Combining Texts

All the ideas for 'fragments/reports', 'The Laws of Thought' and 'Could There Be Unicorns?'

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14 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
8083 Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]
     Full Idea: Boole proposed to use the entire apparatus of a school algebra class, with operations such as addition and multiplication, methods to solve equations, and the like, to produce an algebra of thought.
     From: report of George Boole (The Laws of Thought [1854]) by Keith Devlin - Goodbye Descartes Ch.3
     A reaction: The Stoics didn’t use any algebraic notation for their study of propositions, so Boole's idea launched full blown propositional logic, and the rest of modern logic followed. Nice one.
7727 Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner]
     Full Idea: Boole introduced a new symbolic notation in which it was possible to represent both syllogisms and propositional arguments, ...but not both at once.
     From: report of George Boole (The Laws of Thought [1854], Ch.3) by Joan Weiner - Frege
     A reaction: How important is the development of symbolic notations for the advancement of civilisations? Is there a perfect notation, as used in logical heaven?
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
16951 It was realised that possible worlds covered all modal logics, if they had a structure [Dummett]
     Full Idea: The new discovery was that with a suitable structure imposed on the space of possible worlds, the Leibnizian idea would work for all modal logics.
     From: Michael Dummett (Could There Be Unicorns? [1983], 1)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
16953 Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett]
     Full Idea: If T is only possible if S obtains, T and S hold in the actual world, and S does not obtain in world v possible relative to the actual world, then the actual is not possible relative to v, since T holds in the actual. Accessibility can't be symmetrical.
     From: Michael Dummett (Could There Be Unicorns? [1983], 1)
16952 If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett]
     Full Idea: If T is only possible if S obtains, and S is possible but doesn't obtain, then T is only possible in the world where S obtains, but T is not possible in the actual world. It follows that the relation of relative possibility is not transitive.
     From: Michael Dummett (Could There Be Unicorns? [1983], 1)
     A reaction: [compressed]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
16960 If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett]
     Full Idea: If some world is 'a way the world might be considered to be if things were different in a certain respect', that might show that the accessibility relation should not be taken to be transitive, and we should have to adopt modal logic T.
     From: Michael Dummett (Could There Be Unicorns? [1983], 8)
     A reaction: He has already rejected symmetry from the relation, for reasons concerning relative identity. He is torn between T and S4, but rejects S5, and opts not to discuss it.
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
16958 In S4 the actual world has a special place [Dummett]
     Full Idea: In S4 logic the actual world is, in itself, special, not just from our point of view.
     From: Michael Dummett (Could There Be Unicorns? [1983], 8)
     A reaction: S4 lacks symmetricality, so 'you can get there, but you can't get back', which makes the starting point special. So if you think the actual world has a special place in modal metaphysics, you must reject S5?
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
8686 Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
     Full Idea: Boole (followed by Frege) began to turn logic from a branch of philosophy into a branch of mathematics. He brought an algebraic approach to propositions, and introduced the notion of a quantifier and a type of probabilistic reasoning.
     From: report of George Boole (The Laws of Thought [1854], 3.2) by Michčle Friend - Introducing the Philosophy of Mathematics
     A reaction: The result was that logic not only became more mathematical, but also more specialised. We now have two types of philosopher, those steeped in mathematical logic and the rest. They don't always sing from the same songsheet.
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
22277 Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
     Full Idea: Boole's work was an early example of the axiomatic method, whereby intellectual economy is achieved by studying a set of axioms in which the primitive terms have multiple interpretations.
     From: report of George Boole (The Laws of Thought [1854]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Boole'
     A reaction: Unclear about this. I suppose the axioms are just syntactic, and a range of semantic interpretations can be applied. Are De Morgan's Laws interpretations, or implications of the syntactic axioms? The latter, I think.
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
16957 Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett]
     Full Idea: The equation of a possible world with the way that the (actual) world might be is wrong: the way a distant world might be is not a way the world might be, but a way we might allow it to be given how some intervening world might be.
     From: Michael Dummett (Could There Be Unicorns? [1983], 8)
     A reaction: The point here is that a system of possible worlds must include relative possibilities as well as actual possibilities. Dummett argues against S5 modal logic, which makes them all equal. Things impossible here might become possible. Nice.
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
16959 If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett]
     Full Idea: If our space of possible worlds has no structure, as in the semantics for S5, then, from the standpoint of the semantics, all possible worlds are on the same footing; it then becomes difficult to resist the claim that all are equally real.
     From: Michael Dummett (Could There Be Unicorns? [1983], 8)
     A reaction: This is a rather startling and interesting claim, given that modern philosophy seems full of thinkers who both espouse S5 for metaphysics, and also deny Lewisian realism about possible worlds. I'll ponder that one. Must read the new Williamson….
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
     Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
     From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
16956 To explain generosity in a person, you must understand a generous action [Dummett]
     Full Idea: It cannot be explained what it is for a person to be generous without first explaining what it is for an action to be generous.
     From: Michael Dummett (Could There Be Unicorns? [1983], 4)
     A reaction: I presume a slot machine can't be 'generous', even if it favours the punter, so you can't specify a generous action without making reference to the person. A benign circle, as Aristotle says.
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
16954 Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett]
     Full Idea: In my view, Kripke's promotion of 'natural kinds', coverning chemical substances and animal and plant species, is unfortunate, since these are rather different types of things, and words used for them behave differently.
     From: Michael Dummett (Could There Be Unicorns? [1983], 2)
     A reaction: My view is that the only significant difference among natural kinds is their degree of stability in character. Presumably particles, elements and particular molecules are fairly invariant, but living things evolve.