86 ideas
| 9108 | From an impossibility anything follows [William of Ockham] |
| Full Idea: From an impossibility anything follows ('quod ex impossibili sequitur quodlibet'). | |
| From: William of Ockham (Summa totius logicae [1323], III.c.xxxvi) | |
| A reaction: The hallmark of a true logician, I suspect, is that this opinion is really meaningful and important to them. They yearn to follow the logic wherever it leads. Common sense would seem to say that absolutely nothing follows from an impossibility. |
| 16676 | Why use more things when fewer will do? [William of Ockham] |
| Full Idea: It is pointless to do through more things something that can be done through fewer. | |
| From: William of Ockham (Tractatus de corpore Christi [1323], Ch. 29), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.3 | |
| A reaction: The more famous formulation isn't found in his works, so I'm delighted to find an authentic quotation from the man. |
| 6806 | Do not multiply entities beyond necessity [William of Ockham] |
| Full Idea: Do not multiply entities beyond necessity. | |
| From: William of Ockham (works [1335]) | |
| A reaction: This is the classic statement of Ockham's Razor, though it is not found in his printed works. It appears to be mainly aimed at Plato's Theory of Forms. It is taken to refer to types of entities, not numbers. One seraph is as bad as a hundred. |
| 9107 | A proposition is true if its subject and predicate stand for the same thing [William of Ockham] |
| Full Idea: If in the proposition 'This is an angel' subject and predicate stand for the same thing, the proposition is true. | |
| From: William of Ockham (Summa totius logicae [1323], II.c.ii) | |
| A reaction: An interesting statement of what looks like a correspondence theory, employing the idea that both the subject and the predicate have a reference. I think Frege would say that 'x is an angel' is unsaturated, and so lacks reference. |
| 16300 | Ockham had an early axiomatic account of truth [William of Ockham, by Halbach] |
| Full Idea: Theories structurally very similar to axiomatic compositional theories of truth can be found in Ockham's 'Summa Logicae'. | |
| From: report of William of Ockham (Summa totius logicae [1323]) by Volker Halbach - Axiomatic Theories of Truth 3 |
| 10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
| Full Idea: Three traditional names for rules are 'Simplification' (P from 'P and Q'), 'Addition' ('P or Q' from P), and 'Disjunctive Syllogism' (Q from 'P or Q' and 'not-P'). | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
| Full Idea: In S4 necessity is said to be informal 'provability', and in S5 it is said to be 'true in every possible world'. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: It seems that the S4 version is proof-theoretic, and the S5 version is semantic. |
| 11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
| Full Idea: In fuzzy logic, besides fuzzy predicates, which define fuzzy sets, there are also fuzzy quantifiers (such as 'most' and 'few') and fuzzy modifiers (such as 'usually'). | |
| From: Stephen Read (Thinking About Logic [1995], Ch.7) |
| 11011 | Same say there are positive, negative and neuter free logics [Read] |
| Full Idea: It is normal to classify free logics into three sorts; positive free logics (some propositions with empty terms are true), negative free logics (they are false), and neuter free logics (they lack truth-value), though I find this unhelpful and superficial. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.5) |
| 11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
| Full Idea: Hard-headed realism tends to embrace the full Comprehension Principle, that every well-defined concept determines a set. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.8) | |
| A reaction: This sort of thing gets you into trouble with Russell's paradox (though that is presumably meant to be excluded somehow by 'well-defined'). There are lots of diluted Comprehension Principles. |
| 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') |
| 10986 | Not all validity is captured in first-order logic [Read] |
| Full Idea: We must recognise that first-order classical logic is inadequate to describe all valid consequences, that is, all cases in which it is impossible for the premisses to be true and the conclusion false. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: This is despite the fact that first-order logic is 'complete', in the sense that its own truths are all provable. |
| 10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
| Full Idea: The non-emptiness of the domain is characteristic of classical logic. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
| Full Idea: For the realist, study of semantic structures comes before study of proofs. In higher-order logic is has to, for the logics are incomplete. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.9) | |
| A reaction: This seems to be an important general observation about any incomplete system, such as Peano arithmetic. You may dream the old rationalist dream of starting from the beginning and proving everything, but you can't. Start with truth and meaning. |
| 10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
