98 ideas
| 23277 | Modern pragmatism sees objectivity as possible, despite its gradual evolution [Misak] |
| Full Idea: One of the pillars of the new pragmatism is the thought that the standards of objectivity come into being and evolve over time, but that being historically situated in this way does not detract from their objectivity. | |
| From: Cheryl Misak (Introduction to 'New Pragmatists' [2007], p.2) | |
| A reaction: This looks to me like pragmatism finally coming to its senses. I would say that being any sort of 'social construct' (beloved of cultural relativists) in no way detracts from its capacity for objectivity and truth. |
| 9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
| Full Idea: A contextual definition shows how to analyse an expression in situ, by replacing a complete sentence (of a particular form) in which the expression occurs by another in which it does not. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: This is a controversial procedure, which (according to Dummett) Frege originally accepted, and later rejected. It might not be the perfect definition that replacing just the expression would give you, but it is a promising step. |
| 10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
| Full Idea: When a definition contains a quantifier whose range includes the very entity being defined, the definition is said to be 'impredicative'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Presumably they are 'impredicative' because they do not predicate a new quality in the definiens, but make use of the qualities already known. |
| 19108 | Truth is proper assertion, but that has varying standards [Misak] |
| Full Idea: The pragmatist will say that truth is proper assertion, but different discourses have different standards for proper assertion. | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 4) | |
| A reaction: This remark shows that there is a pragmatic attitude towards truth behind most attempts to analyse the concept of assertion. When and why is assertion legitimate, and what motivates it? |
| 19094 | For pragmatists the loftiest idea of truth is just a feature of what remains forever assertible [Misak] |
| Full Idea: For pragmatists there is an unseverable connection between making an assertion and claiming that it is true. ...Were we to get to a belief that is forever assertible...then we would have a true belief. There is nothing higher or better we could ask of it. | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 1) | |
| A reaction: She is particularly drawing on Peirce. She says his 'ideal end of enquiry' idea is a small aspect of his view of truth, which is mainly given here. I had taken the pragmatic view of truth to be silly, but I may rethink. |
| 19105 | Truth isn't a grand elusive property, if it is just the aim of our assertions and inquiries [Misak] |
| Full Idea: If truth is what satisfies our aims in first-order assertion and inquiry (as the pragmatist says), then there is no search for an elusive property, or a metaphysical property, or a property which we cannot grasp. | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 3) | |
| A reaction: This pragmatic approach is much more persuasive than the usual caricature of pragmatic truth (Idea 19097), but I'm beginning to wonder how you distinguish an 'inquiry' (or 'assertion') from other modes of thought. Do I smell a circularity? |
| 19100 | Truth makes disagreements matter, or worth settling [Misak] |
| Full Idea: The role of truth is to make disagreements matter, or to make sense of wanting to resolve disagreements. | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 2) | |
| A reaction: [She cites Huw Price 2003] This suggests that the most important use of 'truth' is forensic. It is hard to make any sense of a law court without a robust sense of truth. Trial by jury, rather than some great personage, shows this value. |
| 19099 | 'True' is used for emphasis, clarity, assertion, comparison, objectivity, meaning, negation, consequence... [Misak] |
| Full Idea: 'P is true' is used to emphasise p, and avoid logic problems. The pragmatists says there are plenty of other uses: the aim of assertion or deliberation, the improvement of our views, distinguishing objectivity, explaining meaning, negation, consequence... | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 2) | |
| A reaction: Pragmatism seems to break 'true' down into its many uses, rather than having a specific theory of truth. This might be where ordinary language philosophy (how is the word 'true' used) meets pragmatism (how is the concept [true] used). |
| 19103 | 'That's true' doesn't just refer back to a sentence, but implies sustained evidence for it [Misak] |
| Full Idea: The pragmatist says 'That's so' or 'that's true' are not just 'pro-sentential', but carry with them the thought that evidence does currently speak in favour of the statement asserted, and the prediction that it will continue to speak in favour. | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 3) | |
| A reaction: This is a very nice point made by a pragmatist against the flimsy view of truth held by various deflationary views. You ought to believe what is true, and stand by what you hold to be true. |
| 19101 | Disquotation is bivalent [Misak] |
| Full Idea: The disquotational schema entails bivalence. | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 2 n10) | |
| A reaction: A simple but interesting observation. Critics of Tarski observe that he depends on a bivalent logic. |
| 19096 | Disquotationalism resembles a telephone directory [Misak] |
| Full Idea: Disquotationalism is more like a telephone directory than a theory. | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 2 n7) | |
| A reaction: [She cites Wilfred Sellars 1962:33] The idea is that there is a schema - 'p' is true iff p - and that all the acceptable sentences of a language can be expressed in this way, making a vast but finite list. It seems to replace 'theories'. |
| 19106 | Disquotations says truth is assertion, and assertion proclaims truth - but what is 'assertion'? [Misak] |
