Q&A: Infinity and Causality
Infinity and Causality
Question
Hi Michi, have a good week. My name is Asaf, I’m 19, and I have two questions.
1) How can infinity exist? Because if we had an infinite line and divided it once into segments of 5 cm and another time into segments of 30 cm (for the sake of the example), we would have the same number of segments. So there seems to be a problem here in logic. But in mathematics we do have infinity, like with pi, which is an infinite ratio.
2) I once heard you say that there are two kinds of causes: one where the cause is a sufficient condition and the other where it is a necessary condition. Can you explain what that means? I didn’t really understand, sorry.
Thank you very much 🙂
Answer
Have a good week, Asaf.
1. Indeed, in both cases there would be the same number of segments. So what? Why do you think that 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 those two sets of segments (that is how equality between infinite numbers is defined). You should read on Wikipedia about Hilbert’s Hotel.
2. I didn’t say such a thing. There is a debate among philosophers whether a cause has to be a necessary and sufficient condition or only a sufficient condition. Don’t you know what a necessary condition and a sufficient condition are?
Regarding 1: the problem I “think” is here is that in every 30-length segment we have 6 of the 5-length ones, so logically it feels a bit uncomfortable to me. I don’t know how to explain what the contradiction is here; it’s kind of intuitive. I’ll read about Hilbert’s Hotel, thanks. 🙁