| Full Idea: Those who believe mathematics goes beyond logic use that fact to argue that classical logic is right to exclude second-order logic. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 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') |
| 10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
| Full Idea: A theory of logical consequence, while requiring a conceptual analysis of consequence, also searches for a set of techniques to determine the validity of particular arguments. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
| Full Idea: If classical logic insists that logical consequence is just a matter of the form, we fail to include as valid consequences those inferences whose correctness depends on the connections between non-logical terms (such as 'round' and 'square'). | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: He suggests that an inference such as 'round, so not square' should be labelled as 'materially valid'. |
| 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'. |
| 10973 | A theory is logically closed, which means infinite premisses [Read] |
| Full Idea: A 'theory' is any logically closed set of propositions, ..and since any proposition has infinitely many consequences, including all the logical truths, so that theories have infinitely many premisses. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: Read is introducing this as the essential preliminary to an account of the Compactness Theorem, which relates these infinite premisses to the finite. |
| 11007 | Quantifiers are second-order predicates [Read] |
| Full Idea: Quantifiers are second-order predicates. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.5) | |
| A reaction: [He calls this 'Frege's insight'] They seem to be second-order in Tarski's sense, that they are part of a metalanguage about the sentence, rather than being a part of the sentence. |
| 9106 | The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham] |
| Full Idea: The syncategorematic word 'every' does not signify any fixed thing, but when added to 'man' it makes the term 'man' stand for all men actually. | |
| From: William of Ockham (Summa totius logicae [1323], I.c.iv) | |
| A reaction: Although quantifiers may have become a part of formal logic with Frege, their importance is seen from Aristotle onwards, and it is clearly a key part of William's understanding of logic. |
| 10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
| Full Idea: The defining factor of second-order logic is that, while the domain of its individual variables may be arbitrary, the range of the first-order variables is all the properties of the objects in its domain (or, thinking extensionally, of the sets objects). | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: The key point is that the domain is 'all' of the properties. How many properties does an object have. You need to decide whether you believe in sparse or abundant properties (I vote for very sparse indeed). |
| 10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
| Full Idea: Logical truth is a degenerate, or extreme, case of consequence. A logical truth is the conclusion of a valid inference with no premisses, or a proposition in the premisses of an argument which is unnecessary or may be suppressed. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10988 | Any first-order theory of sets is inadequate [Read] |
| Full Idea: Any first-order theory of sets is inadequate because of the Löwenheim-Skolem-Tarski property, and the consequent Skolem paradox. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: The limitation is in giving an account of infinities. |
| 10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
| Full Idea: Classical logical consequence is compact, which means that any consequence of an infinite set of propositions (such as a theory) is a consequence of some finite subset of them. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
| Full Idea: Compactness does not deny that an inference can have infinitely many premisses. It can; but classically, it is valid if and only if the conclusion follows from a finite subset of them. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
| Full Idea: Compact consequence undergenerates - there are intuitively valid consequences which it marks as invalid, such as the ω-rule, that if A holds of the natural numbers, then 'for every n, A(n)', but the proof of that would be infinite, for each number. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
| Full Idea: Compactness is a virtue - it makes the consequence relation more manageable; but it is also a limitation - it limits the expressive power of the logic. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: The major limitation is that wholly infinite proofs are not permitted, as in Idea 10977. |
| 11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
| Full Idea: It cannot be self-reference alone that is at fault. Rather, what seems to cause the problems in the paradoxes is the combination of self-reference with falsity. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.6) |
| 11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
| Full Idea: Every potential infinity seems to suggest an actual infinity - e.g. generating successors suggests they are really all there already; cutting the line suggests that the point where the cut is made is already in place. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.8) | |
