Combining Texts

All the ideas for 'Later Letters to Dedekind', 'What Price Bivalence?' and 'Letter on Freedom'

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4 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason

5042	For every event it is possible for an omniscient being to give a reason for its occurrence [Leibniz]
	Full Idea: Nothing ever takes place without its being possible for one who knew everything to give some reason why it should have happened rather than not.
	From: Gottfried Leibniz (Letter on Freedom [1689], p.112)
	A reaction: Presumably there will be GOOD reason why genocide occurs. Note that there is a reason for every 'event'. Is there a reason for every truth? Presumably not, or there would have to be reasons for self-evident truths.

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

17831	Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake]
	Full Idea: Cantor gives informal versions of the axioms of ZF as ways of getting from one set to another.
	From: report of George Cantor (Later Letters to Dedekind [1899]) by John Lake - Approaches to Set Theory 1.6
	A reaction: Lake suggests that it should therefore be called CZF.

5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence

19043	Bivalence applies not just to sentences, but that general terms are true or false of each object [Quine]
	Full Idea: It is in the spirit of bivalence not just to treat each closed sentence as true or false; as Frege stressed, each general term must be definitely true or false of each object, specificiable or not.
	From: Willard Quine (What Price Bivalence? [1981], p.36)
	A reaction: But note that this is only the 'spirit' of the thing. If you had (as I do) doubts about whether predicates actually refer to genuine 'properties', you may want to stick to the whole sentence view, and not be so fine-grained.

7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic

19042	Terms learned by ostension tend to be vague, because that must be quick and unrefined [Quine]
	Full Idea: A term is apt to be vague if it is to be learned by ostension, since its applicability must admit of being judged on the spot and so cannot hinge of fine distinctions laboriously drawn.
	From: Willard Quine (What Price Bivalence? [1981], p.32)
	A reaction: [Quine cites C. Wright for this] Presumably precision can steadily increased by repeated ostension. After the first 'dog' it's pretty vague; after hundreds of them we are pretty clear about it. Long observation of borderline 'clouds' could do the same.