Combining Texts

Ideas for 'Science and Method', 'Grounding Concepts' and 'The Justification of Deduction'

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

display all the ideas for this combination of texts

---

2 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

10245	One geometry cannot be more true than another [Poincaré]
	Full Idea: One geometry cannot be more true than another; it can only be more convenient.
	From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics
	A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

17730	Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
	Full Idea: We might arrive to the concept of infinity by composing concepts of negation and finiteness.
	From: Carrie Jenkins (Grounding Concepts [2008], 5.3)
	A reaction: Presumably lots of concepts can be arrived at by negating prior concepts (such as not-wet, not-tall, not-loud, not-straight). So not-infinite is perfectly plausible, and is a far better account than some a priori intuition of pure infinity. Love it.