display all the ideas for this combination of texts
12 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). |
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. |
14684 | A world is 'accessible' to another iff the first is possible according to the second [Salmon,N] |
Full Idea: A world w' is accessible to a consistent world w if and only if w' is possible in w. Being 'inaccessible to' or 'possible relative to' a consistent world is simply being possible according to that world, nothing more and nothing less. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) | |
A reaction: More illuminating than just saying that w can 'see' w'. Accessibility is internal to worIds. It gives some connection to why we spend time examining modal logic. There is no more important metaphysical notion than what is possible according to actuality. |
14669 | For metaphysics, T may be the only correct system of modal logic [Salmon,N] |
Full Idea: Insofar as modal logic is concerned exclusively with the logic of metaphysical modality, ..T may well be the one and only (strongest) correct system of (first-order) propositional logic. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro) | |
A reaction: This contrasts sharply with the orthodox view, that S5 (or at the very least S4) is the correct system for metaphysics. |
14692 | System B implies that possibly-being-realized is an essential property of the world [Salmon,N] |
Full Idea: Friends of B modal logic commit themselves to the loaded claim that it is logically true that the property of possibly being realized (or being a way things might have been) is an essential property of the world. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], V) | |
A reaction: I think this 'loaded' formulation captures quite nicely the dispositional view I favour, that the possibilities of the actual world are built into the actual world, and define its nature just as much as the 'categorial' facts do. |
14667 | System B has not been justified as fallacy-free for reasoning on what might have been [Salmon,N] |
Full Idea: Even the conventionally accepted system B, which is weaker than S5 and independent of S4, has not been adequately justified as a fallacy-free system of reasoning about what might have been. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro) |
14668 | In B it seems logically possible to have both p true and p is necessarily possibly false [Salmon,N] |
Full Idea: The characteristic of B has the form φ⊃□◊φ. ...Even if these axioms are necessarily true, it seems logically possible for p to be true while the proposition that p is necessarily possible is at the same time false. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro) |
14671 | What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N] |
Full Idea: We can say of a wooden table that it would have been possible for it to have originated from some different matter, even though it is not actually possible. So what is necessary fails to be necessarily necessary, and S4 modal logic is fallacious. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], I) | |
A reaction: [compressed] |
14686 | S5 modal logic ignores accessibility altogether [Salmon,N] |
Full Idea: When we ignore accessibility altogether, we have finally zeroed in on S5 modal logic. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) |
14691 | S5 believers say that-things-might-have-been-that-way is essential to ways things might have been [Salmon,N] |
Full Idea: Believers in S5 as a correct system of propositional reasoning about what might have been must claim that it is an essential property of any way things might have been that things might have been that way. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], V) | |
A reaction: Salmon is working in a view where you are probably safe to substitute 'necessary' for 'essential' without loss of meaning. |
14693 | The unsatisfactory counterpart-theory allows the retention of S5 [Salmon,N] |
Full Idea: Counterpart-theoretic modal semantics allows for the retention of S5 modal propositional logic, at a considerable cost. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], V n18) | |
A reaction: See the other ideas in this paper by Salmon for his general attack on S5 as the appropriate system for metaphysical necessity. He favours the very modest System T. |
14670 | Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..) [Salmon,N] |
Full Idea: Metaphysical modal logic concerns metaphysical (or alethic) necessity and metaphysical (alethic) possibility, or necessity and possibility tout court - as opposed to such other types of modality as physical necessity, epistemic necessity etc. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro n2) |