Combining Texts
Ideas for
'On Motion', 'Action' and 'Logic for Philosophy'
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20 ideas
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
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13678
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The most popular account of logical consequence is the semantic or model-theoretic one [Sider]
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13679
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Maybe logical consequence is more a matter of provability than of truth-preservation [Sider]
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13682
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Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider]
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13680
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Maybe logical consequence is a primitive notion [Sider]
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5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
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13722
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A 'theorem' is an axiom, or the last line of a legitimate proof [Sider]
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
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13696
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When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider]
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5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
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13700
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A 'total' function must always produce an output for a given domain [Sider]
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5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
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13703
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λ can treat 'is cold and hungry' as a single predicate [Sider]
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5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
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13688
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Good axioms should be indisputable logical truths [Sider]
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13687
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No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider]
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5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
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13690
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Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider]
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13691
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Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider]
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5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
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13685
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Natural deduction helpfully allows reasoning with assumptions [Sider]
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5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
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13686
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We can build proofs just from conclusions, rather than from plain formulae [Sider]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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13697
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Valuations in PC assign truth values to formulas relative to variable assignments [Sider]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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13684
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The semantical notion of a logical truth is validity, being true in all interpretations [Sider]
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13704
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It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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13724
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In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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13698
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In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
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13699
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Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider]
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