Combining Texts

All the ideas for 'Through the Looking Glass', 'Words without Objects' and 'Must We Believe in Set Theory?'

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

21 ideas

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 / E. Structures of Logic / 4. Variables in Logic
12797 If plural variables have 'some values', then non-count variables have 'some value' [Laycock]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
12794 Plurals are semantical but not ontological [Laycock]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17694 Some non-count nouns can be used for counting, as in 'several wines' or 'fewer cheeses' [Laycock]
17695 Some apparent non-count words can take plural forms, such as 'snows' or 'waters' [Laycock]
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 / 3. Being / e. Being and nothing
21982 I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
12792 The category of stuff does not suit reference [Laycock]
12799 Descriptions of stuff are neither singular aggregates nor plural collections [Laycock]
7. Existence / C. Structure of Existence / 8. Stuff / b. Mixtures
12818 We shouldn't think some water retains its identity when it is mixed with air [Laycock]
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 / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
12795 Parts must be of the same very general type as the wholes [Laycock]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
17696 'Humility is a virtue' has an abstract noun, but 'water is a liquid' has a generic concrete noun [Laycock]
19. Language / B. Reference / 1. Reference theories
12791 It is said that proper reference is our intellectual link with the world [Laycock]