Not at all. We can reason about infinity without actually doing anything an infinite number of times. If someone (God, perhaps) were to add up Banno's infinitely many fractions or carry out my multiplication to infinitely many decimal places, then the result would be 1 in either case. — aletheist
The problem is, that this feat of adding infinitely many fractions would never be finished, so 1 would never be reached. Therefore it is false to say that it equals one. — Metaphysician Undercover
Mathematics is entirely a matter of necessary reasoning about hypothetical states of affairs. There is no falsity whatsoever in saying that if someone were to add infinitely many fractions in a particular series, then the result would be 1. The fact that no one can actually add infinitely many fractions is completely irrelevant. — aletheist
I already know you can do whatever you want with maths, just make it up as you go, and prove whatever you want to prove. — Metaphysician Undercover
Anyway, either both distance and duration are discrete, or both are not. Modeling both with the continuum works, and has the bonus of numbers like π and e. — jorndoe
↪Metaphysician Undercover
No; because history shows you cannot understand mathematics.
https://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_⋯ — Banno
It is really no different from philosophy in this regard; it all boils down to one's assumptions. To get us back on topic, Zeno's alleged paradox exploits this by smuggling in the idea that any finite interval of space consists of infinitely many individual points, such that one must somehow pass through them all in order to get from one place to another. Once we dispense with that misconception and recognize that space is continuous, and the only actual points are the ones that we arbitrarily define, the paradox dissolves. — aletheist
You are confusing actual possibility with logical possibility. Mathematics deals with the latter, not the former. It is indeed actually impossible to add infinitely many fractions, but it is not logically impossible. — aletheist
Logic cannot be wrong; but it can be inappropriate. Given a paradox, one ought look for a better grammar, a new logic; rejecting logic as "wrong" shows a profound misunderstanding. Logic is mere grammatical structure. — Banno
The issue is the assumption that space is infinitely divisible. Zeno assumes that in theory, space is infinitely divisible. However, in practise space is not infinitely divisible. — Metaphysician Undercover
Your premise states "if someone does a thing which is actually impossible to do...". So I judge it as an impossibility and therefore a falsity. And so I judge your conclusion as a falsity as well. — Metaphysician Undercover
For practical purposes we say it "equals" 1, but it actually only approaches 1, as it's clear 1 is the boundary, but to say it "equals' 1 the same as 2+2 "equals" 4 is equivocation. So, I don't buy into your mathematical solution even if math could dictate metaphysics.Can you see that the series ½ + ¼ + ⅛... is infinity long, and yet adds to 1? — Banno
meaning any movement whatsover is impossible — Hanover
So after one gets half way, one continues on to the end. — Banno
You dropped the italicised bit in.
One can count the rational numbers without putting them in sequence.
Just list the fractions between one and two; 3/2, 4/3, 5/3, 5/4, 7/4... — Banno
Although there are infinitely many potential locations between two defined locations A and B, there is no need to account for all of those intermediate points in actually moving from point A to point B, because they are not actual points. — aletheist
The only reason we cannot do it is because we could never count infinitely fast which is what we would need to be able to do to complete the series. — John
It was explicitly mentioned several times, and implied any time it wasn't, that the counting is sequential, given that it's an analogy to the movement between two points, which would involve an object passing sequentially through each rationally-numbered coordinate between them. — Michael
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