Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'What are Sets and What are they For?' and '(Nonsolipsistic) Conceptual Role Semantics'

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32 ideas

2. Reason / A. Nature of Reason / 6. Coherence
12596 Reasoning aims at increasing explanatory coherence [Harman]
12599 Reason conservatively: stick to your beliefs, and prefer reasoning that preserves most of them [Harman]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
14240 The empty set is something, not nothing! [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
12595 We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
12597 I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
14245 Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
14246 If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
7. Existence / D. Theories of Reality / 3. Reality
12598 Reality is the overlap of true complete theories [Harman]
15. Nature of Minds / A. Nature of Mind / 6. Anti-Individualism
12602 There is no natural border between inner and outer [Harman]
12603 We can only describe mental attitudes in relation to the external world [Harman]
15. Nature of Minds / B. Features of Minds / 5. Qualia / c. Explaining qualia
12601 The way things look is a relational matter, not an intrinsic matter [Harman]
18. Thought / D. Concepts / 5. Concepts and Language / a. Concepts and language
12592 Concepts in thought have content, but not meaning, which requires communication [Harman]
19. Language / A. Nature of Meaning / 6. Meaning as Use
12590 Take meaning to be use in calculation with concepts, rather than in communication [Harman]
12593 The use theory attaches meanings to words, not to sentences [Harman]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
12588 Meaning from use of thoughts, constructed from concepts, which have a role relating to reality [Harman]
12589 Some regard conceptual role semantics as an entirely internal matter [Harman]
12600 The content of thought is relations, between mental states, things in the world, and contexts [Harman]
19. Language / F. Communication / 3. Denial
12594 If one proposition negates the other, which is the negative one? [Harman]
19. Language / F. Communication / 6. Interpreting Language / a. Translation
12591 Mastery of a language requires thinking, and not just communication [Harman]