| A reaction: Finding a new gambit in chess suggests it was there waiting for us, but we obviously invented chess. Daft. |
| 10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
| Full Idea: Second-order arithmetic is categorical - indeed, there is a single formula of second-order logic whose only model is the standard model ω, consisting of just the natural numbers, with all of arithmetic following. It is nevertheless incomplete. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: This is the main reason why second-order logic has a big fan club, despite the logic being incomplete (as well as the arithmetic). |
| 10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
| Full Idea: Second-order arithmetic can rule out the non-standard models (with non-standard numbers). Its induction axiom crucially refers to 'any' property, which gives the needed categoricity for the models. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) |
| 10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
| Full Idea: The Von Neumann numbers have a structural isomorphism to the natural numbers - each number is the set of all its predecessors, so 2 is the set of 0 and 1. This helps proofs, but is unacceptable. 2 is not a set with two members, or a member of 3. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) |
| 9113 | Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham] |
| Full Idea: Number is nothing but the actual numbered things themselves. Hence just as unity is not an accident added to the thing which is one, so number is not an accident of the things which are numbered. | |
| From: William of Ockham (Summa totius logicae [1323], I.c.xliv) | |
| A reaction: [William does not necessarily agree with this view] It strikes me as a key point here that any account of the numbers had better work for 'one', though 'zero' might be treated differently. Some people seem to think unity is a property of things. |
| 9110 | The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham] |
| Full Idea: The words 'thing' and 'to be' (esse) signify one and the same thing, but the one in the manner of a noun and the other in the manner of a verb. | |
| From: William of Ockham (Summa totius logicae [1323], III,II,c,xxvii) | |
| A reaction: Well said - as you would expect from a thoroughgoing nominalist. I would have thought that this was the last word on the subject of Being, thus rendering any need for me to read Heidegger quite superfluous. Or am I missing something? |
| 11016 | Would a language without vagueness be usable at all? [Read] |
| Full Idea: We must ask whether a language without vagueness would be usable at all. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.7) | |
| A reaction: Popper makes a similar remark somewhere, with which I heartily agreed. This is the idea of 'spreading the word' over the world, which seems the right way of understanding it. |
| 11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
| Full Idea: The supervaluation approach to vagueness is to construe vague predicates not as ones with fuzzy borderlines and no cut-off, but as having a cut-off somewhere, but in no particular place. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.7) | |
| A reaction: Presumably you narrow down the gap by supervaluation, then split the difference to get a definite value. |
| 11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
| Full Idea: A 'supervaluation' says a proposition is true if it is true in all classical extensions of the original partial valuation. Thus 'A or not-A' has no valuation for an empty name, but if 'extended' to make A true or not-true, not-A always has opposite value. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.5) |
| 11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
| Full Idea: In supervaluations, the Law of Identity has no value for empty names, and remains so if extended. The Indiscernibility of Identicals also fails if extending it for non-denoting terms, where Fa comes out true and Fb false. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.5) |
| 16608 | Ockham was an anti-realist about the categories [William of Ockham, by Pasnau] |
| Full Idea: Ockham is the scholastic paradigm of anti-realism with respect to the categories. | |
| From: report of William of Ockham (Summula philosophiae naturalis [1320]) by Robert Pasnau - Metaphysical Themes 1274-1671 05.3 | |
| A reaction: These are the ten categories mentioned in Aristotle's book 'Categories'. |
| 16654 | Our words and concepts don't always correspond to what is out there [William of Ockham] |
| Full Idea: It should not be said that as distinct words and intentions or concepts are distinct from one another, so too the corresponding things are distinct. Those distinctions do not always line up with distinctions among things that are signified. | |
| From: William of Ockham (Predest.,God's foreknowledge and contingents [1320], 7.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.2 | |
| A reaction: [compressed] This is the great nominalist opponent of the idea that Aristotle's ten categories give an accurate map of reality. He proposed just substance and accidents, and based categorisation on the questions we ask. |
| 18529 | Relations are expressed either as absolute facts, or by a relational concept [William of Ockham] |
