On 5/7/2020 9:30 AM, Bruno Marchal wrote:
I can imagine a materialist psychologist claiming that the natural numbers are not primitive but explainable by a cultural anthropo-evolutionary genetic, say. But 1) he is confusing the human natural number theories with arithmetic, and 2) he is cheating, as his explanation will make only sense by an implicit acceptance of some universal machinery equivalent to the belief in RA, so, he is just confusing level of explanation.
It's not confusion when you explain something in terms of what you understand. Confusion is to say things must be explained in terms of something infinite and incomprhensible...and then claim it's incomprehensibility proves it's primitive because is can't have an explanation.
Brent
Yes, the human number theory is a fascinating subject, and it sustains the idea that 2+2=4 is “really absolutely” true, as all humans agree on this, and even many other mammals, actually. But that is a different subject matter than the one number theory is build for. This one avoid the philosophy of numbers by using the axiomatic method. It should be obvious that with mechanism, the discovery of the numbers by the numbers is part of the meta-arithmetic that Gödel’s showed embeddable in arithmetic. The real bomb is still Gödel’s 1931, even if it is the two theorems of Solovay which sums it all in G, and G*.
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