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All the ideas for 'Commentary on 'De Anima'', 'Formal and Material Consequence' and 'The Laws of Thought'

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12 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?

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 Michèle 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 / A. Overview of Logic / 4. Pure Logic

14187	If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read]
	Full Idea: The topic-neutrality of logic need not mean there is a pure subject matter for logic; rather, that the logician may need to go everywhere, into mathematics and even into metaphysics.
	From: Stephen Read (Formal and Material Consequence [1994], 'Logic')

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

14188	Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read]
	Full Idea: Belief that every valid argument is valid in virtue of form is a myth. ..Validity is a question of the impossibility of true premises and false conclusion for whatever reason, and some arguments are materially valid and the reason is not purely logical.
	From: Stephen Read (Formal and Material Consequence [1994], 'Logic')
	A reaction: An example of a non-logical reason is the transitive nature of 'taller than'. Conceptual connections are the usual example, as in 'it's red so it is coloured'. This seems to be a defence of the priority of semantic consequence in logic.

14182	If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read]
	Full Idea: In 'A is taller than B, and B is taller than C, so A is taller than C' this can been seen as a matter of meaning - it is part of the meaning of 'taller' that it is transitive, but not of logic. Logic is now seen as the study of formal consequence.
	From: Stephen Read (Formal and Material Consequence [1994], 'Reduct')
	A reaction: I think I find this approach quite appealing. Obviously you can reason about taller-than relations, by putting the concepts together like jigsaw pieces, but I tend to think of logic as something which is necessarily implementable on a machine.

14183	Maybe arguments are only valid when suppressed premises are all stated - but why? [Read]
	Full Idea: Maybe some arguments are really only valid when a suppressed premise is made explicit, as when we say that 'taller than' is a transitive concept. ...But what is added by making the hidden premise explicit? It cannot alter the soundness of the argument.
	From: Stephen Read (Formal and Material Consequence [1994], 'Suppress')

5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens

14184	In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read]
	Full Idea: A puzzle about modus ponens is that the major premise is either false or unnecessary: A, If A then B / so B. If the major premise is true, then B follows from A, so the major premise is redundant. So it is false or not needed, and contributes nothing.
	From: Stephen Read (Formal and Material Consequence [1994], 'Repres')
	A reaction: Not sure which is the 'major premise' here, but it seems to be saying that the 'if A then B' is redundant. If I say 'it's raining so the grass is wet', it seems pointless to slip in the middle the remark that rain implies wet grass. Good point.

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

14186	Logical connectives contain no information, but just record combination relations between facts [Read]
	Full Idea: The logical connectives are useful for bundling information, that B follows from A, or that one of A or B is true. ..They import no information of their own, but serve to record combinations of other facts.
	From: Stephen Read (Formal and Material Consequence [1994], 'Repres')
	A reaction: Anyone who suggests a link between logic and 'facts' gets my vote, so this sounds a promising idea. However, logical truths have a high degree of generality, which seems somehow above the 'facts'.

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 / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals

14185	Conditionals are just a shorthand for some proof, leaving out the details [Read]
	Full Idea: Truth enables us to carry various reports around under certain descriptions ('what Iain said') without all the bothersome detail. Similarly, conditionals enable us to transmit a record of proof without its detail.
	From: Stephen Read (Formal and Material Consequence [1994], 'Repres')
	A reaction: This is his proposed Redundancy Theory of conditionals. It grows out of the problem with Modus Ponens mentioned in Idea 14184. To say that there is always an implied 'proof' seems a large claim.

22. Metaethics / B. Value / 2. Values / e. Death

16764	The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus]
	Full Idea: Every accident of a living thing, as well as all its organs and temperaments and its dispositions are conserved by the soul. We see this from experience, since when that soul recedes, all these dissolve and become corrupted.
	From: Franciscus Toletus (Commentary on 'De Anima' [1572], II.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.5
	A reaction: A nice example of observing a phenemonon, but not being able to observe the dependence relation the right way round. Compare Descartes in Idea 16763.