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Single Idea 10553
[filed under theme 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
]
Full Idea
For Frege, in 'Grundgesetze', a number is a class of classes of the same cardinality.
Gist of Idea
A number is a class of classes of the same cardinality
Source
report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14
Book Ref
Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.510
The
12 ideas
from 'Grundgesetze der Arithmetik 2 (Basic Laws)'
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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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9889
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Real numbers are ratios of quantities
[Frege, by Dummett]
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10553
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A number is a class of classes of the same cardinality
[Frege, by Dummett]
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10020
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Frege's biggest error is in not accounting for the senses of number terms
[Hodes on Frege]
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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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9890
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The modern account of real numbers detaches a ratio from its geometrical origins
[Frege]
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9891
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The first demand of logic is of a sharp boundary
[Frege]
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10019
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Only what is logically complex can be defined; what is simple must be pointed to
[Frege]
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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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9887
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Formalism misunderstands applications, metatheory, and infinity
[Frege, by Dummett]
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8751
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Only applicability raises arithmetic from a game to a science
[Frege]
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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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