Combining Texts
Ideas for
'Folk Psychology', 'Logic for Philosophy' and 'Could There Be Unicorns?'
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14 ideas
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
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16951
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It was realised that possible worlds covered all modal logics, if they had a structure [Dummett]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
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16952
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If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett]
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16953
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Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett]
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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 / d. System T
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16960
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If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett]
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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 / g. System S4
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16958
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In S4 the actual world has a special place [Dummett]
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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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