Combining Texts

All the ideas for 'Thinking About Mathematics', 'Does Conceivability Entail Possibility?' and 'Brainchildren'

expand these ideas     |    start again     |     specify just one area for these texts

25 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
8729 Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
8763 The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
18249 Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
8764 Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
8762 Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
8760 Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
8761 A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
8744 Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
8749 Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
8750 Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
8752 Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8753 Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
8731 Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8730 'Impredicative' definitions refer to the thing being described [Shapiro]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
2526 Philosophers regularly confuse failures of imagination with insights into necessity [Dennett]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
16473 Modal Rationalism: conceivability gives a priori access to modal truths [Chalmers, by Stalnaker]
19258 Evaluate primary possibility from some world, and secondary possibility from this world [Chalmers, by Vaidya]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
2523 That every mammal has a mother is a secure reality, but without foundations [Dennett]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
2528 Does consciousness need the concept of consciousness? [Dennett]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / c. Parts of consciousness
2525 Maybe language is crucial to consciousness [Dennett]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
2527 Unconscious intentionality is the foundation of the mind [Dennett]
17. Mind and Body / C. Functionalism / 1. Functionalism
2530 Could a robot be made conscious just by software? [Dennett]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
2524 A language of thought doesn't explain content [Dennett]
18. Thought / D. Concepts / 5. Concepts and Language / c. Concepts without language
2529 Maybe there can be non-conscious concepts (e.g. in bees) [Dennett]