| Full Idea: Socrates and Plato are similar if they are both white. Yet the mind can express this either by an 'absolute concept' (as 'Socrates is white' and 'Plato is white'), or by a 'relative concept', as 'Socrates is similar to Plato with respect to whiteness. | |
| From: William of Ockham (Seven Quodlibets [1332], VI q.25), quoted by John Heil - The Universe as We Find It 7 | |
| A reaction: Presumably he takes the facts of the matter to be the absolute concept, and the relative concept to be a contribution of the intellect. |
| 22132 | Species and genera are individual concepts which naturally signify many individuals [William of Ockham] |
| Full Idea: In his mature nominalism, species and genera are identified with certain mental qualities called concepts or intentions of the mind. Ontologically they are individuals too, like everthing else, ...but they naturally signify many different individuals. | |
| From: William of Ockham (works [1335]), quoted by Claude Panaccio - William of Ockham p.1056 | |
| A reaction: 'Naturally' is the key word, because the concepts are not fictions, but natural responses to encountering individuals in the world. I am an Ockhamist. |
| 9103 | A universal is not a real feature of objects, but only a thought-object in the mind [William of Ockham] |
| Full Idea: I maintain that a universal is not something real that exists in a subject [of inherence], either inside or outside the mind, but that it has being only as a thought-object in the mind. | |
| From: William of Ockham (Ordinatio [1320], DII Qviii prima redactio) | |
| A reaction: [A footnote says that William later abandoned this view] I don't see a clear distinction here between having real existence in the mind, and being a thought-object in the mind. Maybe we should say 'merely' a thought-object? |
| 15388 | Universals are single things, and only universal in what they signify [William of Ockham] |
| Full Idea: Every universal is one particular thing and it is not a universal except in its signification, in its signifying many thing. | |
| From: William of Ockham (Summa totius logicae [1323]), quoted by Claude Panaccio - Medieval Problem of Universals 'William' | |
| A reaction: Sounds as if William might have liked tropes. It seems to leave the problem unanswered (the 'ostrich' problem?). How are they able to signify in this universal way, if each thing is just distinct and particular? |
| 10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
| Full Idea: The haecceitist (a neologism coined by Duns Scotus, pronounced 'hex-ee-it-ist', meaning literally 'thisness') believes that each thing has an individual essence, a set of properties which are essential to it. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: This seems to be a difference of opinion over whether a haecceity is a set of essential properties, or a bare particular. The key point is that it is unique to each entity. |
| 16779 | Cut wood doesn't make a new substance, but seems to make separate subjects [William of Ockham] |
| Full Idea: When a piece of wood is divided in two halves, no new substance is generated. But there are now two substances, or the accidents of the two halves would be without a subject. They existed before hand, and were one piece of wood, but not in the same place. | |
| From: William of Ockham (Seven Quodlibets [1332], IV.19), quoted by Richard S. Westfall - Never at Rest: a biography of Isaac Newton 26.2 | |
| A reaction: A nice example, demonstrating that there are substances within substances, contrary to the view of Duns Scotus. If a substance is just a subject for properties, it is hard to know what to make of this case. |
| 16757 | Hot water naturally cools down, which is due to the substantial form of the water [William of Ockham] |
| Full Idea: It is clear to the senses that hot water, if left to its own nature, reverts to coldness; this coldness cannot be caused by anything other than the substantial form of the water. | |
| From: William of Ockham (Seven Quodlibets [1332], III.6), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.4 | |
| A reaction: Unfortunately this is very bad science (even for its time), but it shows how many scholastics treated hylomorphism as a very physical and causal theory. |
| 16599 | Ockham says matter must be extended, so we don't need Quantity [William of Ockham, by Pasnau] |
| Full Idea: Ockham regards Quantity as an entirely superfluous ontological category, …because matter is intrinsically extended. | |
| From: report of William of Ockham (Summula philosophiae naturalis [1320]) by Robert Pasnau - Metaphysical Themes 1274-1671 04.4 |
| 16681 | Matter gets its quantity from condensation and rarefaction, which is just local motion [William of Ockham] |
| Full Idea: Matter is made to have a greater or lesser quantity not through its receiving any absolute accident, but through condensation and rarefaction alone. Parts come more or less close together, which can happen with local motion. | |
| From: William of Ockham (Summula philosophiae naturalis [1320], I.13), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 15.1 | |
| A reaction: This is Ockham at his most modern, rejecting the odd idea of Quantity in favour of a modern corpuscular view of the mere motions of matter. |
| 9109 | If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham] |
