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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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19377
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A monad and its body are living, so life is everywhere, and comes in infinite degrees [Leibniz]
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Full Idea:
Each monad, together with a particular body, makes up a living substance. Thus, there is not only life everywhere, joined to limbs or organs, but there are also infinite degrees of life in the monads, some dominating more or less over others.
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From:
Gottfried Leibniz (Principles of Nature and Grace based on Reason [1714], 4)
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A reaction:
Two key ideas: that each monad is linked to a body (which is presumably passive), and the infinite degrees of life in monads. Thus rocks consist of monads, but at an exceedingly low degree of life. They are stubborn and responsive.
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19353
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'Perception' is basic internal representation, and 'apperception' is reflective knowledge of perception [Leibniz]
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Full Idea:
We distinguish between 'perception', the internal state of the monad representing external things, and 'apperception', which is consciousness, or the reflective knowledge of this internal state, not given to all souls, nor at all times to a given soul.
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From:
Gottfried Leibniz (Principles of Nature and Grace based on Reason [1714], §4)
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A reaction:
The word 'apperception' is standard in Kant. I find it surprising that modern analytic philosophers don't seem to use it when they write about perception. It strikes me as useful, but maybe specialists have a reason for avoiding it.
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5061
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Animals are semi-rational because they connect facts, but they don't see causes [Leibniz]
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Full Idea:
There is a connexion between the perceptions of animals, which bears some resemblance to reason: but it is based only on the memory of facts or effects, and not at all on the knowledge of causes.
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From:
Gottfried Leibniz (Principles of Nature and Grace based on Reason [1714], §5)
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A reaction:
This amounts to the view that animals can do Humean induction (where you see regularities), but not Leibnizian induction (where you see necessities). I say all minds perceive patterns, but only humans can think about the patterns they have perceived.
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16002
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The self is a combination of pairs of attributes: freedom/necessity, infinite/finite, temporal/eternal [Kierkegaard]
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Full Idea:
A human being is essentially spirit, but what is spirit? Spirit is to be a self. But what is the Self? In short, it is a synthesis of the infinite and the finite, of the temporal and the eternal, of freedom and necessity.
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From:
Søren Kierkegaard (Sickness unto Death [1849], p.59)
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A reaction:
The dense language of his first paragraph was to poke fun at fashionable Hegelian writing. The book gets very lucid afterwards! [SY]
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