| Full Idea: The point of the disquotational schema is that to say that a sentence is true is to assert it, and to assert a sentence is to say that it is true. We must then ask what it is to assert or endorse a proposition. | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 4) | |
| A reaction: [She is referring to the views of Crispin Wright] Most people would say that we assert something because we think it is true, and truth is obviously prior. Clearly if it has been asserted, that was because someone thought it was true. |
| 19098 | Deflating the correspondence theory doesn't entail deflating all the other theories [Misak] |
| Full Idea: We must not move seamlessly from the thought that the correspondence theory must be deflated to the thought that any theory of truth must be deflated. | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 2) | |
| A reaction: This rather good essay offers the idea that Peircean pragmatic approaches to truth can meet the deflationary desires of the opponents of correspondence, without jettisoning all the crucial naturalistic connections with reality. Interesting. |
| 19104 | Deflationism isn't a theory of truth, but an account of its role in natural language [Misak] |
| Full Idea: Deflationist theories are not theories of truth, or theories of what truth is. ...They are theories which try to explain the role that 'true' plays in natural languages. | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 3) | |
| A reaction: [She cites Dorothy Grover 2001,2002] If so, then the modern axiomatic theory of truth sounds appealing, because it tries to give a fuller and more precise account than a mere list is disquotations could possibly give. |
| 10098 | The 'power set' of A is all the subsets of A [George/Velleman] |
| Full Idea: The 'power set' of A is all the subsets of A. P(A) = {B : B ⊆ A}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10099 | The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman] |
| Full Idea: The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}}. The existence of this set is guaranteed by three applications of the Axiom of Pairing. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10100 for the Axiom of Pairing. |
| 10101 |
Cartesian Product A x B: the set of all ordered pairs |
| Full Idea: The 'Cartesian Product' of any two sets A and B is the set of all ordered pairs <a, b> in which a ∈ A and b ∈ B, and it is denoted as A x B. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |
| Full Idea: The idea of grouping together objects that share some property is a common one in mathematics, ...and the technique most often involves the use of equivalence relations. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
| Full Idea: A relation is an equivalence relation if it is reflexive, symmetric and transitive. The 'same first letter' is an equivalence relation on the set of English words. Any relation that puts a partition into clusters will be equivalence - and vice versa. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is a key concept in the Fregean strategy for defining numbers. |
| 10096 | Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman] |
| Full Idea: ZFC is a theory concerned only with sets. Even the elements of all of the sets studied in ZFC are also sets (whose elements are also sets, and so on). This rests on one clearly pure set, the empty set Φ. ..Mathematics only needs pure sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This makes ZFC a much more metaphysically comfortable way to think about sets, because it can be viewed entirely formally. It is rather hard to disentangle a chair from the singleton set of that chair. |
| 10097 | Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman] |
| Full Idea: The Axiom of Extensionality says that for all sets x and y, if x and y have the same elements then x = y. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems fine in pure set theory, but hits the problem of renates and cordates in the real world. The elements coincide, but the axiom can't tell you why they coincide. |
| 10100 | Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman] |
| Full Idea: The Axiom of Pairing says that for all sets x and y, there is a set z containing x and y, and nothing else. In symbols: ∀x∀y∃z∀w(w ∈ z ↔ (w = x ∨ w = y)). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10099 for an application of this axiom. |
| 17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |
| Full Idea: The Axiom of Reducibility ...had the effect of making impredicative definitions possible. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10109 | ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman] |
| Full Idea: Sets, unlike extensions, fail to correspond to all concepts. We can prove in ZFC that there is no set corresponding to the concept 'set' - that is, there is no set of all sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: This is rather an important point for Frege. However, all concepts have extensions, but they may be proper classes, rather than precisely defined sets. |
| 10108 | As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman] |
| Full Idea: The problem with reducing arithmetic to ZFC is not that this theory is inconsistent (as far as we know it is not), but rather that is not completely general, and for this reason not logical. For example, it asserts the existence of sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Note that ZFC has not been proved consistent. |
| 22246 | A train of reasoning must be treated as all happening simultaneously [Recanati] |
| Full Idea: For logic purposes, a train of reasoning has to be construed as synchronic. | |
| From: François Recanati (Mental Files in Flux [2016], 5.2) | |
| A reaction: If we are looking for a gulf between logic and the real world this is a factor to be considered, along with Nietzsche's observation about necessary simplification. [ref to Kaplan 'Afterthoughts' 1989, 584-5] |
