101 ideas
| 18019 | People have dreams which involve category mistakes [Magidor] |
| Full Idea: It is an empirical fact that people often sincerely report having had dreams which involve category mistakes. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.4) | |
| A reaction: She doesn't give any examples, but I was thinking that this might be the case before I read this idea. Dreams seem to allow you to live with gaps in reality that we don't tolerate when awake. |
| 17998 | Category mistakes are either syntactic, semantic, or pragmatic [Magidor] |
| Full Idea: A plausible case can be made for explaining the phenomenon of category mistakes in terms of each of syntax, semantics, and pragmatics. | |
| From: Ofra Magidor (Category Mistakes [2013], 1.1) | |
| A reaction: I want to explain them in terms of (structured) ontology, but she totally rejects that on p.156. Her preferred account is that they are presupposition failures, which is pragmatics. She splits the semantic view into truth-valued and non-truth-valued. |
| 18011 | Category mistakes seem to be universal across languages [Magidor] |
| Full Idea: The infelicity of category mistakes seems to be universal across languages. | |
| From: Ofra Magidor (Category Mistakes [2013], 2.3) | |
| A reaction: Magidor rightly offers this fact to refute the claim that category mistakes are purely syntax (since syntax obviously varies hugely across languages). I also take the fact to show that category mistakes concern the world, and not merely language. |
| 18012 | Category mistakes as syntactic needs a huge number of fine-grained rules [Magidor] |
| Full Idea: A syntactic theory of category mistakes would require not only general syntactic features such as must-be-human, but also highly particular ones such as must-be-a-grape. | |
| From: Ofra Magidor (Category Mistakes [2013], 2.3) | |
| A reaction: Her grape example comes from Hebrew, but an English example might be the verb 'to hull', which is largely exclusive to strawberries. The 'must-be' form is one of Chomsky's 'selectional features'. |
| 18013 | Embedded (in 'he said that…') category mistakes show syntax isn't the problem [Magidor] |
| Full Idea: The embedding data (such as 'John said that the number two is green', compared to '*John said that me likes apples') strongly suggests that category mistakes are not syntactically ill-formed. | |
| From: Ofra Magidor (Category Mistakes [2013], 2.4) | |
| A reaction: Sounds conclusive. The report of John's category error, unlike the report of his remark about apples, seems perfectly syntactically acceptable. |
| 18021 | Category mistakes are meaningful, because metaphors are meaningful category mistakes [Magidor] |
| Full Idea: Metaphors must have literal meanings. …Since many metaphors involving category mistakes manage to achieve their metaphorical purpose, they must also have literal meanings, so category mistakes must be (literally) meaningful. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: Hm. 'This guy is so weird that to meet him is to encounter a circular square'. |
| 18015 | The normal compositional view makes category mistakes meaningful [Magidor] |
| Full Idea: The principle that if a competent speaker understands some terms then they understand a sentence made up of them entails that category mistakes are meaningful (as in understanding 'the number two' and 'is green'). | |
| From: Ofra Magidor (Category Mistakes [2013], 3.2.1) | |
| A reaction: [compressed version] It is normal to impose restrictions on plausible compositionality, and thus back away from this claim, but I rather sympathise with it. She adds to a second version of the principle the proviso 'IF the sentence is meaningful'. |
| 18017 | If a category mistake is synonymous across two languages, that implies it is meaningful [Magidor] |
| Full Idea: Two sentences are synonymous if they have the same meaning, suggesting that they must both be meaningful. On the face of it the English 'two is green' and French 'deux est vert' are synonymous, suggesting meaningful category mistakes. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.3) | |
| A reaction: I'm fairly convinced already that most category mistakes are meaningful, and this seems to confirm the view. Some mistakes could be so extreme that no auditor could compute their meaning, especially if you concatenated lots of them. |
| 18031 | If a category mistake has unimaginable truth-conditions, then it seems to be meaningless [Magidor] |
| Full Idea: One motivation for taking category mistakes to be meaningless is that one cannot even imagine what it would take for 'Two is green' to be true. …Underlying this complaint is sometimes the thought that the meaning of a sentence is its truth-conditions. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.6) | |
| A reaction: I defend the view that most sentences are meaningful if they compose from meaningful parts, but you have to acknowledge this view. It seems to come in degrees. Sentences can have fragmentary meaning, or be almost meaningful, or offer a glimpse of meaning? |
