So I thought I would comment on a section of the book, as appropriate for today’s date.

Nagel leaves no doubt that he is troubled by reductive materialism.  I am not at all sure why.  It is my experience that most scientists are skeptical of reductionism.  And even those who claim to be materialist do not seem to as materialist as Nagel thinks they are.  As far as I can tell, the strongest statements of materialism and reductionism come from philosophers, not from scientists.  And when philosophers express a particularly strong view, one suspects that they are deliberately staking out an extreme position as a way of doing philosophy.