78 ideas
| 11006 | Russell started a whole movement in philosophy by providing an analysis of descriptions [Read on Russell] |
| Full Idea: Russell started a whole movement in philosophy by providing an analysis of descriptions. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Stephen Read - Thinking About Logic Ch.5 |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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. |
| 18944 | Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer on Russell] |
| Full Idea: Russell's account of names and definite descriptions was concerned to preserve the law of excluded middle, according to which every sentence is either true or false (but it is not obvious that the law ought to be preserved). | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Sarah Sawyer - Empty Names 3 | |
| A reaction: That is the strongest form of excluded middle, but things work better if every sentence is either 'true' or 'not true', leaving it open whether 'not true' actually means 'false'. |
| 7758 | 'Elizabeth = Queen of England' is really a predication, not an identity-statement [Russell, by Lycan] |
| Full Idea: On Russell's view 'Elizabeth II = Queen of England' is only superficially an identity-statement; really it is a predication, and attributes a complex relational property to Elizabeth. | |
| From: report of Bertrand Russell (On Denoting [1905]) by William Lycan - Philosophy of Language Ch.1 | |
| A reaction: The original example is 'Scott = author of Waverley'. Why can't such statements be identities, in which the reference of one half of the identity is not yet known? 'The murderer is violent' and 'Smith is violent' suggests 'Smith is the murderer'. |
| 5772 | The idea of a variable is fundamental [Russell] |
| Full Idea: I take the notion of the variable as fundamental. | |
| From: Bertrand Russell (On Denoting [1905], p.42) | |
| A reaction: A key idea of twentieth century philosophy, derived from Frege and handed on to Quine. A universal term, such as 'horse', is a variable, for which any particular horse can be its value. You can calculate using x, and generalise about horses. |
| 18941 | Names don't have a sense, but are disguised definite descriptions [Russell, by Sawyer] |
| Full Idea: Russell proposed that names do not express a Fregean sense, ...but are disguised definite descriptions, of the form 'the F'. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Sarah Sawyer - Empty Names 3 | |
| A reaction: Of course, Russell then has a famous theory about definite descriptions, which turns them into quantifications. |
| 4945 | Russell says names are not denotations, but definite descriptions in disguise [Russell, by Kripke] |
| Full Idea: Russell (and Frege) thought that Mill was wrong about names: really a proper name, properly used, simply was a definite description abbreviated or disguised. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Saul A. Kripke - Naming and Necessity lectures Lecture 1 | |
| A reaction: It is tempting to oversimplify this issue, one way or the other, but essentially one has to agree with Kripke that naming does not inherently involve description, but is a 'baptism', without initial content. Connotations and descriptions accrue to a name. |
| 18942 | Russell says a name contributes a complex of properties, rather than an object [Russell, by Sawyer] |
| Full Idea: Russell's view of names, understood as a definite description, which is understood as a quantificational phrase, is not to contribute an object to propositions, but to contribute a complex of properties. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Sarah Sawyer - Empty Names 3 | |
| A reaction: This seems to contradict the role of constants in first-logic, which are the paradigm names, picking out an object in the domain. Kripke says names and definite descriptions have different modal profiles. |
| 7745 | Are names descriptions, if the description is unknown, false, not special, or contains names? [McCullogh on Russell] |
| Full Idea: Russell's proposal that a natural name is an abbreviated description invites four objections: not all speakers can produce descriptions; the description could be false; no one description seems special; and descriptions usually contain names. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Gregory McCullogh - The Game of the Name 8.74 | |
| A reaction: The best reply on behalf of Russell is probably to concede all of these points, but deny that any of them are fatal. Most replies will probably say that they are possible true descriptions, rather than actual limited, confused or false ones. |
| 10449 | Logically proper names introduce objects; definite descriptions introduce quantifications [Russell, by Bach] |
| Full Idea: For Russell, a logically proper name introduces its referent into the proposition, whereas a description introduces a certain quantificational structure, not its denotation. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Kent Bach - What Does It Take to Refer? 22.2 L0 | |
| A reaction: I have very strong resistance to the idea that the actual referent could ever become part of a proposition. I am not, and never have been, part of a proposition! Russell depended on narrow 'acquaintance', which meant that few things qualified. |
| 15159 | The meaning of a logically proper name is its referent, but most names are not logically proper [Russell, by Soames] |
