Combining Texts

All the ideas for 'Letters to Edward Stillingfleet', 'Universal Arithmetick' and 'Semantics for Propositional Attitudes'

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5 ideas

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic

17783	A number is not a multitude, but a unified ratio between quantities [Newton]
	Full Idea: By a Number we understand not so much a Multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same Kind, which we take for unity.
	From: Isaac Newton (Universal Arithmetick [1669]), quoted by John Mayberry - What Required for Foundation for Maths? p.407-2
	A reaction: This needs a metaphysics of 'kinds' (since lines can't have ratios with solids). Presumably Newton wants the real numbers to be more basic than the natural numbers. This is the transition from Greek to modern.

7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment

15785	Our commitments are to an 'ontology', but also to an 'ideology', or conceptual system [Hintikka]
	Full Idea: We must distinguish between what we are committed to existing in the actual world or a possible world ('ontology'), and what we are committed to as a part of our ways of dealing with the world conceptually, as a part of our conceptual system ('ideology').
	From: Jaakko Hintikka (Semantics for Propositional Attitudes [1969], p.95), quoted by William Lycan - The Trouble with Possible Worlds 02
	A reaction: I think this is the most illuminating idea I have read on the subject of ontological commitment. I'm fighting for the idea that what we think is true should be kept separate from what we think exists. Ideology is a nice addition to the mix.

9. Objects / D. Essence of Objects / 3. Individual Essences

15990	Every individual thing which exists has an essence, which is its internal constitution [Locke]
	Full Idea: I take essences to be in everything that internal constitution or frame for the modification of substance, which God in his wisdom gives to every particular creature, when he gives it a being; and such essences I grant there are in all things that exist.
	From: John Locke (Letters to Edward Stillingfleet [1695], Letter 1), quoted by Simon Blackburn - Quasi-Realism no Fictionalism
	A reaction: This is the clearest statement I have found of Locke's commitment to essences, for all his doubts about whether we can know such things. Alexander says (ch.13) Locke was reacting against scholastic essence, as pertaining to species.

10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds

15786	Commitment to possible worlds is part of our ideology, not part of our ontology [Hintikka]
	Full Idea: Quantification over members of one particular world is a measure of ideology, quantification that crosses possible worlds is often a measure of ideology.
	From: Jaakko Hintikka (Semantics for Propositional Attitudes [1969], p.95), quoted by William Lycan - The Trouble with Possible Worlds 02
	A reaction: I like this. See Idea 15785 for the underlying distinction. It leaves the question open of what we might mean by 'ideological commitment'.

11. Knowledge Aims / B. Certain Knowledge / 1. Certainty

15994	If it is knowledge, it is certain; if it isn't certain, it isn't knowledge [Locke]
	Full Idea: What reaches to knowledge, I think may be called certainty; and what comes short of certainty, I think cannot be knowledge.
	From: John Locke (Letters to Edward Stillingfleet [1695], Letter 2), quoted by Simon Blackburn - Quasi-Realism no Fictionalism
	A reaction: I much prefer that fallibilist approach offered by the pragmatists. Knowledge is well-supported belief which seems (and is agreed) to be true, but there is a small shadow of doubt hanging over all of it.