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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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16771
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A composite is a true unity if all of its parts fall under one essence [Scheibler]
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Full Idea:
A composite entity is a unum per se if the partial entities that are in it are contained under one common essence. …In water, all those parts are contained under one essence of water.
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From:
Chistoph Scheibler (Metaphysics [1650], I.4.1 n9), quoted by Robert Pasnau - Metaphysical Themes 1274-1671
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A reaction:
Water mixed with wine is said to be an 'ens per accidens'. This is an unusual but possible view, that all the water there is is a single thing, united by its compositional essence. When we talk about 'water', we include possible water, and past water.
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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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