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13412
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Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
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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.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165)
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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.
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13413
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We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
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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.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166)
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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.
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13411
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If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
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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.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164)
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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.
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6866
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It is disturbing if we become unreal when we die, but if time is unreal, then we remain real after death [Le Poidevin]
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Full Idea:
For the A-theorists called 'presentists' the past is as unreal as the future, and reality leaves us behind once we die, which is disturbing; but B-theorists, who see time as unreal, say we are just as real after our deaths as we were beforehand.
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From:
Robin Le Poidevin (Interview with Baggini and Stangroom [2001], p.174)
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A reaction:
See Idea 6865 for A and B theories. I wonder if this problem is only superficially 'disturbing'. Becoming unreal may sound more drastic than becoming dead, but they both sound pretty terminal to me.
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6865
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A-theory says past, present, future and flow exist; B-theory says this just reports our perspective [Le Poidevin]
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Full Idea:
The A-theory regards our intuitive distinction of time into past, present and future as objective, and takes seriously the idea that time flows; the B-theory says this just reflects our perspective, like the spatial distinction between here and there.
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From:
Robin Le Poidevin (Interview with Baggini and Stangroom [2001], p.174)
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A reaction:
The distinction comes from McTaggart. Physics seems to be built on an objective view of time, and yet Einstein makes time relative. What possible evidence could decide between the two theories?
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