Mathematical Platonism Is True Because it is Useful

I have briefly discussed mathematical Platonism in previous articles. This post is going to contain my current thoughts about it.

Mathematical Platonism is distinct from classic Platonism (so nothing about ideal forms, for instance) and holds that three propositions are true.

1. Mathematical objects exist.

2. Mathematical objects are independent of human beings.

3. Mathematical objects are abstract

Or, in condensed form, mathematical objects exist abstractly and independently of human beings. All possible mathematical objects exist, have always existed and will always exist, even if no mathematician ever ponders them.

In this post, I will argue that while there is no fact of the matter regarding whether mathematical objects exist, it is sensible and useful to treat them as if they do, and that this is enough to justify mathematical Platonism.

Dualism is Not a Dirty Word

There are two major flavours of naturalism - methodological naturalism and metaphysical or philosophical naturalism. The former essentially means adopting the attitude that the latter is true as a pragmatic step without actually committing to the view that it is literally so. As such, only metaphysical naturalism is really in need of clarification.

I have already explained on this blog that I am a metaphysical naturalist, and what I think this entails, in particular the distinction between the supernatural and the natural. All too often these are unhelpfully defined simply as antonyms of each other.

To recap briefly on that earlier article, and I think to clarify and expand it in the light of recent thinking on the subject, I propose the following definition:

Naturalism is the view that the physical universe is fundamentally intelligible.

Let's extend this to make a number of other statements which I regard as equivalent or derivable from that basic definition.

(For the purposes of this discussion, a physical phenomenon or effect is an object, event or series of events which could in principle be objectively detected or verified by independent observers.)

In the naturalist view:

• All physical effects have physical causes
• All high-level physical phenomena can in principle be described in terms of lower-level physical phenomena
• The most fundamental, basic level of physical phenomena corresponds to the fundamental laws of physics, which are expressible in terms of mathematics

In my view, this definition rules out libertarian free will, for example, because the decisions of people have physical effects yet libertarians reject any physical, deterministic account of human decision-making.

Most naturalists seem to be physicalists, believing only physical stuff such as matter and energy to exist, and many even think that physicalism is identical to naturalism. It isn't though, and this distrust of the non-physical is partly responsible for an unwarranted contempt for the alternative view - dualism.

In Defence of Strong AI: The Modal Argument Refuted

In this video, philosopher and Christain theologian Alvin Plantinga outlines his modal argument, which in my view successfully establishes that he is not identical with his brain or body.

He interprets this to mean that he is something more than physical, and presumably that he has a soul. Physicalism refuted? Nope!