Combining Texts

All the ideas for 'fragments/reports', 'Begriffsschrift' and 'Must We Believe in Set Theory?'

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

32 ideas

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
22270 Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege]
2. Reason / B. Laws of Thought / 1. Laws of Thought
8939 We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher]
4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC
4971 I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
17745 For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10482 The logic of ZF is classical first-order predicate logic with identity [Boolos]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10492 A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
10485 Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10484 The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
7728 Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner]
16881 The laws of logic are boundless, so we want the few whose power contains the others [Frege]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
7622 In 1879 Frege developed second order logic [Frege, by Putnam]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
7729 Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner]
5. Theory of Logic / G. Quantification / 1. Quantification
9950 A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
9991 For Frege the variable ranges over all objects [Frege, by Tait]
10536 Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
7730 Frege introduced quantifiers for generality [Frege, by Weiner]
7742 Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh]
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
13824 Proof theory began with Frege's definition of derivability [Frege, by Prawitz]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
13609 Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10483 Mathematics and science do not require very high orders of infinity [Boolos]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17855 It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10490 Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10607 Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P]
7. Existence / A. Nature of Existence / 1. Nature of Existence
11008 Existence is not a first-order property, but the instantiation of a property [Frege, by Read]
8. Modes of Existence / D. Universals / 1. Universals
10488 It is lunacy to think we only see ink-marks, and not word-types [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10487 I am a fan of abstract objects, and confident of their existence [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
19. Language / C. Assigning Meanings / 4. Compositionality
22280 Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
541 Virtue comes more from habit than character [Critias]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
7741 The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner]
28. God / C. Attitudes to God / 5. Atheism
542 Fear of the gods was invented to discourage secret sin [Critias]