Strict Finitism and Transhumanism
- December 16, 2014 at 10:14 pm #25814PeterMember
Whatever position you take on finitism, this obscure area of the philosophy of mathematics is well worth understanding.
[See the full post at: Strict Finitism and Transhumanism]December 18, 2014 at 10:46 am #25852Eray OzkuralParticipant
A most erudite piece, thank you.December 24, 2014 at 12:55 am #25902MarcosParticipant
Yes. Infinity is merely a breakdown of your current axiomatic framework. A singularity, in the original meaning of the term of course. (gotta qualify that among these ‘circles’ =P)
This is not to say they are not useful, in fact the opposite is true (for monkeys at least, yes). When the quantities converge, as a particularly philosophical instantiation of your mathematics of limits example, take Zeno’s “paradox” — Achilles distance to the tortoise will converge to zero at a specific point in time — you get a valid answer back, even on your current, limited (you had to appeal to infinity, haven’t you?), conceptual context. However, if they diverge, they cannot exist, being then true paradoxes.
For an opposite example, that of a breakdown, develop the area of a circle by integration. I’d first suggest you change your framework, in this case your coordinate system, from Cartesian to circular / polar, otherwise the breakdown is too obvious (you’ll get the wrong answer, as far as I know, however finite). Yet, even then you’ll naturally be giving rise to Pi, an “infinity” for sure. (there are ways to prove these things without actually enumerating them, you know =) assume you can write Pi as A / B then reach a contradiction)
One would have to “move into the world of Pi” (just down the road to the “world” of Platonic Forms, LoL) for true circles and spheres to actually exist. But, as you very well stated, only approximations of this are possible. I chose the term “true” because, as philosophers we both know, “perfect” entities MUST exist. At least in the Cartesian “world”. 😉
PS.: “not that amazing monkey minds. Perhaps there is hope for us yet.”
yes, from time to time, a handful of monkeys show promise =)
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