Combining Texts

All the ideas for 'Remarks on the Foundations of Mathematics', 'Papers of 1906' and 'Negation'

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17 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
18781 Inconsistency doesn't prevent us reasoning about some system [Mares]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
11074 'It is true that this follows' means simply: this follows [Wittgenstein]
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 / 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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
11073 Two and one making three has the necessity of logical inference [Wittgenstein]
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]
18. Thought / A. Modes of Thought / 6. Judgement / b. Error
22306 To explain false belief we should take belief as relating to a proposition's parts, not to the whole thing [Russell]
19. Language / C. Assigning Meanings / 2. Semantics
18791 In 'situation semantics' our main concepts are abstracted from situations [Mares]