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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23609
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I act justly if I follow my Prince in an apparently unjust war, and refusing to fight would be injustice [Hobbes]
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Full Idea:
If I wage war at the commandment of my Prince, conceiving the war to be justly undertaken, I do not therefore do unjustly, but rather if I refuse to do it, arrogating to myself the knowledge of what is just and unjust, which pertains only to my Prince.
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From:
Thomas Hobbes (De Cive [1642], 12.II), quoted by Jeff McMahan - Killing in War 2.6
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A reaction:
Hobbes early says that Princes make things just by commanding them. This presumably assumes divine authority in the Prince. This is, of course, ancient pernicious nonsense.
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