Combining Texts

Ideas for 'Parmenides', 'Introduction to the Theory of Logic' and 'Set Theory'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

---

2 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction

10891	If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
	Full Idea: Defining a set by induction enables us to use the method of proof by induction to establish that all the elements of the set have a certain property.
	From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.3)

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

16150	One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
	Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it.
	From: Plato (Parmenides [c.364 BCE], 144a)
	A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed.