Combining Texts

All the ideas for 'Through the Looking Glass', 'Knowledge:Readings in Cont.Epist' 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]
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]
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]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
3756 Perception, introspection, testimony, memory, reason, and inference can give us knowledge [Bernecker/Dretske]
12. Knowledge Sources / B. Perception / 7. Causal Perception
3757 Causal theory says true perceptions must be caused by the object perceived [Bernecker/Dretske]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
3759 You can acquire new knowledge by exploring memories [Bernecker/Dretske]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
3752 Justification can be of the belief, or of the person holding the belief [Bernecker/Dretske]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
3753 Foundationalism aims to avoid an infinite regress [Bernecker/Dretske]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
3754 Infallible sensations can't be foundations if they are non-epistemic [Bernecker/Dretske]
13. Knowledge Criteria / C. External Justification / 1. External Justification
3755 Justification is normative, so it can't be reduced to cognitive psychology [Bernecker/Dretske]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
3761 Modern arguments against the sceptic are epistemological and semantic externalism, and the focus on relevance [Bernecker/Dretske]
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
3760 Predictions are bound to be arbitrary if they depend on the language used [Bernecker/Dretske]
18. Thought / C. Content / 6. Broad Content
3758 Semantic externalism ties content to the world, reducing error [Bernecker/Dretske]