display all the ideas for this combination of texts
14 ideas
8077 | Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin] |
Full Idea: In Stoic logic propositions are treated the way atoms are treated in present-day chemistry, where the focus is on the way atoms fit together to form molecules, rather than on the internal structure of the atoms. | |
From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2 | |
A reaction: A nice analogy to explain the nature of Propositional Logic, which was invented by the Stoics (N.B. after Aristotle had invented predicate logic). |
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) |
20791 | Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius] |
Full Idea: Chrysippus has five indemonstrables that do not need demonstration:1) If 1st the 2nd, but 1st, so 2nd; 2) If 1st the 2nd, but not 2nd, so not 1st; 3) Not 1st and 2nd, the 1st, so not 2nd; 4) 1st or 2nd, the 1st, so not 2nd; 5) 1st or 2nd, not 2nd, so 1st. | |
From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.80-81 | |
A reaction: [from his lost text 'Dialectics'; squashed to fit into one quote] 1) is Modus Ponens, 2) is Modus Tollens. 4) and 5) are Disjunctive Syllogisms. 3) seems a bit complex to be an indemonstrable. |
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) |
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) |
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) |
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. |
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) |
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) |
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) |
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. |