| Full Idea: Russell defined a logically proper name to be one the meaning of which is its referent. However, his internalist epistemology led him to deny that the words we ordinarily call names are logically proper. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Scott Soames - Philosophy of Language 1.25 |
| 2612 | Russell rewrote singular term names as predicates [Russell, by Ayer] |
| Full Idea: Russell's theory used quantification to eliminate singular terms, which could be meaningful without denoting anything. He reparsed such sentences so they appeared as predicates instead of names. | |
| From: report of Bertrand Russell (On Denoting [1905]) by A.J. Ayer - The Central Questions of Philosophy IX.A.2 |
| 7757 | "Nobody" is not a singular term, but a quantifier [Russell, by Lycan] |
| Full Idea: Though someone just beginning to learn English might take it as one, "nobody" is not a singular term, but a quantifier. | |
| From: report of Bertrand Russell (On Denoting [1905]) by William Lycan - Philosophy of Language Ch.1 | |
| A reaction: If someone replies to "nobody's there" with "show him to me!", presumably it IS a singular term - just one that doesn't work very well. If you want to get on in life, treat it as a quantifier; if you just want to have fun... |
| 18943 | Russell implies that all sentences containing empty names are false [Sawyer on Russell] |
| Full Idea: Russell's account implies that all sentences composed of an empty name and a predicate are false, including 'Pegasus was a mythical creature'. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Sarah Sawyer - Empty Names 4 | |
| A reaction: Russell insists that such sentences contain a concealed existence claim, which they clearly don't. |
| 6411 | Critics say definite descriptions can refer, and may not embody both uniqueness and existence claims [Grayling on Russell] |
| Full Idea: The main objections to Russell's theory of descriptions are to say that definite descriptions sometime are referring expressions, and disputing the claim that definite descriptions embody both uniqueness and existence claims. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: The first one seems particularly correct, as you can successfully refer with a false description. See Colin McGinn (Idea 6067) for criticism of the existence claim made by the so-called 'existential' quantifier. |
| 10433 | Definite descriptions fail to refer in three situations, so they aren't essentially referring [Russell, by Sainsbury] |
| Full Idea: Russell's reasons for saying that definite descriptions are not referring expressions are: some definite descriptions have no referent, and they cannot be referring when used in negative existential truths, or in informative identity sentences. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Mark Sainsbury - The Essence of Reference 18.5 | |
| A reaction: The idea is that by 'parity of form', if they aren't referring in these situations, they aren't really referring in others. Sainsbury notes that if there are two different forms of definite description (referential and attributive) these arguments fail. |
| 1608 | The theory of descriptions eliminates the name of the entity whose existence was presupposed [Russell, by Quine] |
| Full Idea: When a statement of being or non-being is analysed by Russell's theory of descriptions it ceases to contain any expression which even purports to name the alleged entity, so the being of such an entity is no longer presupposed. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Willard Quine - On What There Is p.6 |
| 7754 | Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity [Russell, by Lycan] |
| Full Idea: Russell showed that his theory of definite descriptions affords solutions to each of four vexing logical problems: the Problems of Apparent Reference to Non-existents and Negative existentials, Frege's Puzzle about Identity, and Substitutivity. | |
| From: report of Bertrand Russell (On Denoting [1905]) by William Lycan - Philosophy of Language 2.Over | |
| A reaction: You must seek elsewhere for the explanations of the four problems, but this gives some indication of why Russell's theory was famous, and was felt to be a breakthrough in explaining logical forms. |
| 21529 | Russell showed how to define 'the', and thereby reduce the ontology of logic [Russell, by Lackey] |
| Full Idea: With the devices of the Theory of Descriptions at hand, it was no longer necessary to take 'the' as indefinable, and it was possible to diminish greatly the number of entities to which a logical system is ontologically committed. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.13 | |
| A reaction: Illuminating, because it shows that ontology is what drove Russell at this time, and really they were all searching for Quine's 'desert landscapes', which minimalise commitment. |
| 6333 | The theory of definite descriptions reduces the definite article 'the' to the concepts of predicate logic [Russell, by Horwich] |
| Full Idea: Russell's theory of definite descriptions reduces the definite article 'the' to the notions of predicate logic - specifically, 'some', 'every', and 'same as'. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Paul Horwich - Truth (2nd edn) Ch.2.7 | |
