Ideas of Philip Kitcher, by Theme

[British, b.1947, Studied at Cambridge, then pupil of Thomas Kuhn. Professor at Columbia.]

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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18074 Intuitionists rely on assertability instead of truth, but assertability relies on truth
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
12430 Classical logic is our preconditions for assessing empirical evidence
12431 I believe classical logic because I was taught it and use it, but it could be undermined
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
6298 Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Resnik]
12392 Mathematical a priorism is conceptualist, constructivist or realist
18078 The interest or beauty of mathematics is when it uses current knowledge to advance undestanding
12426 The 'beauty' or 'interest' of mathematics is just explanatory power
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
12395 Real numbers stand to measurement as natural numbers stand to counting
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
12425 Complex numbers were only accepted when a geometrical model for them was found
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
18071 A one-operation is the segregation of a single object
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
18066 The old view is that mathematics is useful in the world because it describes the world
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
18083 With infinitesimals, you divide by the time, then set the time to zero
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
12393 Intuition is no basis for securing a priori knowledge, because it is fallible
12420 If mathematics comes through intuition, that is either inexplicable, or too subjective
18061 Mathematical intuition is not the type platonism needs
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
12387 Mathematical knowledge arises from basic perception
12412 My constructivism is mathematics as an idealization of collecting and ordering objects
18065 We derive limited mathematics from ordinary things, and erect powerful theories on their basis
18077 The defenders of complex numbers had to show that they could be expressed in physical terms
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12423 Analyticity avoids abstract entities, but can there be truth without reference?
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
18068 Arithmetic is made true by the world, but is also made true by our constructions
18069 Arithmetic is an idealizing theory
18070 We develop a language for correlations, and use it to perform higher level operations
18072 Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori)
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
18063 Conceptualists say we know mathematics a priori by possessing mathematical concepts
18064 If meaning makes mathematics true, you still need to say what the meanings refer to
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
18067 Abstract objects were a bad way of explaining the structure in mathematics
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
12428 Many necessities are inexpressible, and unknowable a priori
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
12429 Knowing our own existence is a priori, but not necessary
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
12390 A priori knowledge comes from available a priori warrants that produce truth
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
12418 In long mathematical proofs we can't remember the original a priori basis
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
12389 Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge
12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective
12416 We have some self-knowledge a priori, such as knowledge of our own existence
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
12413 A 'warrant' is a process which ensures that a true belief is knowledge
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
20473 If experiential can defeat a belief, then its justification depends on the defeater's absence [Casullo]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
18075 Idealisation trades off accuracy for simplicity, in varying degrees