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All the ideas for 'Unconscious Cerebral Initiative', 'Logicism, Some Considerations (PhD)' and 'Abduction and Induction'

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8 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers

13412	Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
	Full Idea: Not all numbers could possibly have been learned à la Frege-Russell, because we could not have performed that many distinct acts of abstraction. Somewhere along the line a rule had to come in to enable us to obtain more numbers, in the natural order.
	From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165)
	A reaction: Follows on from Idea 13411. I'm not sure how Russell would deal with this, though I am sure his account cannot be swept aside this easily. Nevertheless this seems powerful and convincing, approaching the problem through the epistemology.

13413	We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
	Full Idea: Both ordinalists and cardinalists, to account for our number words, have to account for the fact that we know so many of them, and that we can 'recognize' numbers which we've neither seen nor heard.
	From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166)
	A reaction: This seems an important contraint on any attempt to explain numbers. Benacerraf is an incipient structuralist, and here presses the importance of rules in our grasp of number. Faced with 42,578,645, we perform an act of deconstruction to grasp it.

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers

13411	If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
	Full Idea: If we accept the Frege-Russell analysis of number (the natural numbers are the cardinals) as basic and correct, one thing which seems to follow is that one could know, say, three, seventeen, and eight, but no other numbers.
	From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164)
	A reaction: It seems possible that someone might only know those numbers, as the patterns of members of three neighbouring families (the only place where they apply number). That said, this is good support for the priority of ordinals. See Idea 13412.

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

13415	An adequate account of a number must relate it to its series [Benacerraf]
	Full Idea: No account of an individual number is adequate unless it relates that number to the series of which it is a member.
	From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.169)
	A reaction: Thus it is not totally implausible to say that 2 is several different numbers or concepts, depending on whether you see it as a natural number, an integer, a rational, or a real. This idea is the beginning of modern structuralism.

14. Science / D. Explanation / 3. Best Explanation / a. Best explanation

14790	'Abduction' is beginning a hypothesis, particularly if it includes preference of one explanation over others [Peirce]
	Full Idea: The first starting of a hypothesis and the entertaining of it …is an inferential step which I propose to call 'abduction'. This will include a preference for any one hypothesis over others which would equally explain the facts.
	From: Charles Sanders Peirce (Abduction and Induction [1901], I)
	A reaction: I take there to be no more important function within human thought than the procedure by which we give preference to one particular explanation. It only makes sense, I think, if we take it as part of a coherence theory of justification.

14791	Abduction involves original suggestions, and not just the testing involved in induction [Peirce]
	Full Idea: It is of the nature of abduction to involve an original suggestion; while typical induction has no originality in it, but only tests a suggestion already made.
	From: Charles Sanders Peirce (Abduction and Induction [1901], I)
	A reaction: Peirce's 'abduction' is not, then, just the choice of a best explanation. He came up with the idea because he was keen to capture the creative and imaginative character of rational thought.

20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act

7861	Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau]
	Full Idea: Libet himself points out that the conscious decisions still have the power to 'endorse' or 'cancel', so to speak, the processes initiated by the earlier cortical activity: no action will result if the action's execution is consciously countermanded.
	From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by David Papineau - Thinking about Consciousness 1.4
	A reaction: This is why Libet's findings do not imply 'epiphenomenalism'. It seems that part of a decisive action is non-conscious, undermining the all-or-nothing view of consciousness. Searle tries to smuggle in free will at this point (Idea 3817).

6660	Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe]
	Full Idea: Libet found that a subject's conscious choice to move was about a fifth of a second before movement, and thus later than the onset of the brain's so-called 'readiness potential', which seems to imply that unconscious processes initiates action.
	From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.9
	A reaction: Of great interest to philosophers! It seems to make conscious choices epiphenomenal. The key move, I think, is to give up the idea of consciousness as being all-or-nothing. My actions are still initiated by 'me', but 'me' shades off into unconsciousness.