| 18030 | A good explanation of why category mistakes sound wrong is that they are meaningless [Magidor] |
| Full Idea: The meaninglessness view does seem to offer a simple and compelling explanation for the fact that category mistakes are highly infelicitous. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.6) | |
| A reaction: However, I take there to be quite a large gulf between why meaningless sentences like 'squares turn happiness into incommensurability', which I would call 'category blunders', and subtle category mistakes, which are meaningful. |
| 18032 | Category mistakes are neither verifiable nor analytic, so verificationism says they are meaningless [Magidor] |
| Full Idea: No sense experience shows that 'two is green' is true or false. But neither is 'two is green' analytically true or false. So it fails to have legitimate verification conditions and hence, by the lights of traditional verificationism, it is meaningless. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.6.2) | |
| A reaction: If a category mistake is an error in classification, then it would seem to be analytically false. If it wrongly attributes a property to something, that makes it verifiably false. The problem is to verify anything at all about 'two'. |
| 18034 | Category mistakes play no role in mental life, so conceptual role semantics makes them meaningless [Magidor] |
| Full Idea: One might argue that conceptual role semantics entails that category mistakes are meaningless. Sentences such as 'two is green' play no role in the cognitive life of any agent. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.6.2) | |
| A reaction: [She quotes Block's definition of conceptual role semantics] I would have thought that if a category mistake is believed by an agent, it could play a huge role in their cognitive life. |
| 18037 | Maybe when you say 'two is green', the predicate somehow fails to apply? [Magidor] |
| Full Idea: One might argue that although 'two' refers to the number two, and 'is green' expresses the property of being green, in 'two is green' the property somehow fails to apply to the number two. | |
| From: Ofra Magidor (Category Mistakes [2013], 4.2) | |
| A reaction: It is an interesting thought that you say something which applies a predicate to an object, but the predicate then 'fails to apply' for reasons of its own, over which you have no control. The only possible cause of the failure is the nature of reality. |
| 18039 | If category mistakes aren't syntax failure or meaningless, maybe they just lack a truth-value? [Magidor] |
| Full Idea: Having rejected the syntactic approach and the meaninglessness view, one might feel that the last resort for explaining the defectiveness of category mistakes is to claim that they are truth-valueless (even if meaningful). | |
| From: Ofra Magidor (Category Mistakes [2013], 4.3.1) | |
| A reaction: She rejects this one as well, and votes for a pragmatic explanation, in terms of presupposition failure. The view I incline towards is just that they are false, despite being well-formed, meaningful and truth-valued. |
| 18016 | Two good sentences should combine to make a good sentence, but that might be absurd [Magidor] |
| Full Idea: The principle that if 'p' and 'q' are meaningful sentences then 'p and q' is a meaningful sentence seems highly plausible. But now consider the following example: 'That is a number and that is green'. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.2.2) | |
| A reaction: This challenges the defence of the meaningfulness of category mistakes on the basis of strong compositionality. |
| 18058 | Maybe the presuppositions of category mistakes are the abilities of things? [Magidor] |
| Full Idea: The most promising way to characterise the presuppositions involved in category mistakes might be to rephrase them in modal terms ('x is able to be pregnant', 'x is able to be green'). | |
| From: Ofra Magidor (Category Mistakes [2013], 5.4.3) | |
| A reaction: This catches my attention because it suggests that category mistakes contradict dispositions, rather than contradicting classifications or types. 'Let's use a magnet to repel this iron'? The dispositions of 'two' and 'green' in 'two is green'? Hm |
| 18041 | Category mistakes suffer from pragmatic presupposition failure (which is not mere triviality) [Magidor] |
| Full Idea: I argue that category mistakes are infelicitous because they suffer from (pragmatic) presupposition failure, ...but I reject the 'naive pragmatic approach' according to which category mistakes are infelicitous because they are trivially true or false. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.1) | |
| A reaction: She supports her case quite well, but I vote for them being false. The falsity may involve presuppositions. 'Two is green' is a category mistake, and false, because 'two' lacks the preconditions for anything to be coloured (notably, emitting light). |
