Combining Texts

All the ideas for 'Explaining the A Priori', 'Letters to Samuel Masson' and 'Semantics for Propositional Attitudes'

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4 ideas

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

13190	I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz]
	Full Idea: Notwithstanding my infinitesimal calculus, I do not admit any real infinite numbers, even though I confess that the multitude of things surpasses any finite number, or rather any number. ..I consider infinitesimal quantities to be useful fictions.
	From: Gottfried Leibniz (Letters to Samuel Masson [1716], 1716)
	A reaction: With the phrase 'useful fictions' we seem to have jumped straight into Harty Field. I'm with Leibniz on this one. The history of mathematics is a series of ingenious inventions, whenever they seem to make further exciting proofs possible.

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.

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'.

18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts

17722	The concept 'red' is tied to what actually individuates red things [Peacocke]
	Full Idea: The possession conditions for the concept 'red' of the colour red are tied to those very conditions which individuate the colour red.
	From: Christopher Peacocke (Explaining the A Priori [2000], p.267), quoted by Carrie Jenkins - Grounding Concepts 2.5
	A reaction: Jenkins reports that he therefore argues that we can learn something about the word 'red' from thinking about the concept 'red', which is his new theory of the a priori. I find 'possession conditions' and 'individuation' to be very woolly concepts.