| Full Idea: If essence and existence were two things, then no contradiction would be involved if God preserved the essence of a thing in the world without its existence, or vice versa, its existence without its essence; both of which are impossible. | |
| From: William of Ockham (Summa totius logicae [1323], III,II,c,xxvii) | |
| A reaction: Not that William is using the concept of a supreme mind as a tool in argument. His denial of essence as something separable is presumably his denial of the Aristotelian view of universals, as well as of the Platonic view. |
| 16792 | If parts change, the whole changes [William of Ockham] |
| Full Idea: That is not the same whole that does not have the same parts. | |
| From: William of Ockham (Commentary on the Sentences [1320], IV.13), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 29.2 | |
| A reaction: In isolation, this is mereological essentialism (as Pasnau confirms), which is incredibly implausible, if I cease to be the same person when I cut one of my fingernails. |
| 11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
| Full Idea: The equation of 'necessity' with 'true in every possible world' is known as the S5 conception, corresponding to the strongest of C.I.Lewis's five modal systems. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: Are the worlds naturally, or metaphysically, or logically possible? |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| Full Idea: The point of conditionals is to show that one will accept modus ponens. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.3) | |
| A reaction: [He attributes this idea to Frank Jackson] This makes the point, against Grice, that the implication of conditionals is not conversational but a matter of logical convention. See Idea 21396 for a very different view. |
| 10989 | The standard view of conditionals is that they are truth-functional [Read] |
| Full Idea: The standard view of conditionals is that they are truth-functional, that is, that their truth-values are determined by the truth-values of their constituents. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.3) |
| 11017 | Some people even claim that conditionals do not express propositions [Read] |
| Full Idea: Some people even claim that conditionals do not express propositions. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.7) | |
| A reaction: See Idea 14283, where this appears to have been 'proved' by Lewis, and is not just a view held by some people. |
| 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. |
| 10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
| Full Idea: The modal Platonist denies that knowledge always depends on a causal relation. The reality of possible worlds is an ontological requirement, to secure the truth-values of modal propositions. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: [Reply to Idea 10982] This seems to be a case of deriving your metaphyics from your semantics, of which David Lewis seems to be guilty, and which strikes me as misguided. |
| 10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
| Full Idea: If modal Platonism was true, how could we ever know the truth of a modal proposition? | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: I take this to be very important. Our knowledge of modal truths must depend on our knowledge of the actual world. The best answer seems to involve reference to the 'powers' of the actual world. A reply is in Idea 10983. |
| 10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
| Full Idea: There are two main forms of actualism: reductionism, which seeks to construct possible worlds out of some more mundane material; and moderate realism, in which the actual concrete world is contrasted with abstract, but none the less real, possible worlds. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: I am a reductionist, as I do not take abstractions to be 'real' (precisely because they have been 'abstracted' from the things that are real). I think I will call myself a 'scientific modalist' - we build worlds from possibilities, discovered by science. |
| 10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
| Full Idea: A possible world is a complete determination of the truth-values of all propositions over a certain domain. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.2) | |
| A reaction: Even if the domain is very small? Even if the world fitted the logic nicely, but was naturally impossible? |
| 11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
| Full Idea: If each possible world constitutes a concrete reality, then no object can be present in more than one world - objects may have 'counterparts', but cannot be identical with them. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: This explains clearly why in Lewis's modal realist scheme he needs counterparts instead of rigid designation. Sounds like a slippery slope. If you say 'Humphrey might have won the election', who are you talking about? |
| 9089 | Knowledge is a quality existing subjectively in the soul [William of Ockham] |
| Full Idea: Knowledge is a certain quality which exists in the soul as its subject ('existens subiective in anima'). | |
| From: William of Ockham (Expositio super viii libros [1340], Prologue) | |