| 18056 | Category mistakes because of presuppositions still have a truth value (usually 'false') [Magidor] |
| Full Idea: I am assuming that even in those contexts in which the presupposition of 'the number two is green' fails and the utterance is infelicitious, it nevertheless receives a bivalent truth-value (presumably 'false'). | |
| From: Ofra Magidor (Category Mistakes [2013], 5.4.1) | |
| A reaction: It seems to me obvious that, in normal contexts, 'the number two is green' is false, rather than meaningless. Is 'the number eight is an odd number' meaningless? |
| 18055 | In 'two is green', 'green' has a presupposition of being coloured [Magidor] |
| Full Idea: My proposal is that the truth-conditional content of 'green' (in 'two is green') is the property of being green, and its presuppositional content is the property of being coloured. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.4.1) | |
| A reaction: This requires a two-dimensional semantics of truth-conditional and presuppositional content. I fear it may have a problem she spotted elsewhere, of overgenerating presuppositions. Eyes are presupposed by 'green'. Ambient light is required. |
| 18057 | 'Numbers are coloured and the number two is green' seems to be acceptable [Magidor] |
| Full Idea: 'The number two is green' is normally infelicitous, but, interestingly, 'numbers are coloured and the number two is green' is not infelicitous. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.4.1) | |
| A reaction: A nice example, which gives good support for her pragmatic account of category mistakes in terms of presupposition failure. But how about 'figures can have contradictory shapes, and this square is circular'? Numbers are not coloured!!! |
| 18059 | The presuppositions in category mistakes reveal nothing about ontology [Magidor] |
| Full Idea: My pragmatic account of category mistakes does not support a key role for them in metaphysics. It is highly doubtful that the presuppositions associated with category mistakes reveal anything about the fundamental nature of ontological categories. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.6) | |
| A reaction: Thus she dashes my hope, without even bothering to offer a reason. I think she should push her enquiry further, and ask why we presuppose things. Why do we take presuppositions for granted? Why are they obvious? |
| 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) |
| 18040 | Intensional logic maps logical space, showing which predicates are compatible or incompatible [Magidor] |
| Full Idea: Intensional logic aims to capture necessary relations between certain predicates, such as that 'green all over' and 'red all over' cannot be co-instantiated. Each predicate is allocated a set of points in logical space, and every object has one point. | |
| From: Ofra Magidor (Category Mistakes [2013], 4.4) | |
| A reaction: This produces an intriguing model of reality, as a vast and rich space of multiply overlapping modal predicates. Things can be blue, square, dangerous and large. They can't be small and large, or square and round. Objects are optional extras! |
| 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. |
| 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) |
| 17997 | Some suggest that the Julius Caesar problem involves category mistakes [Magidor] |
| Full Idea: Various authors have argued that identity statements arising in the context of the 'Julius Caesar' problem in philosophy of mathematics constitute category mistakes. | |
| From: Ofra Magidor (Category Mistakes [2013], 1.1 n1) | |
| A reaction: [She cites Benacerraf 1965 and Shapiro 1997:79] |
| 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) |
| 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) |
| 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. |
| 18060 | We can explain the statue/clay problem by a category mistake with a false premise [Magidor] |
| Full Idea: Since 'the lump of clay is Romanesque' is a category mistake, a pragmatic account of that phenomenon is key to pursuing the strategy of saying that the problem rests on a false premise. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.6) | |
| A reaction: [compressed] |
| 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? |
| 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. |
| 18020 | Propositional attitudes relate agents to either propositions, or meanings, or sentence/utterances [Magidor] |
| Full Idea: Three views of the semantics of propositional attitudes: they are relations between agents and propositions ('propositional' view); relations between individuals and meanings (Fregean); or relations of individuals and sentences/utterances ('sentential'). | |
| From: Ofra Magidor (Category Mistakes [2013], 3.4) | |
| A reaction: I am a propositionalist on this one. Meanings are too vague, and sentences are too linguistic. |