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| Full Idea: A hallmark of our realist stance towards the natural world is that we are prepared to assert the Law of Excluded Middle for all statements about it. For all statements S, either S is true, or not-S is true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Personally I firmly subscribe to realism, so I suppose I must subscribe to Excluded Middle. ...Provided the statement is properly formulated. Or does liking excluded middle lead me to realism? |
| 16357 | Mental files are the counterparts of singular terms [Recanati] |
| Full Idea: Mental files are the mental counterparts of singular terms. | |
| From: François Recanati (Mental Files [2012], 3.3) | |
| A reaction: A thoroughly satisfactory theory. We can build up a picture of filing merging, duplication, ambiguity, error etc. Eventually neuroscience will map the whole system, and we will have cracked it. |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| Full Idea: A 'model' of a theory is an assignment of meanings to the symbols of its language which makes all of its axioms come out true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: If the axioms are all true, and the theory is sound, then all of the theorems will also come out true. |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| Full Idea: Mathematicians tend to regard the differences between isomorphic mathematical structures as unimportant. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems to be a pointer towards Structuralism as the underlying story in mathematics. The intrinsic character of so-called 'objects' seems unimportant. How theories map onto one another (and onto the world?) is all that matters? |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
| Full Idea: Consistency is a purely syntactic property, unlike the semantic property of soundness. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| Full Idea: If there is a sentence such that both the sentence and its negation are theorems of a theory, then the theory is 'inconsistent'. Otherwise it is 'consistent'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| Full Idea: Soundness is a semantic property, unlike the purely syntactic property of consistency. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
| Full Idea: If there is a sentence such that neither the sentence nor its negation are theorems of a theory, then the theory is 'incomplete'. Otherwise it is 'complete'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: Interesting questions are raised about undecidable sentences, irrelevant sentences, unknown sentences.... |
| 10106 | Rational numbers give answers to division problems with integers [George/Velleman] |
| Full Idea: We can think of rational numbers as providing answers to division problems involving integers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Cf. Idea 10102. |
| 10102 | The integers are answers to subtraction problems involving natural numbers [George/Velleman] |
| Full Idea: In defining the integers in set theory, our definition will be motivated by thinking of the integers as answers to subtraction problems involving natural numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Typical of how all of the families of numbers came into existence; they are 'invented' so that we can have answers to problems, even if we can't interpret the answers. It it is money, we may say the minus-number is a 'debt', but is it? Cf Idea 10106. |
| 10107 | Real numbers provide answers to square root problems [George/Velleman] |
| Full Idea: One reason for introducing the real numbers is to provide answers to square root problems. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Presumably the other main reasons is to deal with problems of exact measurement. It is interesting that there seem to be two quite distinct reasons for introducing the reals. Cf. Ideas 10102 and 10106. |
| 9946 | Logicists say mathematics is applicable because it is totally general [George/Velleman] |
| Full Idea: The logicist idea is that if mathematics is logic, and logic is the most general of disciplines, one that applies to all rational thought regardless of its content, then it is not surprising that mathematics is widely applicable. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Frege was keen to emphasise this. You are left wondering why pure logic is applicable to the physical world. The only account I can give is big-time Platonism, or Pythagoreanism. Logic reveals the engine-room of nature, where the design is done. |
| 10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |
| Full Idea: Unlike the intuitionist, the classical mathematician believes in an actual set that contains all the real numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 17899 | Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman] |
| Full Idea: The first-order version of the induction axiom is weaker than the second-order, because the latter applies to all concepts, but the first-order applies only to concepts definable by a formula in the first-order language of number theory. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7 n7) |
| 10128 | The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman] |
| Full Idea: The idea behind the proofs of the Incompleteness Theorems is to use the language of Peano Arithmetic to talk about the formal system of Peano Arithmetic itself. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: The mechanism used is to assign a Gödel Number to every possible formula, so that all reasonings become instances of arithmetic. |
| 17902 | A successor is the union of a set with its singleton [George/Velleman] |
| Full Idea: For any set x, we define the 'successor' of x to be the set S(x) = x U {x}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is the Fregean approach to successor, where the Dedekind approach takes 'successor' to be a primitive. Frege 1884:§76. |
| 10133 | Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman] |
