P.Tsunami said:
almostnot said:
A.Because it is apriori knowledge in the words of Descartes. Numbers are simply arbitrary and in doing so define each other. So 2+2=4 because we agree it does.
As much as I hate to interrupt this lovely game, this is actually wrong. Descartes never used the term apriori, so I'm sure you're thinking of Immanuel Kant. Personally, I favor Descartes metaphysics. Essentially, half-way through his metaphysical theory (at the point where he formulates the famous "Cogito Ergo Sum"), Descartes would argue that 2+2 does not equal 4. Or, at least, that we can't know that for sure. Of course, he pussied out and brought in the proof of God after that. I was down with Descartes while he was hardcore.
I disagree; Descartes' entire argument for the existence of God is based upon his concept that there are things we are born knowing (a priori knowledge) such as mathmatical truths and, as you rightly called, his pussying out on the subject of God, the existence of an all powerful creator. Whilst Kant also use these terms, Descartes used them way before him as part of his ontological/a priori arguments:
"Descartes often compares the ontological argument to a geometric demonstration, arguing that necessary existence cannot be excluded from idea of God anymore than the fact that its angles equal two right angles, for example, can be excluded from the idea of a triangle. The analogy underscores once again the argument's supreme simplicity. God's existence is purported to be as obvious and self-evident as the most basic mathematical truth. It also attempts to show how the "logic" of the demonstration is rooted in our ordinary reasoning practices."
http://plato.stanford.edu/entries/descartes-ontological/
And yes, I too think the very early work of Descartes is legendary, before that messy God business...
Edit: And in fairness, Plato beat them both to the concept by a very long way...