| 18035 | Two sentences with different meanings can, on occasion, have the same content [Magidor] |
| Full Idea: It is commonly assumed that meaning and content can come apart: the sentence 'I am writing' and 'Ofra is writing' may have different meanings, even if, as currently uttered, they express the same content. | |
| From: Ofra Magidor (Category Mistakes [2013], 4.1) | |
| A reaction: From that, I would judge 'content' to mean the same as 'proposition'. |
| 18018 | To grasp 'two' and 'green', must you know that two is not green? [Magidor] |
| Full Idea: Is it a necessary condition on possessing the concepts of 'two' and 'green' that one does not believe that two is green? I think this claim is false. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.4) | |
| A reaction: To see that it is false one only has to consider much more sophisticated concepts, which are grasped without knowing their full implications. I might think two is green because I fully grasp 'two', but have not yet mastered 'green'. |
| 18008 | Generative semantics says structure is determined by semantics as well as syntactic rules [Magidor] |
| Full Idea: Generative semanticists claimed that the structure of a sentence is determined by both 'syntactic' and 'semantic' considerations which interact with each other in complex ways. | |
| From: Ofra Magidor (Category Mistakes [2013], 1.3) | |
| A reaction: [She mentions George Lakoff for this view] You need to study a range of examples, but this sounds a better view to me than the tidy picture of producing a syntactic structure and then adding a semantics. We make up sentences while speaking them. |
| 18010 | 'John is easy to please' and 'John is eager to please' have different deep structure [Magidor] |
| Full Idea: The sentences 'John is easy to please' and 'John is eager to please' can have very different deep structure (with the latter concerning John as a pleaser, while the former concerns John as the one being pleased). | |
| From: Ofra Magidor (Category Mistakes [2013], 2.1) | |
| A reaction: This demolishes the old idea of grammar as 'parts of speech' strung together according to superficial rules. The question is whether we now just have deeper syntax, or whether semantics is part of the process. |
| 18053 | The semantics of a sentence is its potential for changing a context [Magidor] |
| Full Idea: The basic semantics of sentences are not truth-conditions, but rather context change potential, which is a rule which determines what the effect of uttering the sentence would be on the context. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.2) | |
| A reaction: [I. Heim's 'renowned' 1983 revision of Stalnaker] This means the semantics of a sentence can vary hugely, depending on context. It is known as 'dynamic semantics'. 'I think you should go ahead and do it'. |
| 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. |
| 18000 | Weaker compositionality says meaningful well-formed sentences get the meaning from the parts [Magidor] |
| Full Idea: A weaker principle of compositionality states that if a syntactically well-formed sentence is meaningful, then its meaning is a function of the meaning of its parts. | |
| From: Ofra Magidor (Category Mistakes [2013], 1.1) | |
| A reaction: I would certainly accept this as being correct. I take the meaning of a sentence to be something which you assemble in your head as you hear the parts of it unfold. ….However, irony might exhibit meaning that only comes from the whole sentence. Hm. |
| 17999 | Strong compositionality says meaningful expressions syntactically well-formed are meaningful [Magidor] |
| Full Idea: In the strong form of the principle of compositionality any meaningful expressions combined in a syntactically well-formed manner compose a meaningful expression. | |
| From: Ofra Magidor (Category Mistakes [2013], 1.1) | |
| A reaction: [She cites Montague as holding this view] I find this plausible, at least. If you look at whole sentences they can seem meaningless, but if you track the process of composition a collective meaning emerges, despite the oddities. |
| 18014 | Understanding unlimited numbers of sentences suggests that meaning is compositional [Magidor] |
| Full Idea: The fact that speakers of natural languages have the capacity to understand indefinitely many new sentences suggests that meaning must be compositional. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.2.1) | |
| A reaction: To some extent, the compositionality of meaning is so obvious as to hardly require pointing out. It is the precise nature of the claim, and the extent to which whole sentences can add to the compositional meaning, that is of interest. |
| 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. |
| 18001 | Are there partial propositions, lacking truth value in some possible worlds? [Magidor] |
| Full Idea: Are there such things as 'partial propositions', which are truth-valueless relative to some possible worlds? | |
