Combining Philosophers
Ideas for David Bostock, Hugo Grotius and Michael Lockwood
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18 ideas
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
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13439
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Venn Diagrams map three predicates into eight compartments, then look for the conclusion [Bostock]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
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13421
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'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope [Bostock]
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13422
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'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope [Bostock]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
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13355
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'Disjunction' says that Γ,φ∨ψ|= iff Γ,φ|= and Γ,ψ|= [Bostock]
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13350
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'Assumptions' says that a formula entails itself (φ|=φ) [Bostock]
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13351
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'Thinning' allows that if premisses entail a conclusion, then adding further premisses makes no difference [Bostock]
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13356
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The 'conditional' is that Γ|=φ→ψ iff Γ,φ|=ψ [Bostock]
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13352
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'Cutting' allows that if x is proved, and adding y then proves z, you can go straight to z [Bostock]
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13353
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'Negation' says that Γ,¬φ|= iff Γ|=φ [Bostock]
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13354
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'Conjunction' says that Γ|=φ∧ψ iff Γ|=φ and Γ|=ψ [Bostock]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
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13610
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A logic with ¬ and → needs three axiom-schemas and one rule as foundation [Bostock]
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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
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18122
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Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock]
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4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
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13846
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A 'free' logic can have empty names, and a 'universally free' logic can have empty domains [Bostock]
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
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18114
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There is no single agreed structure for set theory [Bostock]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
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18107
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A 'proper class' cannot be a member of anything [Bostock]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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18115
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We could add axioms to make sets either as small or as large as possible [Bostock]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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18139
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The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
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18105
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Replacement enforces a 'limitation of size' test for the existence of sets [Bostock]
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