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Mark44

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We don't discuss philosophy at PF, so I'm closing this thread.I am an avid student of philosophy, not mathematics.

I don't think so. What Zeno's Paradox shows is a lack of understanding about how an infinite sum can add up to a finite number.thinkandmull said:I was more interested in these topics for there philosophical implications. It seems to me that Zeno showed the uncountable infinity of space long before Cantor, and that that infinity alone leads directly to Banach-Tarski.

If you really want to understand mathematics, you would be better off reading articles newer than 1696, written by mathematicians.thinkandmull said:I don't know why one's a paradox but not the other. Pierre Bayle (his 1696 article on Zeno), Kant, Hegel and others thought these arguments show that reality is contradictory in the sense that Escher's "Ascending, Descending" picture is.

I don't think this keeps them up at night.thinkandmull said:Mathematicians don't always understand the shock waves they send through the field of philosophy.

thinkandmull said:The Zenonian box: half of it stacked progressively on top of the other half, one fraction at a time, first blue then green, then blue again ect.

Since there can be no last box in an infinite sequence of ever smaller boxes, one can conclude only that traditional philosophy is not true, using the principles of logical arguments. That is, ##p \Rightarrow q## is equivalent to ##\neg q \Rightarrow \neg p##.thinkandmull said:When the box is whole again, will the top be blue or green?

If traditional philosophy is true, there must be one color left on top. Period.

thinkandmull said:But this is definitely a discussion for a different forum. Thanks

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