| Full Idea: The derivability of Peano's Postulates from Hume's Principle in second-order logic has been dubbed 'Frege's Theorem', (though Frege would not have been interested, because he didn't think Hume's Principle gave an adequate definition of numebrs). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8 n1) | |
| A reaction: Frege said the numbers were the sets which were the extensions of the sets created by Hume's Principle. |
| 10130 | Set theory can prove the Peano Postulates [George/Velleman] |
| Full Idea: The Peano Postulates can be proven in ZFC. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10089 | Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman] |
| Full Idea: One might well wonder whether talk of abstract entities is less a solution to the empiricist's problem of how a priori knowledge is possible than it is a label for the problem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Intro) | |
| A reaction: This pinpoints my view nicely. What the platonist postulates is remote, bewildering, implausible and useless! |
| 10131 | If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman] |
| Full Idea: As, in the logicist view, mathematics is about nothing particular, it is little wonder that nothing in particular needs to be observed in order to acquire mathematical knowledge. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002]) | |
| A reaction: At the very least we can say that no one would have even dreamt of the general system of arithmetic is they hadn't had experience of the particulars. Frege thought generality ensured applicability, but extreme generality might entail irrelevance. |
| 10092 | In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman] |
| Full Idea: In the unramified theory of types, all objects are classified into a hierarchy of types. The lowest level has individual objects that are not sets. Next come sets whose elements are individuals, then sets of sets, etc. Variables are confined to types. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: The objects are Type 0, the basic sets Type 1, etc. |
| 10094 | The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman] |
| Full Idea: The theory of types seems to rule out harmless sets as well as paradoxical ones. If a is an individual and b is a set of individuals, then in type theory we cannot talk about the set {a,b}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Since we cheerfully talk about 'Cicero and other Romans', this sounds like a rather disasterous weakness. |
| 10095 | Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman] |
| Full Idea: A problem with type theory is that there are only finitely many individuals, and finitely many sets of individuals, and so on. The hierarchy may be infinite, but each level is finite. Mathematics required an axiom asserting infinitely many individuals. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Most accounts of mathematics founder when it comes to infinities. Perhaps we should just reject them? |
| 17901 | Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman] |
| Full Idea: If a is an individual and b is a set of individuals, then in the theory of types we cannot talk about the set {a,b}, since it is not an individual or a set of individuals, ...but it is hard to see what harm can come from it. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10114 | Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman] |
| Full Idea: In the first instance all bounded quantifications are finitary, for they can be viewed as abbreviations for conjunctions and disjunctions. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) | |
| A reaction: This strikes me as quite good support for finitism. The origin of a concept gives a good guide to what it really means (not a popular view, I admit). When Aristotle started quantifying, I suspect of he thought of lists, not totalities. |
| 10134 | Much infinite mathematics can still be justified finitely [George/Velleman] |
| Full Idea: It is possible to use finitary reasoning to justify a significant part of infinitary mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: This might save Hilbert's project, by gradually accepting into the fold all the parts which have been giving a finitist justification. |
| 10123 | The intuitionists are the idealists of mathematics [George/Velleman] |
| Full Idea: The intuitionists are the idealists of mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10124 | Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman] |
| Full Idea: For intuitionists, truth is not independent of proof, but this independence is precisely what seems to be suggested by Gödel's First Incompleteness Theorem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: Thus Gödel was worse news for the Intuitionists than he was for Hilbert's Programme. Gödel himself responded by becoming a platonist about his unprovable truths. |
| 19109 | The anti-realism debate concerns whether indefeasibility is a plausible aim of inquiry [Misak] |
| Full Idea: If indefeasibility turns out to be something we can't sensibly aim at in a kind of inquiry, then the judgements that arise from that kind of 'inquiry' are not truth-apt. It is here that the realism/anti-realism debate resides. | |
| From: Cheryl Misak (Pragmatism and Deflationism [2007], 4) | |
| A reaction: A very interesting way of presenting the issue, one that makes the debate sound (to me) considerably more interesting than hitherto. I may start using the word 'indefeasible' rather a lot, in my chats with the anti-realist philosophical multitude. |
| 16360 | Identity statements are informative if they link separate mental files [Recanati] |
| Full Idea: An identity statement 'A=B' is informative to the extent that the terms 'A' and 'B' are associated with distinct mental files. | |
| From: François Recanati (Mental Files [2012], 4.1) | |
| A reaction: Hence the information in 'Scott is the author of 'Waverley'' is information about what is in your mind, not what is happening in Scotland. This is Recanati's solution to one of Frege's classic puzzles. 'Morning Star' and 'Evening Star' files. Nice. |
