Combining Texts

All the ideas for '', 'Semantic Relationism' and 'What is Cantor's Continuum Problem?'

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28 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
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 / E. Structures of Logic / 4. Variables in Logic
15590 It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that [Fine,K]
15591 In separate expressions variables seem identical in role, but in the same expression they aren't [Fine,K]
15595 The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K]
15594 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K]
15592 The usual Tarskian interpretation of variables is to specify their range of values [Fine,K]
15593 Variables can be viewed as special terms - functions taking assignments into individuals [Fine,K]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
15599 Cicero/Cicero and Cicero/Tully may differ in relationship, despite being semantically the same [Fine,K]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
9. Objects / F. Identity among Objects / 1. Concept of Identity
15603 I can only represent individuals as the same if I do not already represent them as the same [Fine,K]
9. Objects / F. Identity among Objects / 5. Self-Identity
15604 If Cicero=Tully refers to the man twice, then surely Cicero=Cicero does as well? [Fine,K]
18. Thought / B. Mechanics of Thought / 5. Mental Files
15602 Mental files are devices for keeping track of basic coordination of objects [Fine,K]
18. Thought / C. Content / 1. Content
15588 You cannot determine the full content from a thought's intrinsic character, as relations are involved [Fine,K]
19. Language / C. Assigning Meanings / 2. Semantics
15596 The standard aim of semantics is to assign a semantic value to each expression [Fine,K]
15587 That two utterances say the same thing may not be intrinsic to them, but involve their relationships [Fine,K]
15589 The two main theories are Holism (which is inferential), and Representational (which is atomistic) [Fine,K]
15598 We should pursue semantic facts as stated by truths in theories (and not put the theories first!) [Fine,K]
15600 Referentialist semantics has objects for names, properties for predicates, and propositions for connectives [Fine,K]
15601 Fregeans approach the world through sense, Referentialists through reference [Fine,K]
19. Language / C. Assigning Meanings / 9. Indexical Semantics
15605 I take indexicals such as 'this' and 'that' to be linked to some associated demonstration [Fine,K]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]