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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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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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7903
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The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
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Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
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From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
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A reaction:
What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
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