| A reaction: One might say here that knowledge is a property, and so it might not be susceptible to further analysis. It invites the question of how you could know by introspection that you have got it, which would be an extreme internalist view. |
| 9091 | Sometimes 'knowledge' just concerns the conclusion, sometimes the whole demonstration [William of Ockham] |
| Full Idea: Sometimes 'knowledge' means evident cognition of the conclusion alone, sometimes of the demonstration as a whole. | |
| From: William of Ockham (Expositio super viii libros [1340], Prologue) | |
| A reaction: 'Demonstration' will be something like Greek 'logos' - full understanding, ability to explain and give reasons. William is certainly right about normal usage. I know the answer in a quiz, without any requirement for justifications. |
| 9100 | Our intellect only assents to what we believe to be true [William of Ockham] |
| Full Idea: Our intellect does not assent to anything unless we believe it to be true. | |
| From: William of Ockham (Prologue to Ordinatio [1320], Q 1 N sqq) | |
| A reaction: This strikes me as being a much more accurate and commonsense view of belief than that of Hume, who simply views it phenomenologically. ...But then the remark appears to be circular. Belief requires a belief that it is true. Hm. |
| 9090 | Knowledge is certain cognition of something that is true [William of Ockham] |
| Full Idea: Knowledge is certain cognition of something that is true. | |
| From: William of Ockham (Expositio super viii libros [1340], Prologue) | |
| A reaction: This view has problems. William is not facing up to the sceptical questions which can shake any degree of certainty, and also that someone who lacked self-confidence might know many things while always feeling uncertain about them. 'Cognition' must go! |
| 9101 | Abstractive cognition knows universals abstracted from many singulars [William of Ockham] |
| Full Idea: Abstractive cognition (in one sense) relates to something abstracted from many singulars; and in this sense abstractive cognition is nothing else but cognition of a universal which can be abstracted from many things. | |
| From: William of Ockham (Prologue to Ordinatio [1320], Q 1 N sqq) | |
| A reaction: This strikes me as being correct common sense, even though it has become deeply unfashionable since Frege. We may not be able to see quite how the mind manages to see universals in a bunch of objects, but there is no better story. |
| 9102 | If an animal approached from a distance, we might abstract 'animal' from one instance [William of Ockham] |
| Full Idea: It seems possible that the concept of a genus could be abstracted from one individual, let us say, the concept 'animal', as in the case of one approaching from a distance, when I see enough to judge that I am seeing an animal. | |
| From: William of Ockham (Seven Quodlibets [1332], I Q xiii) | |
| A reaction: This is a rather individualistic view of abstraction, ignoring the shared language and culture. It is hard to imagine a truly virgin mind coming up with the concept after one encounter. The concept 'mind-boggling' seems more likely. |
| 10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
| Full Idea: Ways things might be are real, but only when abstracted from the actual way things are. They are brought out and distinguished by the mind, by abstraction, but are not dependent on mind for their existence. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.4) | |
| A reaction: To me this just flatly contradicts itself. The idea that the mind can 'bring something out' by its operations, with the result being then accepted as part of reality is nonsense on stilts. What is real is the powers that make the possibilities. |
| 9114 | There are no secure foundations to prove the separate existence of mind, in reason or experience [William of Ockham] |
| Full Idea: The existence of an immaterial 'intellective soul' ..cannot be demonstrated; for every reason by which we try to prove it assumes something that is doubtful for a man who follows only his natural reason. Neither can it be proved by experience. | |
| From: William of Ockham (Seven Quodlibets [1332], I Q x) | |
| A reaction: This is splendid honesty from a medieval monk. How would such a clear thinker have responded to modern brain research? Colin McGinn still maintains William's view, despite modern knowledge. Our ignorance produced conceptual dualism. |
| 9104 | A universal is the result of abstraction, which is only a kind of mental picturing [William of Ockham] |
| Full Idea: A universal is not the result of generation, but of abstraction, which is only a kind of mental picturing. | |
| From: William of Ockham (Ordinatio [1320], DII Qviii prima redactio) | |
| A reaction: The phrase 'mental picturing' works very plausibly for the universal 'giraffe', but not so well for 'multiplication' or 'contradiction'. Though we might broaden 'picturing' to being a much less visual concept. Mapping seems basic. |
| 11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
| Full Idea: A problem with compositionality is negative existential propositions. If some of the terms of the proposition are empty, and don't refer, then compositionality implies that the whole will lack meaning too. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.5) | |
