Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Vagueness: a global approach' and 'Introduction to the Philosophy of Mathematics'

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32 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
17926 Rejecting double negation elimination undermines reductio proofs [Colyvan]
17925 Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
23548 Indeterminacy is in conflict with classical logic [Fine,K]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
17924 Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
23539 Classical semantics has referents for names, extensions for predicates, and T or F for sentences [Fine,K]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17929 Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17930 Axioms are 'categorical' if all of their models are isomorphic [Colyvan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17928 Ordinal numbers represent order relations [Colyvan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17923 Intuitionists only accept a few safe infinities [Colyvan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
17941 Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17922 Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17936 Transfinite induction moves from all cases, up to the limit ordinal [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17940 Most mathematical proofs are using set theory, but without saying so [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
17931 Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
17932 If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan]
7. Existence / D. Theories of Reality / 10. Vagueness / a. Problem of vagueness
23544 Local indeterminacy concerns a single object, and global indeterminacy covers a range [Fine,K]
23540 Conjoining two indefinites by related sentences seems to produce a contradiction [Fine,K]
23546 Standardly vagueness involves borderline cases, and a higher standpoint from which they can be seen [Fine,K]
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
23542 Identifying vagueness with ignorance is the common mistake of confusing symptoms with cause [Fine,K]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
23541 Supervaluation can give no answer to 'who is the last bald man' [Fine,K]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
23545 We do not have an intelligible concept of a borderline case [Fine,K]
14. Science / C. Induction / 6. Bayes's Theorem
17943 Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
17939 Mathematics can reveal structural similarities in diverse systems [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / f. Necessity in explanations
17938 Mathematics can show why some surprising events have to occur [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
17934 Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan]
17933 Reductio proofs do not seem to be very explanatory [Colyvan]
17935 If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan]
17942 Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
17937 Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
23547 It seems absurd that there is no identity of any kind between two objects which involve survival [Fine,K]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
23543 We identify laws with regularities because we mistakenly identify causes with their symptoms [Fine,K]