78 ideas
| 18274 | Analysis complicates a statement, but only as far as the complexity of its meaning [Wittgenstein] |
| Full Idea: Analysis makes the statement more complicated than it was; but it cannot and ought not to make it more complicated than its meaning (Bedeutung) was to begin with. When the statement is as complex as its meaning, then it is completely analysed. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 46e) | |
| A reaction: But how do you assess how complex the 'Bedeutung' was before you started? |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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'. |
| 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. |
| 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). |
| 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 |
| 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? |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 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! |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 16908 | We can dispense with self-evidence, if language itself prevents logical mistakes [Jeshion on Wittgenstein] |
| Full Idea: The 'self-evidence' of which Russell talks so much can only be dispensed with in logic if language itself prevents any logical mistake. | |
| From: comment on Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 4) by Robin Jeshion - Frege's Notion of Self-Evidence 4 | |
| A reaction: Jeshion presents this as a key idea, turning against Frege, and is the real source of the 'linguistic turn' in philosophy. If self-evidence is abandoned, then language itself is the guide to truth, so study language. I think I prefer Frege. See Quine? |
| 18276 | A statement's logical form derives entirely from its constituents [Wittgenstein] |
| Full Idea: The logical form of the statement must already be given in the forms of its constituents. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 23e) | |
| A reaction: This would evidently require each constituent to have a 'logical form'. It is hard to see what that could beyond its part of speech. Do two common nouns have the same logical form? |
| 6563 | 'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin] |
| Full Idea: Wittgenstein's 'fundamental idea' is that the 'and' and 'not' which guarantee the truth of "not p and not-p" are meaningful, but do not get their meaning by representing or standing for or referring to some kind of entity; they are non-referring terms. | |
| From: report of Ludwig Wittgenstein (Notebooks 1914-1916 [1915], §37) by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
| A reaction: Wittgenstein then defines the terms using truth tables, to show what they do, rather than what they stand for. This seems to me to be a candidate for the single most important idea in the history of the philosophy of logic. |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 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] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 23472 | The sense of propositions relies on the world's basic logical structure [Wittgenstein] |
| Full Idea: In order for a proposition to be CAPABLE of making sense, the world must already have the logical structure it has. The logic of the world is prior to all truth and falsehood. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], p.14c) | |
| A reaction: It seems that in Tractatus it is propositions about facts which are true or false, but prior to the facts are substance and the objects, and it is there that we find the logical structure of the world. I see this view as modern stoicism. |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 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] |
| 23500 | My main problem is the order of the world, and whether it is knowable a priori [Wittgenstein] |
| Full Idea: The great problem around which everything turns that I write is: is there an order in the world a priori, and if so what does it consist in? | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 15.06.01) | |
| A reaction: Morris identifies this as a 'Kantian question'. I trace it back to stoicism. This question has never bothered me. It just seems weird to think that you can infer reality from the examination of your own thinking. Perhaps I should take it more seriously? |
| 22323 | The philosophical I is the metaphysical subject, the limit - not a part of the world [Wittgenstein] |
| Full Idea: The philosophical I is not the man, not the human body, or the human soul of wh9ch psychology treats, but the metaphysical subject, the limit - not a part of the world. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 1916. 2 Sep), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 58 Intro | |
| A reaction: This is to treat the self as a phenomenon of thought, rather than of a human being. So if a machine could think, would it hence necessarily have a metaphysical self? |
| 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'. |
| 23481 | Propositions assemble a world experimentally, like the model of a road accident [Wittgenstein] |
| Full Idea: In the proposition a world is as it were put together experimentally. (As when in the law court in Paris a motor-car accident is represented by means of dolls, etc). | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 14.09.29) | |
| A reaction: [see Tractatus 4.031] This is the first appearance of LW's picture (or model) theory of meaning. It may well be the best theory of meaning anyone has come up with, since meaning being out in the world strikes me as absurd. |
| 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'. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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'. |
| 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. |
| 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. |
| 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. |
| 4678 | Absolute prohibitions are the essence of ethics, and suicide is the most obvious example [Wittgenstein] |
| Full Idea: If suicide is allowed, then everything is allowed. If anything is not allowed, then suicide is not allowed. This throws a light on the nature of ethics, for suicide is, so to speak, the elementary sin. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], end), quoted by Jonathan Glover - Causing Death and Saving Lives §13 | |
| A reaction: This reveals the religious streak in Wittgenstein. I am reluctant to judge suicide, but this seems wrong. Should a 'jumper' worry if they land on someone else and kill them? Of course they should. |