Combining Philosophers

All the ideas for Anaxarchus, Nuel D. Belnap and Nicholas Bourbaki

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4 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10190 From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]
     Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures.
     From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79
     A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s.
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
     Full Idea: Anaxarchus said that he was not even sure that he knew nothing.
     From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1
14. Science / C. Induction / 5. Paradoxes of Induction / b. Raven paradox
19000 Read 'all ravens are black' as about ravens, not as about an implication [Belnap]
     Full Idea: 'All ravens are black' might profitably be read as saying not that being a raven 'implies' being black, but rather something more like 'Consider the ravens: each one is black'.
     From: Nuel D. Belnap (Conditional Assertion and Restricted Quantification [1970], p.7), quoted by Stephen Yablo - Aboutness 04.5
     A reaction: Belnap is more interested in the logic than in the paradox of confirmation, since he evidently thinks that universal generalisations should not be read as implications. I like Belnap's suggestion.
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
17897 Analytic explanation is wholes in terms of parts; synthetic is parts in terms of wholes or contexts [Belnap]
     Full Idea: Throughout the whole texture of philosophy we distinguish two modes of explanation: the analytic mode, which tends to explain wholes in terms of parts, and the synthetic mode, which explains parts in terms of the wholes or contexts in which they occur.
     From: Nuel D. Belnap (Tonk, Plonk and Plink [1962], p.132)
     A reaction: The analytic would be bottom-up, and the synthetic would be top-down. I'm inclined to combine them, and say explanation begins with a model, which can then be sliced in either direction, though the bottom looks more interesting.