Combining Philosophers
Ideas for Homer, Gerhard Gentzen and Hartry Field
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8 ideas
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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11022
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Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
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10260
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Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
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11065
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The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
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11023
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The logical connectives are 'defined' by their introduction rules [Gentzen]
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11213
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Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
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5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
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13832
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Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]
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5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
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10819
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Tarski gives us the account of truth needed to build a group of true sentences in a model [Field,H]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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10827
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Model theory is unusual in restricting the range of the quantifiers [Field,H]
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