1. ## Contentual number theory

Hello,

Can anyone please explain me the following lines:

According to Hilbert, there is a privileged part of mathematics, contentual elementary number theory, which relies only on a “purely intuitive basis of concrete signs.”

Whereas the operating with abstract concepts was considered “inadequate and uncertain,” there is a realm of extra-logical discrete objects, which exist intuitively as immediate experience before all thought. If logical inference is to be certain, then these objects must be capable of being completely surveyed in all their parts, and their presentation, their difference, their succession (like the objects themselves) must exist for us immediately, intuitively, as something which cannot be reduced to something else."

What is contentual number theory?

2. ## Re: Contentual number theory

Originally Posted by shounakbhatta
Hello,

Can anyone please explain me the following lines:

According to Hilbert, there is a privileged part of mathematics, contentual elementary number theory, which relies only on a “purely intuitive basis of concrete signs.”

Whereas the operating with abstract concepts was considered “inadequate and uncertain,” there is a realm of extra-logical discrete objects, which exist intuitively as immediate experience before all thought. If logical inference is to be certain, then these objects must be capable of being completely surveyed in all their parts, and their presentation, their difference, their succession (like the objects themselves) must exist for us immediately, intuitively, as something which cannot be reduced to something else."

What is contentual number theory?
I suggest you either obtain an appropriate textbook or use Google (I assume you are quoting from here: http://www.tau.ac.il/~corry/teaching...lbert-Zach.pdf)

3. ## Re: Contentual number theory

Originally Posted by mr fantastic
I suggest you either obtain an appropriate textbook or use Google (I assume you are quoting from here: http://www.tau.ac.il/~corry/teaching/philosophy/download/Hilbert-Zach.pdf)
From: Hilbert's Program (Stanford Encyclopedia of Philosophy)