| 16374 | There is a continuum from acquaintance to description in knowledge, depending on the link [Recanati] |
| Full Idea: It is not too difficult to imagine a continuum of cases between straightforward instances of knowledge by acquaintance and straightforward instances of knowledge by description, with more or less tenuous informational links to the referent. | |
| From: François Recanati (Mental Files [2012], 12.2) |
| 18409 | Indexicals apply to singular thought, and mental files have essentially indexical features [Recanati] |
| Full Idea: I defend the applicability of the indexical model to singular thought, and to mental files qua vehicles of singular thought. Mental files, I will argue, possess the essential features of indexicals. | |
| From: François Recanati (Mental Files [2012], 05.1) | |
| A reaction: I love mental files, but am now (thanks to Cappelen and Dever) deeply averse to giving great significance to indexicals. A revised account of files will be needed. |
| 22247 | Indexicality is not just a feature of language; examples show it also occurs in thought [Recanati] |
| Full Idea: People once took indexicality to be exclusively a property of language, ....but a series of examples seemed to establish that the thought expressed by uttering an indexical sentence is itself indexical (and is thus 'essential'). | |
| From: François Recanati (Mental Files in Flux [2016], 6.1) | |
| A reaction: Perry's example of not realising it is him leaking the sugar in a supermarket is the best known example. Was this a key moment for realising that philosophy of thought is (pace Dummett) more important than philosophy of language? |
| 22248 | How can we communicate indexical thoughts to people not in the right context? [Recanati] |
| Full Idea: Indexical thoughts create an obvious problem with regard to communication. How can we manage to communicate such thoughts to those who are not in the right context? | |
| From: François Recanati (Mental Files in Flux [2016], 7.1) | |
| A reaction: One answer is that you often cannot communicate them. If I write on a wall 'I am here now', that doesn't tell the next passer-by very much. But 'it's raining here' said in a telephone call works fine - if you know the location of the caller. |
| 16354 | Indexicality is closely related to singularity, exploiting our direct relations with things [Recanati] |
| Full Idea: Singularity and indexicality are closely related: for indexicals systematically exploit the contextual relations in which we stand to what we talk about. | |
| From: François Recanati (Mental Files [2012], 2.2) | |
| A reaction: Recanati builds a nice case that we may only have an ontology of singular objects because we conceptualise and refer to things in a particular way. He denies the ontology, but that's the bit that interests me. |
| 16371 | Files can be confused, if two files correctly have a single name, or one file has two names [Recanati] |
| Full Idea: Paderewski cases are cases in which a subject associates two distinct files with a single name. Inverse Paderewski cases are cases in which there are two names but the subject associates them with a single file. | |
| From: François Recanati (Mental Files [2012], 10.1) | |
| A reaction: In the inverse there are two people with the same name, and someone thinks they are one person (with their combined virtues and vices). E.g. Einstein the famous physicist, and Einstein the famous musicologist. What a man! |
| 16373 | Encylopedic files have further epistemic links, beyond the basic one [Recanati] |
| Full Idea: The reference of a file is the object to which the subject stands in the relevant epistemic relation. In the case of encylopedic entries there is an arbitrary number of distinct relations. The file grows new links in an opportunistic manner. | |
| From: François Recanati (Mental Files [2012], 11.3) | |
| A reaction: I'm not convinced by Recanati's claim that encylopedic files are a distinct type. My files seem to grow these opportunistic links right from their inception. All files seem to have that feature. A file could have four links at its moment of launching. |
| 16375 | Singular thoughts need a mental file, and an acquaintance relation from file to object [Recanati] |
| Full Idea: The mental file framework rests on two principles: that the subject cannot entertain a singular thought about an object without possessing and exercising a mental file about it, and that this requires an acquaintance relation with the object. | |
| From: François Recanati (Mental Files [2012], 12.3) | |
| A reaction: I'm puzzled by the case where I design and build a completely new object. I seem to assemble a file, and only bestow singularity on it towards the end. Or the singularity can just be a placeholder, referred to as 'something'. […see p.158] |
| 16377 | Expected acquaintance can create a thought-vehicle file, but without singular content [Recanati] |
| Full Idea: On my view, actual acquaintance is not necessary to open a mental file; expected acquaintance will suffice; yet opening a mental file itself is not sufficient to entertain a singular thought-content. It only enables a thought-vehicle. | |
| From: François Recanati (Mental Files [2012], 13.1) | |
| A reaction: I'm not clear why I can't create a file with no expectation at all of acquaintance, as in a fictional case. Depends what 'acquaintance' means. Recanati longs for precise distinctions where they may not be available. |
| 16378 | An 'indexed' file marks a file which simulates the mental file of some other person [Recanati] |
| Full Idea: Files function metarepresentationally if they serve to represent how other subjects think about objects in the world. ..An 'indexed' file has an index referring to the other subject whose files the indexed file stands for or simulates. | |
| From: François Recanati (Mental Files [2012], 14.1) | |
| A reaction: Presumably there is an implicit index on all files, which says in a conversation whether my interlocutor does or does not hold the same file-type as me. Recanati wants many 'types' of files, but I suspect there is just one file type. |
