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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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6213
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A man cannot will to will, or will to will to will, so the idea of a voluntary will is absurd [Hobbes]
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Full Idea:
The will is not voluntary: for a man can no more say he will will, than he will will will, and so make an infinite repetition of the word 'will', which is absurd and insignificant.
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From:
Thomas Hobbes (Human Nature [1640], Ch.XII.5)
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A reaction:
A nice simple point, allied to Nietzsche's notion that thoughts are uncontrollable (Idea 2291). Even Aquinas, who is quite a fan of free will, spotted the problem (Idea 1854). Personally I agree with Hobbes. Free will is a shibboleth.
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6210
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Life has no end (not even happiness), because we have desires, which presuppose a further end [Hobbes]
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Full Idea:
For an utmost end, in which the ancient philosophers have placed felicity, there is no such thing in this world, nor way to it: for while we live, we have desires, and desire presupposeth a further end.
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From:
Thomas Hobbes (Human Nature [1640], Ch.VII.6)
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A reaction:
Kant's definition of happiness (Idea 1452) seems to be the underlying idea, and hence with the same implication (of impossibility). However, an alcoholic locked in a brewery would seem to have all that Hobbes requires for happiness.
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6212
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Lust involves pleasure, and also the sense of power in pleasing others [Hobbes]
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Full Idea:
Lust consists of two appetites together, to please, and to be pleased, and the delight men take in delighting is not sensual, but a pleasure or joy of the mind consisting in the imagination of the power they have so much to please.
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From:
Thomas Hobbes (Human Nature [1640], Ch.IX)
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A reaction:
Hobbes would rather burst a blood-vessel than admit any altruism. If you take pleasure in pleasing someone else, why can't that simply be because of the other person's pleasure, with which we sympathise, rather than relishing our own 'power'?
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