15 ideas
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') |
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') |
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. |
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. |
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'. |
472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
Full Idea: No existing things would be clear to anyone, either in themselves or in their relationship to one another, unless there existed Number and its essence. | |
From: Philolaus (On the Cosmos (lost) [c.435 BCE], B11), quoted by John Stobaeus - Anthology 1.03.8 |
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. |
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. |
1518 | Everything must involve numbers, or it couldn't be thought about or known [Philolaus] |
Full Idea: Everything which is known has number, because otherwise it is impossible for anything to be the object of thought or knowledge. | |
From: Philolaus (On the Cosmos (lost) [c.435 BCE], B04), quoted by John Stobaeus - Anthology 1.21.7b |
1519 | Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus] |
Full Idea: It would have been impossible for the dissimilar and incompatible sources to have been made into an orderly universe unless harmony had been present in some form or other. | |
From: Philolaus (On the Cosmos (lost) [c.435 BCE], B06), quoted by John Stobaeus - Anthology 1.21.7d |
473 | There is no falsehood in harmony and number, only in irrational things [Philolaus] |
Full Idea: The nature of number and harmony admits of no falsehood; for this is unrelated to them. Falsehood and envy belong to the nature of the Unlimited and the Unintelligent and the Irrational. | |
From: Philolaus (On the Cosmos (lost) [c.435 BCE], B11), quoted by (who?) - where? |
469 | Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited [Philolaus] |
Full Idea: Since it is plain that existing things are neither wholly from the Limiting, nor wholly from the Unlimited, clearly the cosmos and its contents were fitted together from both the Limiting and the Unlimited. | |
From: Philolaus (On the Cosmos (lost) [c.435 BCE], B02), quoted by John Stobaeus - Anthology 1.21.7a |
476 | Self-created numbers make the universe stable [Philolaus] |
Full Idea: Number is the ruling and self-created bond which maintains the everlasting stability of the contents of the universe. | |
From: Philolaus (On the Cosmos (lost) [c.435 BCE], B23), quoted by (who?) - where? |
1787 | Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius] |
Full Idea: Philolaus was the first person to affirm that the earth moves in a circle. | |
From: report of Philolaus (On the Cosmos (lost) [c.435 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 08.Ph.3 |