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Ideas for
'Thinking About Mathematics', 'Words without Objects' and 'The Boundary Stones of Thought'
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14 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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 / 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
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 / 2. Excluded Middle
8729
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Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
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 / E. Structures of Logic / 4. Variables in Logic
12797
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If plural variables have 'some values', then non-count variables have 'some value' [Laycock]
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5. Theory of Logic / G. Quantification / 6. Plural Quantification
12794
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Plurals are semantical but not ontological [Laycock]
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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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