83 ideas
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| Full Idea: Until the 1960s standard truth-table semantics were the only ones that there were. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.10.1) | |
| A reaction: The 1960s presumably marked the advent of possible worlds. |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| Full Idea: 'dom R' indicates the 'domain' of a relation, that is, the set of all objects that are members of ordered pairs and that have that relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| Full Idea: 'fld R' indicates the 'field' of a relation, that is, the set of all objects that are members of ordered pairs on either side of the relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| Full Idea: 'ran R' indicates the 'range' of a relation, that is, the set of all objects that are members of ordered pairs and that are related to by the first objects. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| Full Idea: We write F : A → B to indicate that A maps into B, that is, the domain of relating things is set A, and the things related to are all in B. If we add that F = B, then A maps 'onto' B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
|
Full Idea:
F(x) is a 'function', which indicates the unique value which y takes in |
|
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| Full Idea: To know if A ∈ B, we look at the set A as a single object, and check if it is among B's members. But if we want to know whether A ⊆ B then we must open up set A and check whether its various members are among the members of B. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:04) | |
| A reaction: This idea is one of the key ideas to grasp if you are going to get the hang of set theory. John ∈ USA ∈ UN, but John is not a member of the UN, because he isn't a country. See Idea 12337 for a special case. |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| Full Idea: A relation is 'symmetric' on a set if every ordered pair in the set has the relation in both directions. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| Full Idea: A relation is 'transitive' on a set if the relation can be carried over from two ordered pairs to a third. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| Full Idea: The 'ordered pair' <x,y> is defined to be {{x}, {x,y}}; hence it can be proved that <u,v> = <x,y> iff u = x and v = y (given by Kuratowski in 1921). ...The definition is somewhat arbitrary, and others could be used. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:36) | |
| A reaction: This looks to me like one of those regular cases where the formal definitions capture all the logical behaviour of the concept that are required for inference, while failing to fully capture the concept for ordinary conversation. |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| Full Idea: A 'linear ordering' (or 'total ordering') on A is a binary relation R meeting two conditions: R is transitive (of xRy and yRz, the xRz), and R satisfies trichotomy (either xRy or x=y or yRx). | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:62) |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| Full Idea: The 'powerset' of a set is all the subsets of a given set. Thus: PA = {x : x ⊆ A}. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| Full Idea: Two sets are 'disjoint' iff their intersection is empty (i.e. they have no members in common). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| Full Idea: The 'domain' of a relation is the set of all objects that are members of ordered pairs that are members of the relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| Full Idea: A 'relation' is a set of ordered pairs. The ordering relation on the numbers 0-3 is captured by - in fact it is - the set of ordered pairs {<0,1>,<0,2>,<0,3>,<1,2>,<1,3>,<2,3>}. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) | |
| A reaction: This can't quite be a definition of order among numbers, since it relies on the notion of a 'ordered' pair. |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| Full Idea: A 'function' is a relation which is single-valued. That is, for each object, there is only one object in the function set to which that object is related. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| Full Idea: A function 'maps A into B' if the domain of relating things is set A, and the things related to are all in B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| Full Idea: A function 'maps A onto B' if the domain of relating things is set A, and the things related to are set B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| Full Idea: A relation is 'reflexive' on a set if every member of the set bears the relation to itself. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| Full Idea: A relation satisfies 'trichotomy' on a set if every ordered pair is related (in either direction), or the objects are identical. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| Full Idea: A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| Full Idea: Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ. A man with an empty container is better off than a man with nothing. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1.03) |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| Full Idea: It might be thought at first that the empty set would be a rather useless or even frivolous set to mention, but from the empty set by various set-theoretic operations a surprising array of sets will be constructed. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:02) | |
| A reaction: This nicely sums up the ontological commitments of mathematics - that we will accept absolutely anything, as long as we can have some fun with it. Sets are an abstraction from reality, and the empty set is the very idea of that abstraction. |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| Full Idea: Given any x we have the singleton {x}, which is defined by the pairing axiom to be {x,x}. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 2:19) | |
