Our common notion of causality requires the passage of time. What does it mean for something to "begin" to exist, or "have a cause" outside of time? — darthbarracuda
That seems unintelligible, for how can a first cause be simultaneously a final cause? — Brian A
Fishfry and, I expect most of the others that have responded to your thread, is/are perfectly familiar with Hilbert's Hotel, and why it is not an argument for any statement other than 'aren't infinities interesting?' Ditto for Aristotle's notions of potential and actual infinities.To understand why this is you should google up and read the mathematician David Hibert's famous thought experiment , "Hibert's Hotel". — John Gould
Fishfry and, I expect most of the others that have responded to your thread, is/are perfectly familiar with Hilbert's Hotel, and why it is not an argument for any statement other than 'aren't infinities interesting?' Ditto for Aristotle's notions of potential and actual infinities. — andrewk
What you are presuming is that actual infinities really exist. Actual infinity, however is merely an abstract notion , or, if you like, a fiction in the realm of the philosophy of mathematics which proposes that mathematical objects like , say the infinite sequence of negative numbers you refer to above can form a complete totality or "set", I.e. a given object that is a true actual infinity. Actual infinities, though, do not exist, they are not realities. To understand why this is you should google up and read the mathematician David Hibert's famous thought experiment , "Hibert's Hotel". — John Gould
Potential infinity Actual infinity Axiom of induction Axiom of Infinity Peano Cantor 0, 1, 2, 3, ... {0, 1, 2, 3, ...} n+1 given n All of them at once Negative integers Hilbert Hotel
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