Combining Philosophers
Ideas for Hilbert,D/Ackermann,W, Socrates and David Bostock
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10 ideas
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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'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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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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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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13354
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'Conjunction' says that Γ|=φ∧ψ iff Γ|=φ and Γ|=ψ [Bostock]
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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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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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