Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, Ian Rumfitt and Heraclitus

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21 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
18815 Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
9390 Logic guides thinking, but it isn't a substitute for it [Rumfitt]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
18804 The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt]
18805 Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt]
18827 If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
12195 Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
12199 There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
12201 We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]
18813 Logical consequence is a relation that can extended into further statements [Rumfitt]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
18808 Normal deduction presupposes the Cut Law [Rumfitt]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
18840 When faced with vague statements, Bivalence is not a compelling principle [Rumfitt]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
1312 If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus]
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
12194 Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
18802 In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt]
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
12198 Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
18800 Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
18809 Logical truths are just the assumption-free by-products of logical rules [Rumfitt]
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
18807 Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt]