Talk:Pre-intuitionism

Philosophy: Logic / Analytic / Contemporary Mid‑importance

This article is within the scope of WikiProject Philosophy, a collaborative effort to improve the coverage of content related to philosophy on Wikipedia. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the general discussion about philosophy content on Wikipedia.PhilosophyWikipedia:WikiProject PhilosophyTemplate:WikiProject PhilosophyPhilosophy articles

Mid

This article has been rated as Mid-importance on the project's importance scale.

Associated task forces:
/
	Logic
	Analytic philosophy
	Contemporary philosophy

Mathematics Stub‑class

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Stub	This article has been given a rating which conflicts with the project-independent quality rating in the banner shell. Please resolve this conflict if possible.
???	This article has not yet received a rating on the project's priority scale.

Induction[edit]

We know that topics like finite field arithmetic do not require induction. We feel (intuitively?) that topics like analysis are consistent with induction. Are there any examples of mathematical/logical systems which are "infinite" in some sense, but for which induction does not work? That is, has anyone created a (more-or-less consistent) system in which induction was intentionally broken, on purpose, but the system still somehow acheives a notion of infinity? Should I be asking this question on the Peano's axioms talk page instead? linas 05:40, 7 September 2005 (UTC)[reply]