Combining Texts

All the ideas for 'The Varieties of Necessity', 'Reply to Foucher' and 'works'

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6 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

9565	Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara]
	Full Idea: The terms 'set' and 'is a member of' are primitives of Zermelo's 1908 axiomatization of set theory. They are not given model-theoretic analyses or definitions.
	From: report of Ernst Zermelo (works [1920]) by Charles Chihara - A Structural Account of Mathematics 7.5
	A reaction: This looks like good practice if you want to work with sets, but not so hot if you are interested in metaphysics.

3339	For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn]
	Full Idea: For Zermelo's set theory the empty set is zero and the successor of each number is its unit set.
	From: report of Ernst Zermelo (works [1920]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite

19406	I strongly believe in the actual infinite, which indicates the perfections of its author [Leibniz]
	Full Idea: I am so much for the actual infinite that instead of admitting that nature abhors it, as is commonly said, I hold that it affects nature everywhere in order to indicate the perfections of its author.
	From: Gottfried Leibniz (Reply to Foucher [1693], p.99)
	A reaction: I would have thought that, for Leibniz, while infinities indicate the perfections of their author, that is not the reason why they exist. God wasn't, presumably, showing off. Leibniz does not think we can actually know these infinities.

10. Modality / C. Sources of Modality / 1. Sources of Necessity

9216	Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K]
	Full Idea: The three sources of necessity - the identity of things, the natural order, and the normative order - have their own peculiar forms of necessity. The three main areas of human enquiry - metaphysics, science and ethics - each has its own necessity.
	From: Kit Fine (The Varieties of Necessity [2002], 6)
	A reaction: I would treat necessity in ethics with caution, if it is not reducible to natural or metaphysical necessity. Fine's proposal is interesting, but I did not find it convincing, especially in its view that metaphysical necessity doesn't intrude into nature.

13. Knowledge Criteria / C. External Justification / 7. Testimony

9214	Unsupported testimony may still be believable [Fine,K]
	Full Idea: I may have good reason to believe some testimony, for example, even though the person providing the testimony has no good reason for saying what he does.
	From: Kit Fine (The Varieties of Necessity [2002], 5)
	A reaction: Thus small children, madmen and dreamers may occasionally get things right without realising it. I take testimony to be merely one more batch of evidence which has to be assessed in building the most coherent picture possible.

26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism

9215	Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K]
	Full Idea: It would be harder to break P-and-Q implying P than the connection between cause and effect. This difference in strictness means it is more plausible that natural necessities include metaphysical necessities, than vice versa.
	From: Kit Fine (The Varieties of Necessity [2002], 6)
	A reaction: I cannot see any a priori grounds for the claim that causation is more easily disrupted than logic. It seems to be based on the strategy of inferring possibilities from what can be imagined, which seems to me to lead to wild misunderstandings.