| A reaction: This helpfully clarifies Russell's project - to find the logical form of every sentence, expressed in terms which are strictly defined and consistent. This huge project now looks rather too optimistic. Artificial Intelligence would love to complete it. |
| 6412 | Russell implies that 'the baby is crying' is only true if the baby is unique [Grayling on Russell] |
| Full Idea: Russell's analysis of 'the baby is crying' seems to imply that this can only be true if there is just one baby in the world; ..to dispose of the objection, it seems necessary to appeal implicitly or explicitly to a 'domain of discourse'. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: This objection leads to ordinary language philosophy, and the 'pragmatics' of language. It is standard in modern predicate logic to specify the domain over which an expression is quantified. |
| 7743 | Russell explained descriptions with quantifiers, where Frege treated them as names [Russell, by McCullogh] |
| Full Idea: Russell proposed that descriptions be treated along with the quantifiers, which departs from Frege, who treated descriptions as proper names. ...the problem was that names invoke objects, and there is no object in failed descriptions. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Gregory McCullogh - The Game of the Name 2.16 | |
| A reaction: Maybe we just allow intentional objects (such as unicorns) into our ontology? Producing a parsimonious ontology seems to be the main motivation of most philosophy of language. Or maybe names are just not committed to actual existence? |
| 7310 | Russell avoids non-existent objects by denying that definite descriptions are proper names [Russell, by Miller,A] |
| Full Idea: Russell attempted to avoid Meinong's strategy (of saying 'The present King of France' refers to a 'non-existent object') by denying that definite descriptions are proper names. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Alexander Miller - Philosophy of Language 2.7 | |
| A reaction: Russell claimed that there was a covert existence claim built into a definite description. What about descriptions in known counterfactual situations ('Queen of the Fairies')? |
| 12006 | Denying definite description sentences are subject-predicate in form blocks two big problems [Russell, by Forbes,G] |
| Full Idea: Since Russell did not want to introduce non-existent objects, or declare many sentences meaningless, he prevented the problem from getting started, by denying that 'the present King of France is bald' is really a subject-predicate sentence. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Graeme Forbes - The Metaphysics of Modality 4.1 |
| 4569 | Russell says apparent referring expressions are really assertions about properties [Russell, by Cooper,DE] |
| Full Idea: Russell's theory says that sentences which apparently serve to refer to particulars are really assertions about properties. | |
| From: report of Bertrand Russell (On Denoting [1905]) by David E. Cooper - Philosophy and the Nature of Language §4.1 | |
| A reaction: Right. Which is why particulars get marginalised in Russell, and universals take centre stage. I can't help suspecting that talk of de re/de dicto reference handles this problem better. |
| 11009 | Russell's theory must be wrong if it says all statements about non-existents are false [Read on Russell] |
| Full Idea: Russell's theory makes an exciting distinction between logical and grammatical form, but any theory which says that every positive statement, without distinction, about objects which don't exist is false, has to be wrong. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Stephen Read - Thinking About Logic Ch.5 |
| 21549 | The theory of descriptions lacks conventions for the scope of quantifiers [Lackey on Russell] |
| Full Idea: Some logicians charge that the theory of descriptions as it stands is formally inadequate because it lacks explicit conventions for the scope of quantifiers, and that when these conventions are added the theory becomes unduly complex. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.97 | |
| A reaction: [Especially in modal contexts, apparently] I suppose if the main point is to spell out the existence commitments of the description, then that has to include quantification, for full generality. |
| 12796 | Non-count descriptions don't threaten Russell's theory, which is only about singulars [Laycock on Russell] |
| Full Idea: It is sometimes claimed that the behaviour of definite non-count descriptions shows Russell's Theory of Descriptions itself to be false. ....but it isn't a general theory of descriptions, but precisely a theory of singular descriptions. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Henry Laycock - Words without Objects 3.1 |
| 7532 | Denoting is crucial in Russell's account of mathematics, for identifying classes [Russell, by Monk] |
| Full Idea: Denoting phrases are central to mathematics, especially in Russell's 'logicist' theory, in which they are crucial to identifying classes ('the class of all mortal beings', 'the class of natural numbers'). | |
| From: report of Bertrand Russell (On Denoting [1905]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.6 | |
| A reaction: This explains the motivation for Russell's theory of definite descriptions, since he thinks reference is achieved by description. Russell nearly achieved an extremely complete philosophical system. |
