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Unread January 20th, 2006, 07:43 PM
alexandra_k alexandra_k is offline
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Join Date: Jan 2006
Posts: 106
Default Re: Intelligent Design and Why Not

> But here’s the rub: While 1 = 1 is timelessly and objectively true, “1 thing = 1 thing,” in our physical world, probably isn’t since “things” never seem to be truly identical in our physical world.

Ah. At any one moment in time a thing is identical to itself. I think this is one of Leibniz laws (which Wittgenstein went on to mock because it does sound rather trivial indeed). So where you have the same thing on different sides of the = sign then the second equation would be true. Sometimes identity claims are not trivial so for example it was a significant discovery that the morning star = the evening star; that water = H2O (roughly); that superman = clarke kent (though this is disputed a little in the philosophical literature); and the identity theory of the mind-body relation holds that pain = brain state x (where x is to be determined by science).

Philosophy of math (or physics or logic for that matter) isn't really my area... But I guess I think of numbers as sets. There was work (Frege, Russell etc) on trying to reduce mathematics to logic (via set theory I think) and so the meaning of '1' might be a set with one member in it. Apparantly... Their program failed, but anyway... If '1' is a set with one member in it then the identity of the member is irrelevant. Like how if 'money' is defined by its function in social life then it can be multiply realisable on the physical level (could be coins, or paper, or cowrie shells). All that is relevant to numbers is... How many. There could be a set with one coin in it, another set with one piece of paper in it, another set with one cowrie shell in it and they are identical in the relevant respect in the sense that each set has just one member. Maybe we need to introduce a number line to deal with negative numbers... I don't really know...

> Nevertheless, “1 = 1” is a timeless and objective truth that we all seem to have access to, and that existed b/f there were evolved creatures with subjective mental constructs and definitions.

Yes. At any one moment in time... A thing is identical to itself.

> Should anyone unable or unwilling to acknowledge the reality and objective truth of 1 = 1 ever be taken very seriously? I’d say no, but maybe that’s just me.

1=1 is true by definition. If there were a race of alien beings who had a radically different logic or mathematics to us... Then we could not comprehend them. Logic and mathematics are considered to be the two a-priori disciplines. That is to say that (in theory) you don't need to look to the world at all. Once you have grasped the relevant concepts (the meanings of '1' '=' etc then... The rest of it deductively follows.

On a bit of a tangent philosophers often talk about possible worlds.
1) It is possible that I never posted to this board (for instance).
That seems to be true. Why is it true?
2) Because it is true that there is a possible world in which I never posted to this board.
But that entails
3) There is a possible world (that is not the actual world)
And that entails
4) There are possible worlds!
I do believe... David Lewis argues for the reality of possible worlds (or alternative universes causally isolated from our own, if you like) in this vein. He considers that it is too counter-intuitive to common sense to deny the truth of 2 and from there...

Am I giving philosophy a bad name yet?

;-)
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