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Ideas for
'What is Logic?st1=Ian Hacking', 'Nihilism without Self-Contradiction' and 'Grundlagen der Arithmetik (Foundations)'
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10 ideas
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
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'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
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Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
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Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
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Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence [Frege, by Burge]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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The null set is only defensible if it is the extension of an empty concept [Frege, by Burge]
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It is because a concept can be empty that there is such a thing as the empty class [Frege, by Dummett]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
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We can introduce new objects, as equivalence classes of objects already known [Frege, by Dummett]
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Frege introduced the standard device, of defining logical objects with equivalence classes [Frege, by Dummett]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
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Frege, unlike Russell, has infinite individuals because numbers are individuals [Frege, by Bostock]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
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A class is, for Frege, the extension of a concept [Frege, by Dummett]
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