| 11988 | Russell's analysis means molecular sentences are ambiguous over the scope of the description [Kaplan on Russell] |
| Full Idea: Russell's analysis of sentences containing definite descriptions has as an immediate consequence the doctrine that molecular sentences containing definite descriptions are syntactically ambiguous as regards the scope of the definite description. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by David Kaplan - How to Russell a Frege-Church I | |
| A reaction: Presumably this is a virtue of Russell's account, and an advert for analytic philosophy, because it reveals an ambiguity which was there all the time. |
| 6061 | Existence is entirely expressed by the existential quantifier [Russell, by McGinn] |
| Full Idea: Nowadays Russell's position is routinely put by saying that existence is what is expressed by the existential quantifier and only by that. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Colin McGinn - Logical Properties Ch.2 | |
| A reaction: We must keep separate how you express existence, and what it is. Quantifiers seem only to be a style of expressing existence; they don't offer any insight into what existence actually is, or what we mean by 'exist'. McGinn dislikes quantifiers. |
| 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. |
| 18775 | Russell showed that descriptions may not have ontological commitment [Russell, by Linsky,B] |
| Full Idea: Russell's theory of definite descriptions allows us to avoid being ontologically committed to objects simply by virtue of using descriptions which seemingly denote them. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Bernard Linsky - Quantification and Descriptions 1.1.2 | |
| A reaction: This I take to be why Russell's theory is a famous landmark. I personally take ontological commitment to be independent of what we specifically say. Others, like Quine, prefer to trim what we say until the commitments seem sound. |
| 7533 | The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals [Russell, by Monk] |
| Full Idea: The real Platonic entities left standing after the Theory of Descriptions were propositions (not classes or numbers), and their constituents did not include denoting concepts or classes, but only individuals (Socrates) and universals (mortality). | |
| From: report of Bertrand Russell (On Denoting [1905]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.6 | |
| A reaction: Propositions look like being the problem here. If we identify them with facts, it is not clear how many facts there are in the universe, independent of human thought. Indeed, how many universals are there? Nay, how many individuals? See Idea 7534. |
| 6063 | Russell can't attribute existence to properties [McGinn on Russell] |
| Full Idea: Russell's view makes it impossible to attribute existence to properties, and this would have to be declared ill-formed and meaningless. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Colin McGinn - Logical Properties Ch.2 | |
| A reaction: This strikes me as a powerful criticism, used to support McGinn's view that existence cannot be analysed, using quantifiers or anything else. |
| 18777 | If the King of France is not bald, and not not-bald, this violates excluded middle [Linsky,B on Russell] |
| Full Idea: Russell says one won't find the present King of France on the list of bald things, nor on the list of things that are not bald. It would seem that this gives rise to a violation of the law of excluded middle. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Bernard Linsky - Quantification and Descriptions 2 | |
| A reaction: It's a bit hard to accuse the poor old King of violating a law when he doesn't exist. |
| 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) |
| 4567 | Russell argued with great plausibility that we rarely, if ever, refer with our words [Russell, by Cooper,DE] |
| Full Idea: Russell argued with great plausibility that we rarely, if ever, refer with our words. | |
| From: report of Bertrand Russell (On Denoting [1905]) by David E. Cooper - Philosophy and the Nature of Language §4 | |
| A reaction: I'm not sure if I understand this. Presumably phrases which appear to refer actually point at other parts of language rather than the world. |
| 5810 | Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan on Russell] |
| Full Idea: If I am right, referring is not the same as denoting and the referential use of definite descriptions is not recognised on Russell's view. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by Keith Donnellan - Reference and Definite Descriptions §I | |
| A reaction: This introduces a new theory of reference, which goes beyond the mere contents of linguistic experessions. It says reference is an 'external' and 'causal' affair, and so a definite description is not sufficient to make a reference. |
| 16385 | A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati] |
| Full Idea: In Russell's definition of 'denoting', a definite description denotes an entity if that entity fits the description uniquely. | |
| From: report of Bertrand Russell (On Denoting [1905]) by François Recanati - Mental Files 17.2 | |
| A reaction: [Recanati cites Donnellan for this] Hence denoting is not the same thing as reference. A description can denote beautifully, but fail to refer. Donnellan says if denoting were reference, someone might refer without realising it. |