| From: Ofra Magidor (Category Mistakes [2013], 1.1) | |
| A reaction: Presumably this could be expressed without possible worlds. Are there propositions meaningful in New Guinea, and meaningless in England? Do some propositions require the contingent existence of certain objects to be meaningful? |
| 18036 | A sentence can be meaningful, and yet lack a truth value [Magidor] |
| Full Idea: 'That is red' in a context where the demonstrative fails to refer is truth-valueless, despite being meaningful, as is 'the queen of France in 2010 is bald'. ...The claim that some sentences are meaningful but truth-valueless is, then, widely accepted. | |
| From: Ofra Magidor (Category Mistakes [2013], 4.1) | |
| A reaction: The lack of truth value is usually because of reference failure. It is best to say the words are meaningful, but no proposition is expressed. |
| 18051 | In the pragmatic approach, presuppositions are assumed in a context, for successful assertion [Magidor] |
| Full Idea: According to the pragmatic approach, presuppositions are constraints on the context: if a sentence s generates a presupposition p, an assertion of s cannot proceed smoothly unless the context already entails p (p is taken for granted). | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.2) | |
| A reaction: She credits Stalnaker for this approach. There is a choice between the presuppositions being largely driven by internal features of the sentence, or by external features of context. You may not know the context of some statements. |
| 18043 | The infelicitiousness of trivial truth is explained by uninformativeness, or a static context-set [Magidor] |
| Full Idea: In Grice's theory if a sentence is trivially true, asserting it would violate the maxim of quantity. For Stalnaker, if p is trivially true, it involves no update to the context-set, and is thus pointless. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.2) | |
| A reaction: 'Let us remind ourselves, before we proceed, of the following trivial truth: p'. |
| 18042 | The infelicitiousness of trivial falsity is explained by expectations, or the loss of a context-set [Magidor] |
| Full Idea: In Grice's theory if a sentence is trivially false, asserting it would violate the maxim of quality. For Stalnaker if p is trivially false, removing all worlds incompatible with p would result in an empty context-set, preventing any further communication. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.2) | |
| A reaction: [compressed] I'm not sure whether we need to 'explain' the inappropriateness of uttering trivial falsities. I take the main rule of conversation to be 'don't be boring', but we all violate that. |
| 18047 | A presupposition is what makes an utterance sound wrong if it is not assumed? [Magidor] |
| Full Idea: The most obvious test for presupposition would be this: if s generates the presupposition p, then an utterance of s would be infelicitous, unless p is taken for granted by participants in the conversation. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.1.1) | |
| A reaction: The principle of charity seems to be involved here - that we try to make people's utterances sound right, so we add in the presuppositions which would achieve that. The problem, she says, is that the infelicity may have other causes. |
| 18048 | A test for presupposition would be if it provoked 'hey wait a minute - I have no idea that....' [Magidor] |
| Full Idea: A proposed test for presupposition is the 'Hey, wait a minute' test. S presupposes that p, just in case it would be felictious to respond to an utterance of s with something like 'Hey, wait a minute - I had not idea that p!'. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.1.2) | |
| A reaction: [K. Von Finkel 2004 made the suggestion] That is, you think 'hm ...this statement seems to presuppose p'. She says the suggestion vastly over-generates possible presuppositions - unlikely ones, as well as the obvious ones. |
| 18049 | The best tests for presupposition are projecting it to negation, conditional, conjunction, questions [Magidor] |
| Full Idea: The most robust tests for presupposition are the projection tests. If s presupposes p, then ¬s does too. If s1 presupposes p, then 'if s1 then s2' presupposes p. If s1 presupposes p, then 's1 and s2' presupposes p. If s presupposes p, then 's?' does too. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.1.3) | |
| A reaction: [compressed] She also discusses quantifiers. In other words, the presupposition remains stable through various transformations of the underlying proposition. |
| 18050 | If both s and not-s entail a sentence p, then p is a presupposition [Magidor] |
| Full Idea: In the traditional account, a sentence s presupposes p if and only if both s and ¬s entail p. Standardly, this entails that if s presupposes p, then whenever p is false, s must be neither true nor false. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.2) | |
