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.

In Defence of Strong AI: Meta-meaning

Yesterday's post was quite long and wide-ranging, with a lot of examples etc. It focused specifically on how it might be possible to get semantics from syntax, particularly with reference to The Chinese Room thought experiment.

However I feel that I could sum up my position more succinctly by looking at the meaning of the word "meaning" itself.

In Defence of Strong AI: Semantics from Syntax

Is it possible to get semantics from syntax?

If it were impossible to get semantics (meaning) from syntax (symbols and formal rules for manipulating them) then we probably wouldn't have bothered broadcasting the Arecibo image to the universe in the hope of communicating with aliens.

Without any way to explain the meaning of this image, it seems to consist of syntax alone. Whether it could be deciphered by aliens in practice or not, it at least seems possible in principle, which seems to suggest that it may be possible in some cases to derive semantics from syntax.

The assertion that you can't, that there is no way to get from syntax to semantics, is perhaps the strongest response from John Searle to the systems/virtual mind refutation of his Chinese Room thought experiment (as outlined in my post on the topic).

Searle illustrates his point by saying that if he is in The Chinese Room and has a formal system of rules (syntax) for manipulating Chinese words, he has no way to get from this syntax to the semantics of what is being said. If he has no way to do this, then how can the system do it?

In Searle's view, the systems/virtual mind reply to the Chinese Room is just hand-waving until this is explained.

Let's see if I can attempt to do just that.