Infinity and Grandmotherhood

שו”ת › Category: philosophy › Infinity and Grandmotherhood

asked 1 year ago

Hi Miki, good week, my name is Assaf, I’m 19 years old, and I have two questions.
1) How can infinity exist? Because if we had an infinite line and divided it once into 5 cm segments and once into 30 cm segments (for the sake of the example), we would have the same number of segments. So we have a problem with logic here. But in mathematics we do have infinity, as in pi, which is an infinite ratio.
2) I once heard you say that there are two types of reasons, one where the reason is a sufficient condition and the other where it is a necessary condition. Can you explain to me what that means? I didn’t quite understand, sorry.
Thank you very much 🙂

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מיכי Staff answered 1 month ago

Have a good week, Asaf. 1. Indeed, in both cases there was the same number of segments. So what? Why do you think this is a logical contradiction? The claim that it is the same number of segments means that there is a one-to-one correspondence between these two sets of segments (this is how equality between infinite numbers is defined). You should read about Hilbert’s hotel on Wikipedia. 2. I said no such thing. There is a debate among philosophers whether a cause should be a necessary and sufficient condition or just a sufficient condition. Don’t you know what a necessary condition is and what a sufficient condition is?

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אסף replied 1 year ago

Regarding 1. The problem I “think” have here is that in every segment of 30 we have 6 of 5, so that's why it's a bit uncomfortable for me logically (I don't know how to explain what the contradiction is here, it's a bit intuitive). I'll read about Hilbert's hotel, thanks. ( :