On 2011-05-19 14:01, Simon Wise wrote:

Zero ;-)

That's "four matches", not "the number four". If by "number" you mean the characteristic property of all sets of 4 elements, you're perceiving something (the matches) which has that property, but you can't directly perceive the property itself (i.e. its `intension'), because it's a function (in the mathematical sense) from all possible entities (let's ignore possible worlds for now) to a truth value indicating whether or not that entity is a set-of-four. This view is pretty unsatisfying for a number of reasons (for one thing, it doesn't work well for anything other than positive integers), but I hope it suffices to show that "the number four" can't be perceived directly. The same sort of argument goes for other "simple" qualities like volume, mass, density, color etc -- this stuff has had epistemologists tearing their hair out for centuries. There are 2 main camps, and I'm more or less solidly in the one that says "numbers exist" :-)

huh? do you happen to know of one specifically?

... many one, many two, many three, many four, many many, ... many many one, many many two, many many three, many many four, ... LOTS

[courtesy of Terry Pratchett] ;-)

Again, I take issue with the details, but yes: there's a lot of empirical evidence that human cognitive/perceptual apparatus does some specialized handling for small sets, including counting. How we get those sets to be __sets__ (as opposed to arbitrarily co-occuring random perceptual data packets) is quite another matter, and im(ns)ho a much more interesting one.

I'll agree that integers and complex numbers have the same sort and degree of existence, but I don't believe they're `constructs'. If forty-two trees fall in a forest and no one is around to count them, __forty-two__ trees have still fallen.

marmosets, Bryan

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