| 16387 | Reference by mental files is Millian, in emphasising acquaintance, rather than satisfaction [Recanati] |
| Full Idea: The mental file account preserves the original, Millian inspiration of direct reference theories in giving pride of place to acquaintance relations and downplaying satisfaction factors. | |
| From: François Recanati (Mental Files [2012], 17.3) | |
| A reaction: I find this a very satisfying picture, in which reference links to the simple label of a file (which could be a number), and not to its contents. There are tricky cases of non-existents, fictional entities and purely possible entities to consider. |
| 16358 | The reference of a file is fixed by what it relates to, not the information it contains [Recanati] |
| Full Idea: What files refer to is not determined by properties which the subject takes the referent to have (information, or misinformation, in the file), but through the relations on which the files are based. | |
| From: François Recanati (Mental Files [2012], 3.3) | |
| A reaction: Maybe. 'Lot 22'. I can build up a hypothetical file by saying 'Imagine an animal which is F, G, H…', and build a reference that relates to nothing. Maybe Recanati overestimates the role of his 'epistemically rewarding' relations in file creation. |
| 16361 | A mental file treats all of its contents as concerning one object [Recanati] |
| Full Idea: The role of a mental file is precisely to treat all the information as if it concerned one and the same object, from which it derives. | |
| From: François Recanati (Mental Files [2012], 4.1) | |
| A reaction: Recanati's book focuses entirely on singular objects, but we presumably have files for properties, generalisation, groups etc. Can they only be thought about if they are reified? Maybe. |
| 16367 | There are transient 'demonstrative' files, habitual 'recognitional' files, cumulative 'encyclopedic' files [Recanati] |
| Full Idea: A 'demonstrative' file only exists during the demonstrative relation to something; …a 'recognitional' file is based on 'familiarity' (a disposition to recognise); …an 'encylopedic' file contains all the information on something, however it is gained. | |
| From: François Recanati (Mental Files [2012], 6.1-3) | |
| A reaction: [picked as samples of his taxonomy, pp.70-73] I'm OK with this as long as he doesn't think the categories are sharply separated. I'm inclined to think of files as a single type, drifting in and out of different of modes. |
| 16368 | Files are hierarchical: proto-files, then first-order, then higher-order encyclopedic [Recanati] |
| Full Idea: There is a hierarchy of files. Proto-files are the most basic; conceptual files are generated from them. First-order ones are more basic, as the higher-order encylopedic entries presuppose them. | |
| From: François Recanati (Mental Files [2012], 6.3) | |
| A reaction: This hierarchy might fit into a decent account of categories, if a plausible one could be found. A good prospect for exploring categories would be to start with mental file-types, and work outwards through their relations. |
| 16370 | A file has a 'nucleus' through its relation to the object, and a 'periphery' of links to other files [Recanati] |
| Full Idea: I take a file to have a dual structure, with a 'nucleus' of the file consisting of information derived through the relevant epistemically rewarding relation, while the 'periphery' consists of information derived through linking with other files. | |
| From: François Recanati (Mental Files [2012], 8.3) | |
| A reaction: This sounds strikingly like essentialism to me, though what constitutes the essence is different from the usual explanatory basics. The link, though, is in the causal connection. If we naturally 'essentialise', that will control file-formation. |
| 22242 | Mental files are concepts, which are either collections or (better) containers [Recanati] |
| Full Idea: Mental files are entries in the mental encyclopedia, that is, concepts. Some, following Grice, say they are information collections, but I think of them as containers. Collections are determined by their elements, but containers have independent identity. | |
| From: François Recanati (Mental Files in Flux [2016], Pref) | |
| A reaction: [compressed] [Grice reference is 'Vacuous Names' (1969)] I agree with Recanati. The point is that you can invoke a file by a label, even when you don't know what the content is. |
| 22243 | The Frege case of believing a thing is both F and not-F is explained by separate mental files [Recanati] |
| Full Idea: Frege's Constraint says if a subject believes an object is both F and not-F (as in 'Frege cases'), then the subject thinks of that object under distinct modes of presentation. Having distinct mental files of the object is sufficient to generate this. | |
| From: François Recanati (Mental Files in Flux [2016], Pref) | |
| A reaction: [compressed] When you look at how many semantic puzzles (notably from Frege and Kripke) are solved by the existence of labelled mental files, the case for them is overwhelming. |
| 16381 | The content of thought is what is required to understand it (which involves hearers) [Recanati] |
| Full Idea: As Evans emphasises, what matters when we want to individuate semantic content is what would count as a proper understanding of an utterance; but 'understanding' defines the task of the hearer. | |
| From: François Recanati (Mental Files [2012], 16.2) | |
| A reaction: [cites Evans 1982: 92, 143n, 171] I like to place (following Aristotle) understanding at the centre of all of philosophy, so this seems to me an appealing idea. It makes misunderstandings interesting. |
| 10110 | Corresponding to every concept there is a class (some of them sets) [George/Velleman] |
| Full Idea: Corresponding to every concept there is a class (some classes will be sets, the others proper classes). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) |
| 16365 | Mental files are individual concepts (thought constituents) [Recanati] |
