8 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. |
| 12900 | How could 'S knows he has hands' not have a fixed content? [Bach] |
| Full Idea: How can it be that a sentence like 'George knows that he has hands', even with time and references fixed, does not have a fixed propositional content? | |
| From: Kent Bach (The Emperor's New 'Knows' [2005], I) | |
| A reaction: The appeal is to G.E. Moore's common sense view of immediate knowledge (Idea 6349). The reply is simply that the word 'knows' shifts its meaning, having high standards in sceptical philosophy classes, and low standards on the street. |
| 12901 | If contextualism is right, knowledge sentences are baffling out of their context [Bach] |
| Full Idea: Contextualism seems to predict that if you encounter a knowledge attribution out of context you won't be in a position to grasp which proposition the sentence expresses. | |
| From: Kent Bach (The Emperor's New 'Knows' [2005], I) | |
| A reaction: It is only the word 'knows' which is at issue in the sentence. If someone is said to 'know' about the world of the fairies, we might well be puzzled as to what proposition was being expressed. Is the word 'flat' baffling out of context? |
| 12902 | Sceptics aren't changing the meaning of 'know', but claiming knowing is tougher than we think [Bach] |
| Full Idea: When a sceptic brings up far-fetched possibilities and argues that we can't rule them out, he is not raising the standard for the word 'know'. He is showing it is tougher than we realise for a belief to qualify as normal knowledge at all. | |
| From: Kent Bach (The Emperor's New 'Knows' [2005], III) | |
| A reaction: [Bach cites Richard Feldman for this idea] I think that what happens in the contextual account is that 'true', 'belief' and 'know' retain their standard meaning, and it is 'justified' which shifts. 'I am fully justified' can have VERY different meanings! |
| 4316 | Either all action is rational, or reason dominates, or reason is only concerned with means [Cottingham] |
| Full Idea: We can distinguish rational exclusivism (all activity is guided by reason - Plato and Spinoza), rational hegemonism (all action is dominated by reason), and rational instrumentalism (reason assesses means rather than ends - Hume). | |
| From: John Cottingham (Reason, Emotions and Good Life [2000]) | |
| A reaction: The idea that reason is the only cause of actions seems deeply implausible, but I strongly resist Hume's instrumental approach. Action without desire is not a contradiction. |