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All the ideas for '', 'Identity and Existence in Logic' and 'Must We Believe in Set Theory?'

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23 ideas

4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
18767 Free logics has terms that do not designate real things, and even empty domains [Anderson,CA]
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
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
18763 Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
18771 Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA]
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 / 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]
7. Existence / A. Nature of Existence / 2. Types of Existence
18769 Do mathematicians use 'existence' differently when they say some entity exists? [Anderson,CA]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
18770 We can distinguish 'ontological' from 'existential' commitment, for different kinds of being [Anderson,CA]
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]
9. Objects / A. Existence of Objects / 4. Impossible objects
18766 's is non-existent' cannot be said if 's' does not designate [Anderson,CA]
18768 We cannot pick out a thing and deny its existence, but we can say a concept doesn't correspond [Anderson,CA]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
18765 Individuation was a problem for medievals, then Leibniz, then Frege, then Wittgenstein (somewhat) [Anderson,CA]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
18764 The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles [Anderson,CA]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]