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Single Idea 12431
[filed under theme 5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
]
Full Idea
I believe the laws of classical logic, in part because I was taught them, and in part because I think I see how those laws are used in assessing evidence. But my belief could easily be undermined by experience.
Gist of Idea
I believe classical logic because I was taught it and use it, but it could be undermined
Source
Philip Kitcher (A Priori Knowledge Revisited [2000], §VII)
Book Ref
'New Essays on the A Priori', ed/tr. Boghossian,P /Peacocke,C [OUP 2000], p.87
A Reaction
Quine has one genuine follower! The trouble is his first sentence would fit witch-doctoring just as well. Kitcher went to Cambridge; I hope he doesn't just believe things because he was taught them, or because he 'sees how they are used'!
The
36 ideas
from Philip Kitcher
12428
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Many necessities are inexpressible, and unknowable a priori
[Kitcher]
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12429
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Knowing our own existence is a priori, but not necessary
[Kitcher]
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12430
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Classical logic is our preconditions for assessing empirical evidence
[Kitcher]
|
12431
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I believe classical logic because I was taught it and use it, but it could be undermined
[Kitcher]
|
6298
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Kitcher says maths is an idealisation of the world, and our operations in dealing with it
[Kitcher, by Resnik]
|
12387
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Mathematical knowledge arises from basic perception
[Kitcher]
|
12412
|
My constructivism is mathematics as an idealization of collecting and ordering objects
[Kitcher]
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12413
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A 'warrant' is a process which ensures that a true belief is knowledge
[Kitcher]
|
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]
|
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
|
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
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Mathematical intuition is not the type platonism needs
[Kitcher]
|
18063
|
Conceptualists say we know mathematics a priori by possessing mathematical concepts
[Kitcher]
|
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]
|
18065
|
We derive limited mathematics from ordinary things, and erect powerful theories on their basis
[Kitcher]
|
18066
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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
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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
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A one-operation is the segregation of a single object
[Kitcher]
|
12395
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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
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The 'beauty' or 'interest' of mathematics is just explanatory power
[Kitcher]
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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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