Mathematics is mysterious. By this I don't just mean that there are many difficult, unsolved mathematical questions. I mean instead that mathematics itself, as a subject, and as an activity, is mysterious. Our familiarity with elementary mathematics sometimes lets us lose sight of this. This is probably a good thing most of the time. Reflecting on the nature of mathematics is no aid to mathematical problem-solving. But doing mathematics is one thing, understanding the nature of mathematics is another. The first task is mathematical, the second philosophical.
Why is mathematics mysterious? Because it is difficult to see how mathematics fits into our picture of the world. Mathematics concern specific truths and falsehoods: it is true that 1+1=2 and it is false that 1+1=3. It is also true that there is an empty set (a set of things with nothing in it), and false that some sets are members of themselves. These are truths and falsehoods in arithmetic and set theory respectively, which are branches of pure mathematics. Pure mathematics contrasts with applied mathematics, as in applied to the physical world. There are questions about how mathematics manages to apply to the world in all of the unexpected ways it does. The physicist Eugene Wigner famously said that mathematics was 'unreasonably' effective at applying to the world. However, the puzzles I am raising here are even more basic; they concern the most fundamental aspects of pure mathematics itself.
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Anselm (1033-1109)
Martin Jenkins recalls the being of the creator of the ontological argument.
Is Brillo Box an Illustration?
Thomas E. Wartenberg uses Warhol's work to illustrate his theory of illustration.
Why is Freedom So Important To Us?
John Shand explains why free will is basic to humanity.
The Funnel of Righteousness
Peter Worley tells us how to be right, righter, rightest.
We're as Smart as the Universe Gets
James Miles argues, among other things, that E.T. will be like Kim Kardashian, and that the real threat of advanced AI has been misunderstood.
Managing the Mind
Roger Haines contemplates how we consciously manage our minds.
lain McGilchrist's Naturalized Metaphysics
Rogério Severo looks at the brain to see the world anew.
Love & Metaphysics
Peter Graarup Westergaard explains why love is never just physical, with the aid of Donald Davidson's anomalous monism.
Mary Leaves Her Room
Nigel Hems asks, does Mary see colours differently outside her room?
From Birds To Brains
Jonathan Moens considers whether emergence can explain minds from brains.