18253
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I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
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Full Idea:
You need a double transition, from cardinal numbes (Anzahlen) to the rational numbers, and from the latter to the real numbers generally. I wish to go straight from the cardinal numbers to the real numbers as ratios of quantities.
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From:
Gottlob Frege (Letters to Russell [1902], 1903.05.21), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's'
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A reaction:
Note that Frege's real numbers are not quantities, but ratios of quantities. In this way the same real number can refer to lengths, masses, intensities etc.
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18269
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Logical objects are extensions of concepts, or ranges of values of functions [Frege]
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Full Idea:
How are we to conceive of logical objects? My only answer is, we conceive of them as extensions of concepts or, more generally, as ranges of values of functions ...what other way is there?
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From:
Gottlob Frege (Letters to Russell [1902], 1902.07.28), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 epigr
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A reaction:
This is the clearest statement I have found of what Frege means by an 'object'. But an extension is a collection of things, so an object is a group treated as a unity, which is generally how we understand a 'set'. Hence Quine's ontology.
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23224
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That all matter thinks is absurd, and would make each part of our bodies a distinct self-consciousness [Bentley]
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Full Idea:
[Belief in thinking matter] leads to monstrous absurdities. …Every stock and stone would be a percipient and rational creature. …every single Atom of our bodies would be a distinct Animal, endued with self-consciousness and personal sensation of its own.
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From:
Richard Bentley (Matter and Motion Cannot Think [1692], p.14-15), quoted by Matthew Cobb - The Idea of the Brain 2
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A reaction:
Sounds correct, though presumably panpsychists don't think the flickers of consciousness in my toenails and hair constitute full-blown persons. I can't imagine what awareness is being claimed for my toenails.
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