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From Real Clear Religion: Mathematics as a challenge for naturalism

A photograph of the Greek letter pi, created as a large stone mosaic embedded in the ground.
pi in mosaic, Berlin/Holger Motzkau

From M. Anthony Mills:

In fact, more problematic for the materialist than the non-existence of persons is the existence of mathematics. Why? Although a committed materialist might be perfectly willing to accept that you do not really exist, he will have a harder time accepting that numbers do not exist. The trouble is that numbers — along with other mathematical entities such as classes, sets, and functions — are indispensable for modern science. And yet — here’s the rub — these “abstract objects” are not material. Thus, one cannot take science as the only sure guide to reality and at the same time discount disbelief in all immaterial realities.

This stubborn fact has led some philosophers, such as W.V.O. Quine, to argue that naturalism must countenance the existence of abstract objects, or at least those required by modern natural science. The argument goes like this: If we are committed to believing in those (and only those) entities posited by our best scientific theories, and if mathematical objects are among those entities, then we must accept the existence of mathematical objects.

What follows is a type of metaphysical naturalism — or “physicalism” — that is neither materialist nor entirely reductive. … More.

Fair enough but then we confront the question: Is our belief in the truths of mathematics merely an illusion that enables our selfish genes to pass themselves along? In that case, we are back where we started.

See also: Maverick Philosopher on Daniel Dennett, who objects to post-modernism but helps it along anyway (without meaning to)

God’s perfect proofs? Are there such things?

Should we be celebrating Tau Day instead of Pi Day?


The illusion of consciousness sees through itself.

A logic adder is not 'counting'. It is going through the motions. Same with animals. With the human mind, counting is another phenomena altogether, since we can conceive of the numbers themselves. EricMH
"The simple answer, of course is that ‘object’ is a completely unnecessary idea. The universe is just activities of various patterns and periodicities." Neither patterns nor periodicities are objects. Neither are ideas. anthropic
There's no reason to treat numbers and words as objects. Counting is a natural function of animal brains, and probably plant 'nerves' as well. Communicating is a natural function of animals and plants. We've taken counting and communicating to higher levels of abstraction than other animals and plants, but that doesn't mean the processes of enumeration and signification are 'ethereal'. They're just part of the activity of living things, along with breathing and reproducing. If you treat a number as an object, then you should treat each heartbeat or muscle twitch or pheromone squirt as an object. The simple answer, of course is that 'object' is a completely unnecessary idea. The universe is just activities of various patterns and periodicities. polistra
Excellent post. Thank you. Truth Will Set You Free

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