| A reaction: I don't agree. I don't see why compositionality implies holism about sentence-meaning. If I say 'that circular square is a psychopath', you understand the predication, despite being puzzled by the singular term. |
| 10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
| Full Idea: A proposition makes an object out of what is said or expressed by the utterance of a certain sort of sentence, namely, one in the indicative mood which makes sense and doesn't fail in its references. It can then be an object of thought and belief. | |
| From: Stephen Read (Thinking About Logic [1995], Ch.1) | |
| A reaction: Nice, but two objections: I take it to be crucial to propositions that they eliminate ambiguities, and I take it that animals are capable of forming propositions. Read seems to regard them as fictions, but I take them to be brain events. |
| 9105 | Some concepts for propositions exist only in the mind, and in no language [William of Ockham] |
| Full Idea: Conceptual terms and the propositions formed by them are those mental words which do not belong to any language; they remain only in the mind and cannot be uttered exteriorly, though signs subordinated to these can be exteriorly uttered. | |
| From: William of Ockham (Summa totius logicae [1323], I.c.i) | |
| A reaction: [He cites Augustine] A glimmer of the idea of Mentalese, and is probably an integral part of any commitment to propositions. Quine would hate it, but I like it. Logicians seem to dislike anything that cannot be articulated, but brains are like that. |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
| From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
| A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |
| 16675 | Every extended material substance is composed of parts distant from one another [William of Ockham] |
| Full Idea: Every extended material substance is composed of substantial parts distant from one another in place or location. | |
| From: William of Ockham (Tractatus de corpore Christi [1323], Ch. 12) | |
| A reaction: Pasnau glosses this as that 'bodies have corpuscular structure', meaning that they are made up of parts of matter (rather than just enformed matter, I think). |
| 19381 | The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham] |
| Full Idea: Time is composed of non-entities, because it is composed of the past which does not exist now, although it did exist, and of the future, which does not yet exist; therefore time does not exist. | |
| From: William of Ockham (works [1335], 6:496), quoted by Richard T.W. Arthur - Leibniz 7 'Nominalist' | |
| A reaction: I've a lot of sympathy with this! I favour Presentism, so the past is gone and the future is yet to arrive. But we have no coherent concept of a present moment of any duration to contain reality. We are just completely bogglificated by it all. |
| 9111 | God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham] |
| Full Idea: God is not wise, but more-than-wise; God is not good, but more-than-good. | |
| From: William of Ockham (Reportatio [1330], III Q viii) | |
| A reaction: [He is quoting 'Damascene'] I quote this for interest, but I very much doubt whether Damascene or William knew what it meant, and I certainly don't. There seems to have been a politically correct desire to invent super-powers for God. |
| 8010 | William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham] |
| Full Idea: The most notable philosopher who makes God's commandment the basis of goodness, rather than God's goodness a reason for obeying him, is William of Occam. | |
| From: William of Ockham (works [1335]), quoted by Alasdair MacIntyre - A Short History of Ethics Ch.9 | |
| A reaction: Either view has problems. Why choose God to obey? Obey anyone who is powerful? But how do you decide that God is good? How do we know the nature of God's commands, or the nature of God's goodness? Etc. |
| 9112 | We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham] |
| Full Idea: What we abstract is said to belong to perfection in so far as it can be predicated of God and can stand for Him. For if such a concept could not be abstracted from a creature, then in this life we could not arrive at a cognition of God's wisdom. | |
| From: William of Ockham (Reportatio [1330], III Q viii) | |
| A reaction: This seems to be the germ of an important argument. Without the ability to abstract from what is experienced, we would not be able to apply general concepts to things which are beyond experience. It is a key idea for empiricism. |
| 9115 | To love God means to love whatever God wills to be loved [William of Ockham] |
| Full Idea: To love God above all means to love whatever God wills to be loved. | |
| From: William of Ockham (Seven Quodlibets [1332], III Q xiii) | |
| A reaction: A striking thought, which could be meaningful to the non-religious. Is it possible to form an image of what a perfect and ideal mind would love most? This might generate a set of universal values. It is tricky to find out what an actual God loves. |
| 16679 | Even an angel must have some location [William of Ockham, by Pasnau] |
| Full Idea: Ockham dismisses the possibility of non-location out of hand, remarking that even an angel has some location. | |
| From: report of William of Ockham (works [1335]) by Robert Pasnau - Metaphysical Themes 1274-1671 14.4 |