Comment by drdeca
3 days ago
Yes, the answer to the question does assume that 5 exists.
You try answering the question without speaking of 5 or 10.
That is my argument.
3 days ago
Yes, the answer to the question does assume that 5 exists.
You try answering the question without speaking of 5 or 10.
That is my argument.
Numbers are definitely essential concepts for some kinds of reasoning. If that's what you're saying then fine.
The thing is assuming that 5 exists to conclude that 5 exists is obviously circular.
With numbers, I can give an explanation for the phenomenon I described above. If such reasoning cannot be done without reference to numbers, then, if such reasoning is correct, numbers must exist. If there is no other reasoning can be given that provides a good explanation, and as the explanation I gave for the phenomenon is compelling, then I think that a good reason to conclude that the reasoning is correct, and that therefore those particular numbers exist.
In particular, I would expect that if numbers don’t exist, the explanation I gave of the phenomenon I described, couldn’t be correct.
You could say they exist as concepts, that are necessary to use for some reasoning processes, without having any kind of independent existence.
It's similar for the case of programs or algorithms. We can say that a sorting algorithm exists, or a chess-playing program or whatever, which means we know how to implement the logical process in some physical system, but it doesn't mean that they have some kind of existence which is independent of the physical systems. It's just a way of talking about patterns that can be common to many physical systems
1 reply →