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.

Winning the impossible lottery

Photo: Nick See

I wanted to call this post 'The Lottery Paradox', but it turns out that title is already taken by a very similar idea. The version I'm going to discuss is a bit more extreme and has a different focus.

It is inspired by some thoughts I've been having related to the validity of the Anthropic Principle (the subject of my last post), inspired by the comments left by Callum J Hackett on that post.

Suppose the nation of Foobar has a national lottery, but the way it works is that every single day, one of the citizens is chosen at random to win a big prize.

Now suppose that the nation of Foobar has an arbitarily huge number of citizens (say a Googolplex).

I'm going to try to persuade you to believe two completely opposing conclusions about the possibility of believing that you have won this lottery. One of these conclusions is true, and one of them is false. See if you can tell which is which.

Super naturalism

Naturalism is a metaphysical proposition assumed by scientists (at least real scientists!) as they go about their work. Naturalism holds that every phenomenon we observe, and every phenomenon we will observe, is a result of natural processes. Even scientists of faith assume this position, limiting their belief in miracles to their private lives. This keeps us from taking supernatural shortcuts in our scientific investigations. We can never simply shrug and say "God did it!".

For most atheists, this proposition is more than an assumption, it is a belief. But what does this belief actually mean? What differentiates the natural from the supernatural?

Essential identity: The essence of essence

It seems that we cannot tie the identity of a person to their physical characteristics or to the atoms that make up their bodies. The former cannot be true because we regard physically identical individuals to be distinct people. The latter cannot be true because these atoms are recycled constantly.

It seems identity of people and things may be bound up in some sort of non-physical mystical "essence". If this were not so, Christopher Walken could have just bought another watch for Bruce Willis.

Essential identity: Cogito ergo sum

If there's one part of us that we consider to be the seat of our identities, it is our brains.

Essential identity: Physical identity

In continuing the discussion of our intuitive concept of personal identity, I look at ways in which our physical attributes might be the source of our identity.

Essential identity: Introduction

My last blog post discussed the notion that our intuitions are not trustworthy guides to understanding truths that are outside the bounds of our everyday experience. Relativity shows how our intuitions deceive us as to the nature of space and time, while quantum theory shows us the flaws in our common sense notions of matter and energy.

But there are many other ways in which our intuitions may deceive us. Much has been written about free will and whether this is an illusion (I believe it is). Bruce Hood has recently released a book called The Self Illusion, which argues that what we identify with is not a well-integrated self but a collection of competing drives and subconscious processes.

In this post I will introduce the idea that something is wrong with the very notion of personal identity itself.

Intuitive deceptions

As the years pass, and I mull over various philosophical or scientific ideas, it's becoming increasingly obvious to me that our human intuitions lead us astray all to often. We have uncovered numerous phenomena in the scientific world where reality is stranger than our intuitions suppose. In some cases, the nature of reality stretches the capability of our imaginations past breaking point.

Let's look at some examples.