| A reaction: 'I'm looking down on the garden' presupposes 'I'm upstairs'. Why would 'I'm not looking down on the garden' entail 'I'm upstairs'? I seem to have missed something. |
| 18054 | Why do certain words trigger presuppositions? [Magidor] |
| Full Idea: We can ask why a range of lexical items (e.g. 'stop' or 'know') trigger the presuppositions they do. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.2) | |
| A reaction: I'm not sure whether we'll get an answer, but I would approach the question by thinking about mental files. |
| 18024 | One theory says metaphors mean the same as the corresponding simile [Magidor] |
| Full Idea: On standard versions of the simile theory of metaphors, they mean the same as the corresponding simile. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: Magidor points out that this allows the metaphor to work while being meaningless, since all the work is done by the perfectly meaningful simile. But the metaphor must at least mean enough to indicate what the simile is. |
| 18023 | Theories of metaphor divide over whether they must have literal meanings [Magidor] |
| Full Idea: There are theories of metaphors that require them to have literal meanings in order to achieve their metaphorical purpose, and those that do not. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: I take almost any string of proper language to have literal meaning (for compositional reasons), even if the end result is somewhat ridiculous. 'Churchill was a lion' obviously has literal meaning. And so does 'Churchill was a transcendental number'. |
| 18025 | The simile view of metaphors removes their magic, and won't explain why we use them [Magidor] |
| Full Idea: The simile theory of metaphors makes them too easy to figure out, when they cannot be paraphrased in literal terms, …and it does not explain why we use metaphors as well as similes. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: [She cites Davidson for these points] They might just be similes with the added frisson of leaving out 'like', so that they seem at first to be false, until you work out the simile and see their truth. |
| 18026 | Maybe a metaphor is just a substitute for what is intended literally, like 'icy' for 'unemotional' [Magidor] |
| Full Idea: According to the substitution view of metaphors, a word used metaphorically is merely a substitute for another word or phrase that expresses the same meaning literally. Thus 'John is an ice-cube' is a substitute for 'John is cruel and unemotional'. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: This seems to capture the denotation but miss the connotation. Whoever came up with this theory didn't read much poetry. |
| 18028 | Gricean theories of metaphor involve conversational implicatures based on literal meanings [Magidor] |
| Full Idea: Gricean theories of metaphor …assume that conversational implicatures are generated via literal contents, and hence that a sentence cannot generate an implicature without being literally meaningful. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: Magidor gives not details of such theories, but presumably the metaphor is all in the speaker's intention, which is parasitic on the wayward literal meaning, as in cases of irony. |
| 18029 | Non-cognitivist views of metaphor says there are no metaphorical meanings, just effects of the literal [Magidor] |
| Full Idea: According to non-cognitivists there is no such thing as metaphorical meaning. …The effects on the hearer are induced directly via the literal meaning of the metaphor. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: [This is said to be Davidson's view] I wonder how many people defended some explicit 'metaphorical meaning', as opposed to connotations that accumulate as you take in the metaphor? Any second meaning is just a further literal meaning. |
| 18022 | Metaphors tend to involve category mistakes, by joining disjoint domains [Magidor] |
| Full Idea: The fact that most metaphors involve category mistakes is not a coincidence. …A big part of them is to do with connecting objects and properties that normally seem to belong to disjoint domains. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: Metaphysica poets took disjoint domains and 'yoked them together by violence', according to Dr Johnson. |
| 18027 | Metaphors as substitutes for the literal misses one predicate varying with context [Magidor] |
| Full Idea: A problem with the substitution view of metaphors is that the same predicate can have very different metaphorical contributions in different contexts. Consider 'Juliet is the sun' uttered by Romeo, and 'Stalin is the sun' from a devoted communist. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: The substitution view never looked good (especially if you like poetry), and now it looks a lot worse. |
| 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? |