That means that, for example, the number 4 has no essence to speak of. All we can say about 4 is that certain sentences are true about it such as 1+3=4 or 17-13=4 or the square root of 16 is 4. We can go on all day I]listing relations between 4 and other numbers and none of these relations expresses the essence of 4-ness
any better than any other…
You are
begging the question: I asked you what justification you had for thinking there are no essences but just relations all the way down, and your reply is, “the number 4 has no essence to speak of because…none of these relations expresses the essence of 4-ness.” Well duh! Because relations are not essences! You’ve offered no argument yet. But I will repeat my own, deductively demonstrating there **do exist **intrinsic properties of numbers, and if you disagree, you need to tell me where my argument is wrong. It starts by **assuming your position
and performing a reductio leading to ** an absurdity:
(1) Suppose the numbers 4 and 5 have no intrinsic properties that distinguish one from the other.
(2) If they have no intrinsic properties distinguishing one from the other, then the terms flanking each side of the “>” relation can be switched in the formula X > Y, while preserving the truth-value of the original relation because, after all, there is nothing distinct or particularly unique about them as numbers.
(3) If switching the terms flanking both sides of the “>” relation preserves the statement’s truth-value, then 4>5 can be just as equally true as 5>4.
(4) But 4>5 is false.
(5) Therefore, switching the terms flanking both sides of the “>” relation does NOT preserve the statement’s truth-value.
(6) Therefore, there is **something ** perculiar about the numbers 4 and 5 which
prevents us from introducing them into
any such relation as we please.
(7) Therefore, the numbers 4 and 5 do have intrinsic properties that distinguish one from the other.
If the numbers 4 and 5 do not each posses some intrinsic property that distinguished them, then we *would *be able to switch the terms on each side of the “>” sign and preserve the original statement’s truth-value. But it is not permissible to do this. So they are different numbers each with a different intrinsic property. The numbers 4 and 5 would not maintain this consistency in their various relations with other numbers if they did not have some peculiar property about them that
prevented us from doing anything we wanted with them.
How about
being divisible by two? Is this not a property of all even numbers? What about being
prime, or
being a multiple of 5, or
being a product of two odd numbers? The list goes on and on in mathematics and arithematic…
It seems that you would like to think of 4-ness as having existed somewhere “out there” waiting for humans to evolve and start using it and that the Laws of Physics always existed in some way waiting for humans to come along and discover them and that the Moral Law was out there somewhere as well waiting for humans to come along and conform to it. I guess that all could make sense to someone who believes that these ideas could have always existed in the mind of God, but it doesn’t work for me.
So these things don’t exist “out there”? Where then? Do they exist at all? Now your pragmatism is really coming out. Are Moral Laws and the Laws of Physics human inventions? So gravity doesn’t exist independent of my conceptions? Try jumping off a cliff, you’ll quickly find the concept is not an invention. Why would you think this? These absurdities are just bafflling to me.