| 5774 | Denoting phrases are meaningless, but guarantee meaning for propositions [Russell] |
| Full Idea: Denoting phrases never have any meaning in themselves, but every proposition in whose verbal expression they occur has a meaning. | |
| From: Bertrand Russell (On Denoting [1905], p.43) | |
| A reaction: This is the important idea that the sentence is the basic unit of meaning, rather than the word. I'm not convinced that this dispute needs to be settled. Words are pretty pointless outside of propositions, and propositions are impossible without words. |
| 5775 | In 'Scott is the author of Waverley', denotation is identical, but meaning is different [Russell] |
| Full Idea: If we say 'Scott is the author of Waverley', we assert an identity of denotation with a difference of meaning. | |
| From: Bertrand Russell (On Denoting [1905], p.46) | |
| A reaction: This shows Russell picking up Frege's famous distinction, as shown in 'Hesperus is Phosphorus'. To distinguish the meaning from the reference was one of the greatest (and simplest) clarifications ever offered of how language works. |
| 16987 | By eliminating descriptions from primitive notation, Russell seems to reject 'sense' [Russell, by Kripke] |
| Full Idea: Russell, since he eliminates descriptions from his primitive notation, seems to hold in 'On Denoting' that the notion of 'sense' is illusory. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Saul A. Kripke - Naming and Necessity notes and addenda note 04 | |
| A reaction: Presumably we can eliminate sense from formal languages, but natural languages are rich in connotations (or whatever we choose to call them). |
| 4570 | Russell assumes that expressions refer, but actually speakers refer by using expressions [Cooper,DE on Russell] |
| Full Idea: Russell assumes that it is expressions which refer if anything does, but strictly speaking it is WE who refer with the use of expressions. | |
| From: comment on Bertrand Russell (On Denoting [1905]) by David E. Cooper - Philosophy and the Nature of Language §4.1 | |
| A reaction: This sounds right. Russell is part of the overemphasis on language which plagued philosophy after Frege. Words are tools, like searchlights or pointing fingers. |
| 16349 | Russell rejected sense/reference, because it made direct acquaintance with things impossible [Russell, by Recanati] |
| Full Idea: Russell rejected Frege's sense/reference distinction, on the grounds that, if reference is mediated by sense, we lose the idea of direct acquaintance and succumb to Descriptivism. | |
| From: report of Bertrand Russell (On Denoting [1905]) by François Recanati - Mental Files 1.1 | |
| A reaction: [15,000th IDEA in the DB!! 23/3/2013, Weymouth] Recanati claims Russell made a mistake, because you can retain the sense/reference distinction, and still keep direct acquaintance (by means of 'non-descriptive senses'). |
| 7313 | 'Sense' is superfluous (rather than incoherent) [Russell, by Miller,A] |
| Full Idea: Russell does not claim that Frege's notion of sense is incoherent, but rather that it is superfluous. | |
| From: report of Bertrand Russell (On Denoting [1905]) by Alexander Miller - Philosophy of Language 2.9 | |
| A reaction: My initial reaction to this is that the notion of strict and literal meaning (see Idea 7309) is incredibly useful. Some of the best jokes depend on the gap between implications and strict meaning. How could metaphors be explained without it? |
| 7767 | The theory of definite descriptions aims at finding correct truth conditions [Russell, by Lycan] |
| Full Idea: Russell's theory of definite descriptions proceeds by sketching the truth conditions of sentences containing descriptions, and arguing on various grounds that they are the correct truth conditions. | |
| From: report of Bertrand Russell (On Denoting [1905]) by William Lycan - Philosophy of Language Ch.9 | |
| A reaction: It seems important to see both where Russell was going, and where Davidson has come from. The whole project of finding the logical form of sentences (which starts with Frege and Russell) implies that truth conditions is what matters. |
| 21726 | In graspable propositions the constituents are real entities of acquaintance [Russell] |
| Full Idea: In every proposition that we can apprehend, ...all the constituents are real entities with which we have immediate acquaintance. | |
| From: Bertrand Russell (On Denoting [1905], p.56), quoted by Bernard Linsky - Russell's Metaphysical Logic 7.2 | |
| A reaction: This is the clearest statement of the 'Russellian' concept of a proposition. It strikes me as entirely wrong. The examples are always nice concrete objects like Mont Blanc, but as an account of sophisticated general propositions it seem hopeless. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 5773 | The ontological argument begins with an unproven claim that 'there exists an x..' [Russell] |
| Full Idea: 'There is one and only one entity x which is most perfect; that one has all perfections; existence is a perfection; therefore that one exists' fails as a proof because there is no proof of the first premiss. | |
| From: Bertrand Russell (On Denoting [1905], p.54) | |
| A reaction: This is the modern move of saying that existence (which is 'not a predicate', according to Kant) is actually a quantifier, which isolates the existence claim being made about a variable with a bunch of predicates. McGinn denies Russell's claim. |