Combining Texts

All the ideas for 'works', 'Introspection' and 'Sources of Knowledge of Mathematics'

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5 ideas

5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction

10121	Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal]
	Full Idea: Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth.
	From: Blaise Pascal (works [1660]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
	A reaction: [Quoted in Auden and Kronenberger's Book of Aphorisms] Presumably we would now say that contradiction is a purely formal, syntactic notion, and not a semantic one. If you hit a contradiction, something has certainly gone wrong.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

9545	Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara]
	Full Idea: Near the end of his life, Frege completely abandoned his logicism, and came to the conclusion that the source of our arithmetical knowledge is what he called 'the Geometrical Source of Knowledge'.
	From: report of Gottlob Frege (Sources of Knowledge of Mathematics [1922]) by Charles Chihara - A Structural Account of Mathematics Intro n3
	A reaction: We have, rather crucially, lost touch with the geometrical origins of arithmetic (such as 'square' numbers), which is good news for the practice of mathematics, but probably a disaster for the philosophy of the subject.

12. Knowledge Sources / B. Perception / 8. Adverbial Theory

5691	The adverbial account of sensation says not 'see a red image' but be 'appeared to redly' [Shoemaker]
	Full Idea: Some who reject the act-object conception of sensation favour an 'adverbial' account, where (instead of the act of 'seeing a red image') it is better to speak of 'being appeared to redly'.
	From: Sydney Shoemaker (Introspection [1994], p.398)
	A reaction: The point is that you couldn't perceive without a colour (or travel without a speed), so the qualifying adverb is intrinsic to the process, not a separate object. The adverbial theory will imply a fairly minimal account of universals.

16. Persons / C. Self-Awareness / 1. Introspection

5687	For true introspection, must we be aware that we are aware of our mental events? [Shoemaker]
	Full Idea: Some writers distinguish introspection from a pre-introspective awareness of mental phenomena, saying one is not properly introspecting unless one is not only aware of the phenomena, but aware that one is aware of them.
	From: Sydney Shoemaker (Introspection [1994], p.395)
	A reaction: The test question might be what we think animals do. I think I agree with the 'writers'. You are either just aware of the contents or qualia or images of thought, which is not introspection, or you become introspectively aware that you are having them.

5688	Empirical foundationalism says basic knowledge is self-intimating, and incorrigible or infallible [Shoemaker]
	Full Idea: Foundationalist epistemology takes all empirical knowledge to be grounded in the introspective knowledge each mind has of its own states, …holding that introspective judgements are 'incorrigible' or 'infallible', and mental states are 'self-intimating'.
	From: Sydney Shoemaker (Introspection [1994], p.396)
	A reaction: Descartes' foundationalist Cogito also seems to be based on introspection, making introspection the essence of all foundationalism. The standard modern view is that introspective states are incorrigible, but not infallible.