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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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15998
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Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard]
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Full Idea:
To love another in spite of his weaknesses and errors and imperfections is not perfect love. No, to love is to find him lovable in spite of, and together with, his weaknesses and errors and imperfections.
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From:
Søren Kierkegaard (Works of Love [1847], p.158)
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A reaction:
A true romantic at heart, Kierkegaard ideally posits perfect love as unconditional love, and not just of good attributes, predicates and conditions. However, the real question for both me and Kierkegaard is, is perfect love desirable or even possible?[SY]
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20991
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People prepare our dinner from their own self-interest, not from humanity [Smith,A]
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Full Idea:
It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest. We address ourselves, not to their humanity but to their self-love.
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From:
Adam Smith (The Wealth of Nations [1776], p.26-7), quoted by Amartya Sen - The Idea of Justice 08 'Narrowing'
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A reaction:
Sen passionately pleads that this not be taken out of context. It is about the motivation for the relationship of exchange, and not about morality in general, which also includes trust etc. The subsequent lines in Smith show this.
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