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Single Idea 12393

[filed under theme 6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics ]

Full Idea

The process of pure intuition does not measure up to the standards required of a priori warrants not because it is sensuous but because it is fallible.

Clarification

'Warrants' are guarantees of knowledge

Gist of Idea

Intuition is no basis for securing a priori knowledge, because it is fallible

Source

Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.2)

Book Ref

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.53

The 36 ideas from Philip Kitcher

12428 Many necessities are inexpressible, and unknowable a priori [Kitcher]
12429 Knowing our own existence is a priori, but not necessary [Kitcher]
12430 Classical logic is our preconditions for assessing empirical evidence [Kitcher]
12431 I believe classical logic because I was taught it and use it, but it could be undermined [Kitcher]
6298 Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik]
12387 Mathematical knowledge arises from basic perception [Kitcher]
12412 My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher]
12413 A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher]
12389 Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher]
12390 A priori knowledge comes from available a priori warrants that produce truth [Kitcher]
12416 We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher]
12418 In long mathematical proofs we can't remember the original a priori basis [Kitcher]
12392 Mathematical a priorism is conceptualist, constructivist or realist [Kitcher]
12420 If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher]
12393 Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher]
18061 Mathematical intuition is not the type platonism needs [Kitcher]
18063 Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher]
18064 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]
18065 We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher]
18066 The old view is that mathematics is useful in the world because it describes the world [Kitcher]
18067 Abstract objects were a bad way of explaining the structure in mathematics [Kitcher]
18068 Arithmetic is made true by the world, but is also made true by our constructions [Kitcher]
18069 Arithmetic is an idealizing theory [Kitcher]
18070 We develop a language for correlations, and use it to perform higher level operations [Kitcher]
18071 A one-operation is the segregation of a single object [Kitcher]
12395 Real numbers stand to measurement as natural numbers stand to counting [Kitcher]
18074 Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher]
18072 Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher]
18075 Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher]
12425 Complex numbers were only accepted when a geometrical model for them was found [Kitcher]
18077 The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher]
18078 The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher]
12426 The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher]
18083 With infinitesimals, you divide by the time, then set the time to zero [Kitcher]
20473 If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo]