Combining Texts

All the ideas for 'Chomsky on himself', 'The Theory of Logical Types' and 'Negation'

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20 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
18781 Inconsistency doesn't prevent us reasoning about some system [Mares]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18789 Intuitionist logic looks best as natural deduction [Mares]
18790 Intuitionism as natural deduction has no rule for negation [Mares]
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
18787 Three-valued logic is useful for a theory of presupposition [Mares]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
18793 Material implication (and classical logic) considers nothing but truth values for implications [Mares]
18784 In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
18786 Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares]
18780 Standard disjunction and negation force us to accept the principle of bivalence [Mares]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
18782 The connectives are studied either through model theory or through proof theory [Mares]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
21566 'Propositional functions' are ambiguous until the variable is given a value [Russell]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
18783 Many-valued logics lack a natural deduction system [Mares]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
18792 Situation semantics for logics: not possible worlds, but information in situations [Mares]
5. Theory of Logic / K. Features of Logics / 2. Consistency
18785 Consistency is semantic, but non-contradiction is syntactic [Mares]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
21567 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
23457 Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell]
21556 Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
18788 For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
21568 A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
6649 Chomsky now says concepts are basically innate, as well as syntax [Chomsky, by Lowe]
19. Language / C. Assigning Meanings / 2. Semantics
18791 In 'situation semantics' our main concepts are abstracted from situations [Mares]