Combining Texts

All the ideas for 'The Definition of Good', 'Mathematics without Numbers' and 'Formal and Material Consequence'

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11 ideas

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'.

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism

8698	Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
	Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided.
	From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3
	A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'?

9557	Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
	Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort.
	From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3
	A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world).

10263	Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
	Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us.
	From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3
	A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities?

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.

23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism

18671	The ground for an attitude is not a thing's 'goodness', but its concrete characteristics [Ewing]
	Full Idea: The ground for an attitude lies not in some other ethical concept, goodness, but in the concrete, factual characteristics of what we pronounce good. ...We shall not be better off if we interpolate an indefinable characteristic of goodness besides.
	From: A.C. Ewing (The Definition of Good [1948], p.172), quoted by Francesco Orsi - Value Theory 1.4
	A reaction: This is a forerunner of Scanlon's Buck-Passing theory of the source of value (in other properties). I approve of this approach. If I say 'actually this very strong cheese is really good', I'm not adding goodness to the cheese.