10 ideas
| 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. |
| 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. |
| 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. |
| 7628 | Broad rejects the inferential component of the representative theory [Broad, by Maund] |
| Full Idea: Broad, one of the most important modern defenders of the representative theory of perception, explicitly rejects the inferential component of the theory. | |
| From: report of C.D. Broad (Mind and Its Place in Nature [1925]) by Barry Maund - Perception Ch.1 | |
| A reaction: Since the supposed inferences happen much too quickly to be conscious, it is hard to see how we could distinguish an inference from an interpretation mechanism. Personally I interpret things long before the question of truth arises. |
| 22445 | Morality shows murder is wrong, but not what counts as a murder [Foot] |
| Full Idea: While one can determine from the concept of morality that there is an objection to murder one cannot determine completely what will count as murder. | |
| From: Philippa Foot (Morality and Art [1972], p.7) | |
| A reaction: She then refers to abortion, but there are military and criminal problem cases, and killings by neglect or side effect. |
| 22444 | A moral system must deal with the dangers and benefits of life [Foot] |
| Full Idea: A moral system seems necessarily to be one aimed at removing particular dangers and securing certain benefits. | |
| From: Philippa Foot (Morality and Art [1972], p.6) | |
| A reaction: I thoroughly approve of this approach to morality, which anchors it in real life, rather than in ideals or principles of reason. |
| 22447 | Saying something 'just is' right or wrong creates an illusion of fact and objectivity [Foot] |
| Full Idea: When we say that something 'just is' right or wrong we want to give the impression of some kind of fact or authority standing behind our words, ...maintaining the trappings of objectivity though the substance is not there. | |
| From: Philippa Foot (Morality and Art [1972], p.9) | |
| A reaction: Foot favours the idea that such a claim must depend on reasons, and that the reasons arise out of actual living. She's right. |
| 22448 | We sometimes just use the word 'should' to impose a rule of conduct on someone [Foot] |
| Full Idea: It would be more honest to recognise that the 'should' of moral judgement is sometimes merely an instrument by which we (for our own very good reasons) try to impose a rule of conduct even on the uncaring man? | |
| From: Philippa Foot (Morality and Art [1972], p.18) | |
| A reaction: This is a good example, I think, of the ordinary language tradition that Foot grew up in. We load a word like 'should' with a mystical power, but the situations in which it is actually used bring us back down to earth. |
| 22446 | In the case of something lacking independence, calling it a human being is a matter of choice [Foot] |
| Full Idea: In the problem of abortion there is a genuine choice as to whether or not to count as a human being, with the rights of a human being, what would become a human being but is not yet capable of independent life. | |
| From: Philippa Foot (Morality and Art [1972], p.7) | |
| A reaction: There must be some basis for the choice. We can't call a dead person a human being. Choosing to call a tiny zygote a human being seems very implausible. Pre-viability strikes me as implausible. |