Aristotle, Physics 209a
“In addition to this, if something is one of those things that exists, where can it exist? For Zeno’s dilemma asks this kind of question: if everything which is exists in a place, then it is clear that the place is part of a place too and this problem persists endlessly.
Wait, there’s more: if every body is in a place, then the body is also in the entire place. How, then, are were to talk about things that increase and grow? For, based on what we have said, it would be necessary for the place to expand as well so that the space may be neither smaller nor greater than the thing which occupies it.
Because of these arguments we are necessarily in a state of confusion not only about what [a place] is but whether it even exists.”
Ἔτι δὲ καὶ αὐτὸς εἰ ἔστι τι τῶν ὄντων, ποῦ ἔσται; ἡ γὰρ Ζήνωνος ἀπορία ζητεῖ τινα λόγον· εἰ γὰρ πᾶν τὸ ὂν ἐν τόπῳ, δῆλον ὅτι καὶ τοῦ τόπου τόπος ἔσται, καὶ τοῦτο εἰς ἄπειρον πρόεισιν.
Ἔτι ὥσπερ ἅπαν σῶμα ἐν τόπῳ, οὕτω καὶ ἐν τόπῳ ἅπαντι σῶμα· πῶς οὖν ἐροῦμεν περὶ τῶν αὐξανομένων; ἀνάγκη γὰρ ἐκ τούτων συναύξεσθαι τὸν τόπον αὐτοῖς, εἰ μήτ᾿ ἐλάττων μήτε μείζων ὁ τόπος ἑκάστου.
Διὰ μὲν οὖν τούτων οὐ μόνον τί ἐστιν, ἀλλὰ καὶ εἰ ἔστιν, ἀπορεῖν ἀναγκαῖον
[The paradox/dilemma thing is a bit of a misdirection: Zeno actually had multiple paradoxes]. This is funny:
Also, it has been a few months, but I find myself laughing about this every few days:
3 thoughts on “You’ve Heard of Zeno’s Paradox, But What about his Dilemma?”
That’s not one of Zeno’s better paradoxes, my dude. I certainly would not insult my students by lecturing on it in my Paradoxes class, where Achilles and the Racetrack get top billing. 😉
Certainly. it is strange and a little flat….
The normal trick is to assert that a finite distance can be sliced into infinitely many slices. But the time corresponding to these slices must be infinite, rather than infinite slices of a finite time.