Comment by griffzhowl
3 days ago
You've already assumed 5 exists in order to assert that it's prime.
In any case existence of mathematical objects is a different meaning of existence to physical objects. We can say a mathematical object exists just by defining it, as long as it doesn't lead to contradiction.
I think your closing paragraph holds the key. 5 doesn't really exist, it's a constructor that parameterizes over something that does exist, eg. you never have "5", you have "5(something)". Saying 5 is prime is then saying that "for all x, 5(x) has the same structural properties as all other primes".
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.
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