Combining Texts

Ideas for 'The Definition of Good', 'Logic for Philosophy' and 'Introduction to Virtue Ethics'

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12 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
13689 'Theorems' are formulas provable from no premises at all [Sider]
     Full Idea: Formulas provable from no premises at all are often called 'theorems'.
     From: Theodore Sider (Logic for Philosophy [2010], 2.6)
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
13705 Truth tables assume truth functionality, and are just pictures of truth functions [Sider]
     Full Idea: The method of truth tables assumes truth functionality. Truth tables are just pictures of truth functions.
     From: Theodore Sider (Logic for Philosophy [2010], 6.3)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
13706 Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider]
     Full Idea: Deontic accessibility seems not to be reflexive (that it ought to be true doesn't make it true). One could argue that it is serial (that there is always a world where something is acceptable).
     From: Theodore Sider (Logic for Philosophy [2010], 6.3.1)
13710 In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider]
     Full Idea: In D we add to K a new axiom saying that 'what's necessary is possible' (□φ→◊φ), ..and it can then be proved that tautologies are possible and contradictions are not necessary.
     From: Theodore Sider (Logic for Philosophy [2010], 6.4.2)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
13711 System B introduces iterated modalities [Sider]
     Full Idea: With system B we begin to be able to say something about iterated modalities. ..S4 then takes a different stand on the iterated modalities, and neither is an extension of the other.
     From: Theodore Sider (Logic for Philosophy [2010], 6.4.4)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
13708 S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider]
     Full Idea: S5 is the strongest system, since it has the most valid formulas. That's because it has the fewest models; it's easy to be S5-valid since there are so few potentially falsifying models. K is the weakest system, for opposite reasons.
     From: Theodore Sider (Logic for Philosophy [2010], 6.3.2)
     A reaction: Interestingly, the orthodox view is that S5 is the correct logic for metaphysics, but it sounds a bit lax. Compare Idea 13707.
4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
13712 Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider]
     Full Idea: Epistemic accessibility should be required to be reflexive (allowing Kφ→φ). S4 allows the 'KK principle', or 'positive introspection' (Kφ→KKφ), and S5 allows 'negative introspection' (¬Kφ→K¬Kφ).
     From: Theodore Sider (Logic for Philosophy [2010], 7.2)
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
13714 We can treat modal worlds as different times [Sider]
     Full Idea: We can think of the worlds of modal logic as being times, rather than 'possible' worlds.
     From: Theodore Sider (Logic for Philosophy [2010], 7.3.3)
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
13720 Converse Barcan Formula: □∀αφ→∀α□φ [Sider]
     Full Idea: The Converse Barcan Formula reads □∀αφ→∀α□φ (or an equivalent using ◊).
     From: Theodore Sider (Logic for Philosophy [2010], 9.5.2)
     A reaction: I would read that as 'if all the αs happen to be φ, then αs have to be φ'. Put like that, I would have thought that it was obviously false. Sider points out that some new object could turn up which isn't φ.
13718 The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider]
     Full Idea: The Barcan Formula ∀x□Fx→□∀xFx is often regarded as a defect of Simple Quantified Modal Logic, though this most clearly seen in its equivalent form ◊∃xFx→∃x◊Fx.
     From: Theodore Sider (Logic for Philosophy [2010], 9.5.2)
     A reaction: [See Idea 13719 for an explanation why it might be a defect] I translate the first one as 'if xs must be F, then they are always F', and the second one as 'for x to be possibly F, there must exist an x which is possibly F'. Modality needs existence.
13723 System B is needed to prove the Barcan Formula [Sider]
     Full Idea: The proof of the Barcan Formula require System B.
     From: Theodore Sider (Logic for Philosophy [2010], 9.7)
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
13715 You can employ intuitionist logic without intuitionism about mathematics [Sider]
     Full Idea: Not everyone who employs intuitionistic logic is an intuitionist about mathematics.
     From: Theodore Sider (Logic for Philosophy [2010], 7.4.1)
     A reaction: This seems worthy of note, since it may be tempting to reject the logic because of the implausibility of the philosophy of mathematics. I must take intuitionist logic more seriously.