| Full Idea: I want mental files (properly speaking) to serve as individual concepts, i.e. thought constituents. | |
| From: François Recanati (Mental Files [2012], 5.3) | |
| A reaction: This is why the concept of mental files is so neat - it gives you a theory of reference and a theory of concepts. I love the files approach because it precisely fits my own introspective experiences. Hope I'm not odd in that way. |
| 16356 | There may be two types of reference in language and thought: descriptive and direct [Recanati] |
| Full Idea: A widely held view, originating with Russell, says there are two types of reference (both in language and thought): descriptive reference, and direct reference. | |
| From: François Recanati (Mental Files [2012], 3.2) | |
| A reaction: I would rather say is there is just one sort of reference, and as many ways of achieving it as you care to come up with. With that view, most of the problems vanish, as far as I can see. People refer. Sentences are nothing but trouble. |
| 16393 | In super-direct reference, the referent serves as its own vehicle of reference [Recanati] |
| Full Idea: In super-direct reference, the sort of thing Russell was after, there is no mode of presentation: the referent itself serves as its own vehicle, as it were. | |
| From: François Recanati (Mental Files [2012], 18.2) | |
| A reaction: To me this is a step too far, because reference is not some physical object like a chair; it is a mental or linguistic phenomenon. Chair's don't refer themselves; it is people who refer. |
| 16386 | Direct reference is strong Millian (just a tag) or weak Kaplanian (allowing descriptions as well) [Recanati] |
| Full Idea: There are two notions of direct reference, the strong Millian notion (where the expression is like a 'tag' with no satisfaction mechanism), and the weaker Kaplanian notion (where reference is compatible with carrying a descriptive meaning). | |
| From: François Recanati (Mental Files [2012], 17.3) | |
| A reaction: I immediately favour the Millian view, which gives a minimal basis for reference, as just a 'peg' (Marcus) to hang things on. I don't take a Millian reference to be the object itself. The concept of a 'tag' or 'label' is key. Mental files have tags. |
| 16372 | Sense determines reference says same sense/same reference; new reference means new sense [Recanati] |
| Full Idea: To say that sense determines reference is to say that the same sense cannot determine distinct referents - any distinction at the level of reference entails a corresponding distinction at the level of sense. | |
| From: François Recanati (Mental Files [2012], 10.2) | |
| A reaction: Does 'the sentry at the gate' change its sense when the guard is changed? Yes. 'The sentry at the gate will stop you'. 'The sentry at the gate is my cousin'. De re/de dicto reference. So changes of de re reference seem to change the sense? |
| 16388 | We need sense as well as reference, but in a non-descriptive form, and mental files do that [Recanati] |
| Full Idea: My view inherits from Frege 'modes of presentation'. Reference is not enough, and sense is needed. …We must make room for non-descriptive modes of presentation, and these are mental files. | |
| From: François Recanati (Mental Files [2012], 18.1) | |
| A reaction: [compressed] Recanati aims to avoid the standard Kripkean criticisms of descriptivism, while being able to handle Frege's puzzles. I take Recanati's mental files theory to be the most promising approach. |
| 16359 | Sense is a mental file (not its contents); similar files for Cicero and Tully are two senses [Recanati] |
| Full Idea: What plays the role of sense is not information in a file, but the file itself. If there are two distinct files, one for 'Cicero' and one for 'Tully', then there are two distinct (non-descriptive) senses, even if the information in both files is the same. | |
| From: François Recanati (Mental Files [2012], 3.4) | |
| A reaction: This may be the best idea in Recanati's book. A sense might be a 'way of coming at the information', rather than some set of descriptions. |
| 16355 | Problems with descriptivism are reference by perception, by communications and by indexicals [Recanati] |
| Full Idea: Three problems with Frege's idea of descriptions in the head are: reference through perception, reference through communicative chains, and reference through indexicals. | |
| From: François Recanati (Mental Files [2012], 3.1) | |
| A reaction: In the end reference has to occur in the head, even if it is social or causal or whatever, so these are not problems that worry me. |
| 16348 | Descriptivism says we mentally relate to objects through their properties [Recanati] |
| Full Idea: Descriptivism is the view that our mental relation to individual objects goes through properties of those objects. …This is so because our knowledge of objects is mediated by our knowledge of their properties. | |
| From: François Recanati (Mental Files [2012], 1.1) | |
| A reaction: The implication is that if you view an object as just a bundle of properties, then you are obliged to hold a descriptive theory of reference. Hence a 'singularist' theory of reference seems to need a primitive notion of an object's identity. |
| 16384 | Definite descriptions reveal either a predicate (attributive use) or the file it belongs in (referential) [Recanati] |
| Full Idea: A definite description may contribute either the singular predicate it encodes (attributive use) or the mental file to what that predicate belongs (referential use). | |
| From: François Recanati (Mental Files [2012], 17.1) | |
| A reaction: This nicely explains Donnellan's distinction in terms of mental files. 'Green' may refer in a shop, but isn't much use in a wood. What to make of 'He's a bit of a Bismark'? |
| 16352 | A rigid definite description can be attributive, not referential: 'the actual F, whoever he is….' [Recanati] |
| Full Idea: A rigid use of a definite description need not be referential: it may be attributive. Thus I may say: 'The actual F, whoever he is, is G'. | |
