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Single Idea 12426
[filed under theme 6. Mathematics / A. Nature of Mathematics / 1. Mathematics
]
Full Idea
Insofar as we can honor claims about the aesthetic qualities or the interest of mathematical inquiries, we should do so by pointing to their explanatory power.
Gist of Idea
The 'beauty' or 'interest' of mathematics is just explanatory power
Source
Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.4)
Book Ref
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.212
A Reaction
I think this is a good enough account for me (but probably not for my friend Carl!). Beautiful cars are particularly streamlined. Beautiful people look particularly healthy. A beautiful idea is usually wide-ranging.
Related Idea
Idea 18078
The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher]
The
32 ideas
from 'The Nature of Mathematical Knowledge'
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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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]
|
12413
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A 'warrant' is a process which ensures that a true belief is knowledge
[Kitcher]
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12389
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Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge
[Kitcher]
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12390
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A priori knowledge comes from available a priori warrants that produce truth
[Kitcher]
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12416
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We have some self-knowledge a priori, such as knowledge of our own existence
[Kitcher]
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12418
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In long mathematical proofs we can't remember the original a priori basis
[Kitcher]
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12392
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Mathematical a priorism is conceptualist, constructivist or realist
[Kitcher]
|
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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18061
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Mathematical intuition is not the type platonism needs
[Kitcher]
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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]
|
12423
|
Analyticity avoids abstract entities, but can there be truth without reference?
[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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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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18067
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Abstract objects were a bad way of explaining the structure in mathematics
[Kitcher]
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18069
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Arithmetic is an idealizing theory
[Kitcher]
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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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18070
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We develop a language for correlations, and use it to perform higher level operations
[Kitcher]
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18071
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A one-operation is the segregation of a single object
[Kitcher]
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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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18074
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Intuitionists rely on assertability instead of truth, but assertability relies on truth
[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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18075
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Idealisation trades off accuracy for simplicity, in varying degrees
[Kitcher]
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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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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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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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18083
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With infinitesimals, you divide by the time, then set the time to zero
[Kitcher]
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20473
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If experiential can defeat a belief, then its justification depends on the defeater's absence
[Kitcher, by Casullo]
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