Combining Philosophers

Ideas for Eubulides, Kurt Vonnegut and Theodore Sider

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29 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
14980 There is a real issue over what is the 'correct' logic [Sider]
15000 'It is raining' and 'it is not raining' can't be legislated, so we can't legislate 'p or ¬p' [Sider]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
15020 Classical logic is good for mathematics and science, but less good for natural language [Sider]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13678 The most popular account of logical consequence is the semantic or model-theoretic one [Sider]
13679 Maybe logical consequence is more a matter of provability than of truth-preservation [Sider]
13682 Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider]
13680 Maybe logical consequence is a primitive notion [Sider]
15029 Modal accounts of logical consequence are simple necessity, or essential use of logical words [Sider]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
13722 A 'theorem' is an axiom, or the last line of a legitimate proof [Sider]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
15019 Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral [Sider]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13696 When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
13700 A 'total' function must always produce an output for a given domain [Sider]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
13703 λ can treat 'is cold and hungry' as a single predicate [Sider]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
13688 Good axioms should be indisputable logical truths [Sider]
13687 No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
13690 Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider]
13691 Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
15001 'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted [Sider]
13685 Natural deduction helpfully allows reasoning with assumptions [Sider]
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
13686 We can build proofs just from conclusions, rather than from plain formulae [Sider]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
13697 Valuations in PC assign truth values to formulas relative to variable assignments [Sider]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
13684 The semantical notion of a logical truth is validity, being true in all interpretations [Sider]
13704 It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13724 In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider]
5. Theory of Logic / K. Features of Logics / 4. Completeness
13698 In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13699 Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider]
5. Theory of Logic / L. Paradox / 1. Paradox
6007 If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
6006 If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
6008 Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]