| A reaction: An interesting contrivance which is obviously aimed at keeping the axioms to a minimum. If you can do it intuitively with a new axiom, or unintuitively with an existing axiom - prefer the latter! |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| Full Idea: An 'equivalence relation' is a binary relation which is reflexive, and symmetric, and transitive. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| Full Idea: Equivalence classes will 'partition' a set. That is, it will divide it into distinct subsets, according to each relation on the set. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| Full Idea: It was observed by several people that for a satisfactory theory of ordinal numbers, Zermelo's axioms required strengthening. The Axiom of Replacement was proposed by Fraenkel and others, giving rise to the Zermelo-Fraenkel (ZF) axioms. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:15) |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| Full Idea: For functions, we know that for any y there exists an appropriate x, but we can't yet form a function H, as we have no way of defining one particular choice of x. Hence we need the axiom of choice. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:48) |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| Full Idea: The process is dubbed 'conversational implicature' when the inference is not from the content of what has been said, but from the fact that it has been said. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.7.3) |
| 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] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| Full Idea: The point of logic is to give an account of the notion of validity,..in two standard ways: the semantic way says that a valid inference preserves truth (symbol |=), and the proof-theoretic way is defined in terms of purely formal procedures (symbol |-). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.3..) | |
| A reaction: This division can be mirrored in mathematics, where it is either to do with counting or theorising about things in the physical world, or following sets of rules from axioms. Language can discuss reality, or play word-games. |
| 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. |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| Full Idea: A is a logical truth (tautology) (|= A) iff it is a semantic consequence of the empty set of premises (φ |= A), that is, every interpretation makes A true. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.3.4) | |
| A reaction: So the final column of every line of the truth table will be T. |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| Full Idea: A truth assignment 'satisfies' a formula, or set of formulae, if it evaluates as True when all of its components have been assigned truth values. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.2) | |
| A reaction: [very roughly what Enderton says!] The concept becomes most significant when a large set of wff's is pronounced 'satisfied' after a truth assignment leads to them all being true. |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| Full Idea: If every proof-theoretically valid inference is semantically valid (so that |- entails |=), the proof theory is said to be 'sound'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.7) |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| Full Idea: If every semantically valid inference is proof-theoretically valid (so that |= entails |-), the proof-theory is said to be 'complete'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.7) |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| Full Idea: If a wff is tautologically implied by a set of wff's, it is implied by a finite subset of them; and if every finite subset is satisfiable, then so is the whole set of wff's. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 2.5) | |
| A reaction: [Enderton's account is more symbolic] He adds that this also applies to models. It is a 'theorem' because it can be proved. It is a major theorem in logic, because it brings the infinite under control, and who doesn't want that? |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| Full Idea: A set of expressions is 'decidable' iff there exists an effective procedure (qv) that, given some expression, will decide whether or not the expression is included in the set (i.e. doesn't contradict it). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.7) | |
| A reaction: This is obviously a highly desirable feature for a really reliable system of expressions to possess. All finite sets are decidable, but some infinite sets are not. |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| Full Idea: The Enumerability Theorem says that for a reasonable language, the set of valid wff's can be effectively enumerated. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 2.5) | |
| A reaction: There are criteria for what makes a 'reasonable' language (probably specified to ensure enumerability!). Predicates and functions must be decidable, and the language must be finite. |
| 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. |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| Full Idea: Not all sentences using 'if' are conditionals. Consider 'if you want a banana, there is one in the kitchen'. The rough test is that a conditional can be rewritten as 'that A implies that B'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.6.4) |
| 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) |
| 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. |
| 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. |
| 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. |
| 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. |
| 7489 | Joshua said, Sun, stand thou still [Anon (Josh)] |
| Full Idea: Then Joshua spake to the Lord, and he said in the sight of Israel, Sun, stand thou still upon Gibeon; and the Sun stood still. | |
| From: Anon (Josh) (06: Book of Joshua [c.540 BCE], 10.12) | |
| A reaction: This verse became highly significant during the controversies from Copernicus to Galileo about the heliocentric universe. |