| From: François Recanati (Mental Files [2012], 2.2) | |
| A reaction: Recanati offers this as a criticism of the attempted 2-D solution to descriptivist accounts of singularity. The singularity is not strong enough, he says. |
| 22245 | A linguistic expression refers to what its associated mental file refers to [Recanati] |
| Full Idea: Mental files determine the reference of linguistic expressions: an expression refers to what the mental file associated with it refers to (at the time of tokening). | |
| From: François Recanati (Mental Files in Flux [2016], 5) | |
| A reaction: Invites the question of how mental files manage to refer, prior to the arrival of a linguistic expression. A mental file is usually fully of descriptions, but it might be no more than a label. |
| 16353 | Singularity cannot be described, and it needs actual world relations [Recanati] |
| Full Idea: As Peirce insisted, singularity as such cannot be described, it can only be given through actual world relations. | |
| From: François Recanati (Mental Files [2012], 2.2) | |
| A reaction: [Peirce - Exact Logic, Papers 3, 1967, §419] This is the key idea for Recanati's case for basing our grasp of singular things on their relation to a mental file. |
| 16382 | Fregean modes of presentation can be understood as mental files [Recanati] |
| Full Idea: A mental file plays the role which Fregean theory assigns to modes of presentation. | |
| From: François Recanati (Mental Files [2012], 17.1) | |
| A reaction: I'm a fan of mental files, and this is a nice pointer to how the useful Fregean insights can be written in a way better grounded in brain operations. Rewriting Frege in neuroscience terms is a nice project for someone. |
| 16389 | If two people think 'I am tired', they think the same thing, and they think different things [Recanati] |
| Full Idea: If you and I think 'I am tired', there is a sense in which we think the same thing, and another sense in which we think different things. | |
| From: François Recanati (Mental Files [2012], 18.1) | |
| A reaction: This is a very nice simple account of the semantic distinctiveness of indexicals, which obviously requires a 'two-tiered framework'. He cites Kaplan and Perry as background. |
| 16363 | Indexicals (like mental files) determine their reference relationally, not by satisfaction [Recanati] |
| Full Idea: The class of indexicals have the same property as mental files, that their reference is determined relationally rather than satisfactionally. | |
| From: François Recanati (Mental Files [2012], 5.1) | |
| A reaction: Recanati is building an account of reference through mental files. This idea may be the clearest point I have yet encountered about indexicals, showing why they are of particular interest to philosophers. |
| 16364 | Indexical don't refer; only their tokens do [Recanati] |
| Full Idea: Indexicals do not refer; only tokens of an indexical refer | |
| From: François Recanati (Mental Files [2012], 5.1) | |
| A reaction: Thus 'Thurs 23rd March 2013' refers, but 'now' doesn't, unless someone produces an utterance of it. This is why indexicals are sometimes called 'token-reflexives'. |
| 16351 | In 2-D semantics, reference is determined, then singularity by the truth of a predication [Recanati] |
| Full Idea: In the two-dimensional framework, what characterises the singular case is the fact that truth-evaluation (of possessing of the reference-fixing property) takes place at a later stage than reference determination. | |
| From: François Recanati (Mental Files [2012], 2.1) | |
| A reaction: This sounds psychologically plausible, which is a big (and unfashionable) plus for me. 1) what are we talking about? 2) what are we saying about it, 3) is it true? |
| 16350 | Two-D semantics is said to help descriptivism of reference deal with singular objects [Recanati] |
| Full Idea: Descriptivism has trouble catching the singularity of objects, construing them as only directly about properties. …To get the truth-conditions right, it is claimed, the descriptivist only as to go two-dimensional. | |
| From: François Recanati (Mental Files [2012], 2.1) | |
| A reaction: I suspect that the descriptivist only has a problem here because context is being ignored. 'That man on the beach' can quickly be made uniquely singular after a brief chat. |
| 16380 | Russellian propositions are better than Fregean thoughts, by being constant through communication [Recanati] |
| Full Idea: The Russellian notion of a proposition is arguably a better candidate for the status of semantic content than the Fregean notion of a thought. For the proposition remains constant from one person to the next. | |
| From: François Recanati (Mental Files [2012], 16.2) | |
| A reaction: A good point, though I rebel against Russellian propositions because they are too much out in the world, and propositions strike me as features of minds. We need to keep propositions separate from facts. |
| 22250 | There are speakers' thoughts and hearers' thoughts, but no further thought attached to the utterance [Recanati] |
| Full Idea: There is the speaker's thought and the thought formed by the hearer. That is all there is. We don't need an additional entity, the thought expressed by the utterance. | |
| From: François Recanati (Mental Files in Flux [2016], 7.2) | |
| A reaction: This fits my view of propositions nicely. They are the two 'thoughts'. The notion of some further abstract 'proposition' with its own mode of independent existence strikes me as ontologically absurd. |
| 22249 | The Naive view of communication is that hearers acquire exactly the thoughts of the speaker [Recanati] |
| Full Idea: The Naive Conception of Communication rests on the idea that communication is the replication of thoughts: the thought the hearer entertains when he understands what the speaker is saying is the very thought which the speaker expressed. | |
| From: François Recanati (Mental Files in Flux [2016], 7.1) | |
| A reaction: It is hard to believe that any modern thinker would believe such a view, given holistic views of language etc. |