Combining Philosophers
Ideas for Hermarchus, Empedocles and Ian Rumfitt
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20 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211
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If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
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18815
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Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt]
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5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
9390
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Logic guides thinking, but it isn't a substitute for it [Rumfitt]
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5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
18805
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Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt]
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18804
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The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt]
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18827
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If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt]
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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
12195
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Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
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12199
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There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
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12201
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We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]
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18813
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Logical consequence is a relation that can extended into further statements [Rumfitt]
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5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
18808
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Normal deduction presupposes the Cut Law [Rumfitt]
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5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
18840
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When faced with vague statements, Bivalence is not a compelling principle [Rumfitt]
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5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
12194
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Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11212
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The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
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11210
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Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
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18802
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In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt]
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5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
12198
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Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]
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5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
18800
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Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
18809
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Logical truths are just the assumption-free by-products of logical rules [Rumfitt]
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5. Theory of Logic / K. Features of Logics / 10. Monotonicity
18807
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Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt]
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