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Single Idea 12390
[filed under theme 12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
]
Full Idea
X knows a priori that p iff the belief was produced with an a priori warrant, which is a process which is available to X, and this process is a warrant, and it makes p true.
Gist of Idea
A priori knowledge comes from available a priori warrants that produce truth
Source
Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.4)
Book Ref
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.24
A Reaction
[compression of a formal spelling-out] This is a modified version of Goldman's reliabilism, for a priori knowledge. It sounds a bit circular and uninformative, but it's a start.
The
36 ideas
from Philip Kitcher
12428
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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]
|
18069
|
Arithmetic is an idealizing theory
[Kitcher]
|
18068
|
Arithmetic is made true by the world, but is also made true by our constructions
[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]
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