Combining Texts
Ideas for
'Philosophy of Logic', 'Logic for Philosophy' and 'The Advancement of Learning'
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16 ideas
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
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18953
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Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam]
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4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
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18949
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The universal syllogism is now expressed as the transitivity of subclasses [Putnam]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
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13689
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'Theorems' are formulas provable from no premises at all [Sider]
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4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
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13705
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Truth tables assume truth functionality, and are just pictures of truth functions [Sider]
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4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC
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18952
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'⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
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13706
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Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider]
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13710
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In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
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13711
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System B introduces iterated modalities [Sider]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
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13708
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S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider]
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4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
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13712
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Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider]
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4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
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13714
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We can treat modal worlds as different times [Sider]
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4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
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13720
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Converse Barcan Formula: □∀αφ→∀α□φ [Sider]
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13718
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The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider]
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13723
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System B is needed to prove the Barcan Formula [Sider]
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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
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13715
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You can employ intuitionist logic without intuitionism about mathematics [Sider]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
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18958
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In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam]
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