13886
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Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C]
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Full Idea:
Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument.
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From:
report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv
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A reaction:
Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'.
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9845
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We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
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Full Idea:
Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known
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From:
Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66)
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A reaction:
Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher.
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9886
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Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]
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Full Idea:
The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity.
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From:
Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19
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A reaction:
We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals.
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9887
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Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
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Full Idea:
Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence.
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From:
report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics
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A reaction:
The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising.
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11846
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If we abstract the difference between two houses, they don't become the same house [Frege]
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Full Idea:
If abstracting from the difference between my house and my neighbour's, I were to regard both houses as mine, the defect of the abstraction would soon be made clear. It may, though, be possible to obtain a concept by means of abstraction...
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From:
Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §99)
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A reaction:
Note the important concession at the end, which shows Frege could never deny the abstraction process, despite all the modern protests by Geach and Dummett that he totally rejected it.
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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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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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