Combining Texts

Ideas for 'works', 'works' and 'De Corpore (Elements, First Section)'

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

display all the ideas for this combination of texts

4 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17258 If we just say one, one, one, one, we don't know where we have got to [Hobbes]
     Full Idea: By saying one, one, one, one, and so forward, we know not what number we are at beyond two or three.
     From: Thomas Hobbes (De Corpore (Elements, First Section) [1655], 2.12.05)
     A reaction: This makes ordinals sound like meta-numbers.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
3331 If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA on Frege]
     Full Idea: There is a suspicion that Frege's definition of 5 (as the set of all sets with 5 members) may be infected with circularity, …and how can we be sure on a priori grounds that 4 and 5 are not both empty sets, and hence identical?
     From: comment on Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.14
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
16880 Frege aimed to discover the logical foundations which justify arithmetical judgements [Frege, by Burge]
     Full Idea: Frege saw arithmetical judgements as resting on a foundation of logical principles, and the discovery of this foundation as a discovery of the nature and structure of the justification of arithmetical truths and judgments.
     From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations Intro
     A reaction: Burge's point is that the logic justifies the arithmetic, as well as underpinning it.
8689 Eventually Frege tried to found arithmetic in geometry instead of in logic [Frege, by Friend]
     Full Idea: After the problem with Russell's paradox, Frege did not publish for fourteen years, and he then tried to re-found arithmetic in Euclidean geometry, rather than in logic.
     From: report of Gottlob Frege (works [1890], 3.4) by Michèle Friend - Introducing the Philosophy of Mathematics 3.4
     A reaction: I take it that his new road would have led him to modern Structuralism, so I think he was probably on the right lines. Unfortunately Frege had already done enough for one good lifetime.