Combining Philosophers

All the ideas for Anaxarchus, Cian Dorr and Hermann Weyl

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6 ideas

2. Reason / D. Definition / 1. Definitions

15927	Definition just needs negation, known variables, conjunction, disjunction, substitution and quantification [Weyl, by Lavine]
	Full Idea: For mathematics, Weyl arrived (by 1917) at a satisfactory list of definition principles: negation, identification of variables, conjunction, disjunction, substitution of constants, and existential quantification over the domain.
	From: report of Hermann Weyl (works [1917]) by Shaughan Lavine - Understanding the Infinite V.3
	A reaction: Lavine summarises this as 'first-order logic with parameters'.

8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta

14596	Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr]
	Full Idea: Just as there are no numbers or properties, there are no relations (like 'being heavier than' or 'betweenness'), or sets. I will provisionally use 'nominalism' for the conjunction of these four claims.
	From: Cian Dorr (There Are No Abstract Objects [2008], 1)
	A reaction: If you are going to be a nominalist, do it properly! My starting point in metaphysics is strong sympathy with this view. Right now [Tues 22nd Nov 2011, 10:57 am GMT] I think it is correct.

8. Modes of Existence / E. Nominalism / 5. Class Nominalism

14597	Natural Class Nominalism says there are primitive classes of things resembling in one respect [Dorr]
	Full Idea: Natural Class Nominalists take as primitive the notion of a 'natural' class - a class of things that all resemble one another in some one respect and resemble nothing else in that respect.
	From: Cian Dorr (There Are No Abstract Objects [2008], 4)
	A reaction: Dorr rejects this view because he doesn't believe in 'classes'. How committed to classes do you have to be before you are permitted to talk about them? All vocabulary (such as 'resemble') seems metaphysically tainted in this area.

10. Modality / A. Necessity / 11. Denial of Necessity

14598	Abstracta imply non-logical brute necessities, so only nominalists can deny such things [Dorr]
	Full Idea: If there are abstract objects, there are necessary truths about these things that cannot be reduced to truths of logic. So only the nominalist, who denies that there are any such things, can adequately respect the idea that there are no brute necessities.
	From: Cian Dorr (There Are No Abstract Objects [2008], 4)
	A reaction: This is where two plates of my personal philosophy grind horribly against one another. I love nominalism, and I love natural necessities. They meet like a ring-species in evolution. I'll just call it a 'paradox', and move on (swiftly).

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

26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism

10246	The limit of science is isomorphism of theories, with essences a matter of indifference [Weyl]
	Full Idea: A science can determine its domain of investigation up to an isomorphic mapping. It remains quite indifferent as to the 'essence' of its objects. The idea of isomorphism demarcates the self-evident boundary of cognition.
	From: Hermann Weyl (Phil of Mathematics and Natural Science [1949], 25-7), quoted by Stewart Shapiro - Philosophy of Mathematics
	A reaction: Shapiro quotes this in support of his structuralism, but it is a striking expression of the idea that if there are such things as essences, they are beyond science. I take Weyl to be wrong. Best explanation reaches out beyond models to essences.