Combining Philosophers
Ideas for Einstein,A/Infeld,L, Eurytus and Philip Kitcher
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23 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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6298
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Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik]
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12392
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Mathematical a priorism is conceptualist, constructivist or realist [Kitcher]
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18078
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The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher]
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12426
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The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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12395
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Real numbers stand to measurement as natural numbers stand to counting [Kitcher]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
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12425
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Complex numbers were only accepted when a geometrical model for them was found [Kitcher]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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18071
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A one-operation is the segregation of a single object [Kitcher]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
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18066
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The old view is that mathematics is useful in the world because it describes the world [Kitcher]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
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18083
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With infinitesimals, you divide by the time, then set the time to zero [Kitcher]
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6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
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18061
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Mathematical intuition is not the type platonism needs [Kitcher]
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12420
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If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher]
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12393
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Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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12387
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Mathematical knowledge arises from basic perception [Kitcher]
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12412
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My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher]
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18065
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We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher]
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18077
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The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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12423
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Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
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18068
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Arithmetic is made true by the world, but is also made true by our constructions [Kitcher]
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18069
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Arithmetic is an idealizing theory [Kitcher]
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18070
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We develop a language for correlations, and use it to perform higher level operations [Kitcher]
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18072
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Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
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18063
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Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher]
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18064
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If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher]
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