display all the ideas for this combination of philosophers
25 ideas
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5 | |
| A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?). |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| Full Idea: Boolos has proposed an alternative understanding of monadic, second-order logic, in terms of plural quantifiers, which many philosophers have found attractive. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by Stewart Shapiro - Philosophy of Mathematics 3.5 |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth. | |
| From: George Boolos (On Second-Order Logic [1975], p.45) | |
| A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification. |
| 10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
| Full Idea: In an indisputable technical result, Boolos showed how plural quantifiers can be used to interpret monadic second-order logic. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984], Intro) by Řystein Linnebo - Plural Quantification Exposed Intro |
| 10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
| Full Idea: Boolos discovered that any sentence of monadic second-order logic can be translated into plural first-order logic. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984], §1) by Řystein Linnebo - Plural Quantification Exposed p.74 |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts. | |
| From: George Boolos (On Second-Order Logic [1975], p.44) | |
| A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction? |
| 10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
| Full Idea: Indispensable to cross-reference, lacking distinctive content, and pervading thought and discourse, 'identity' is without question a logical concept. Adding it to predicate calculus significantly increases the number and variety of inferences possible. | |
| From: George Boolos (To be is to be the value of a variable.. [1984], p.54) | |
| A reaction: It is not at all clear to me that identity is a logical concept. Is 'existence' a logical concept? It seems to fit all of Boolos's criteria? I say that all he really means is that it is basic to thought, but I'm not sure it drives the reasoning process. |
| 10437 | Names are rigid, making them unlike definite descriptions [Kripke, by Sainsbury] |
| Full Idea: It was important to Kripke to contrast the rigidity of names with the non-rigidity of many or most definite descriptions. | |
| From: report of Saul A. Kripke (Naming and Necessity lectures [1970]) by Mark Sainsbury - The Essence of Reference 18.6 | |
| A reaction: Philosophers always want sharp distinctions, but there are tricky names like 'Homer' and 'Jack the Ripper' where the name is stable, but its referent wobbles. |
| 4949 | Names are rigid designators, which designate the same object in all possible worlds [Kripke] |
| Full Idea: I will call something a 'rigid designator' if in every possible world it designates the same object, ..and I will maintain the intuitive thesis that names are rigid designators. | |
| From: Saul A. Kripke (Naming and Necessity lectures [1970], Lecture 1) | |
| A reaction: The immediate problem seems to be objects that change across possible worlds. Did nature rigidly designate Aristotle (e.g. by his DNA)? Could Aristotle have been shorter, female, cleverer, his own twin? Is the River Thames rigid? |
| 4951 | A bundle of qualities is a collection of abstractions, so it can't be a particular [Kripke] |
| Full Idea: I deny that a particular is nothing but a 'bundle of qualities', whatever that may mean. If a quality is an abstract object, a bundle of qualities is an object of an even higher degree of abstraction, not a particular. | |
| From: Saul A. Kripke (Naming and Necessity lectures [1970], Lecture 1) | |
| A reaction: Supports the 'baptism' view of reference, rather than Searle's bundle of descriptions. It shows that theories of reference must tie in with theories of universals, and that Searle is a nominalist. Is Kripke trying to duck metaphysical responsibility? |
| 17031 | A name can still refer even if it satisfies none of its well-known descriptions [Kripke] |
| Full Idea: Suppose the vote yields no object, that nothing satisfies most, or even any, substantial number, of the φ's. Does that mean the name doesn't refer? No. | |
| From: Saul A. Kripke (Naming and Necessity lectures [1970], Lecture 2) | |
| A reaction: As example he gives the case of 'Gödel' referring to the famous man, even if none of the descriptions of him are true. In Note 42 he blames the descriptivists for relying too much on famous people. |
| 9175 | We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [Kripke] |
| Full Idea: We may fix the reference of 'Cicero' by use of some descriptive phrase, such as 'author of these works'. But once we have this reference fixed, we then use the name 'Cicero' rigidly to designate the man who in fact we have identified by his authorship. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.183) | |
| A reaction: Even supposedly rigid names can shift reference, as Evans's example of 'Madagascar' shows (Idea 9041). Reference is a much more social activity than Kripke is willing to admit. There is a 'tradition' of reference (Dummett) for the name 'Cicero'. |
| 8957 | Some references, such as 'Neptune', have to be fixed by description rather than baptism [Kripke, by Szabó] |
| Full Idea: Kripke explicitly allows for the introduction of names through initial reference-fixing via descriptions. Versions of the causal theory of reference that disallow this would have a difficult time explaining how the name 'Neptune' came to refer. | |
| From: report of Saul A. Kripke (Naming and Necessity lectures [1970]) by Zoltán Gendler Szabó - Nominalism 4.2 n35 | |
| A reaction: The initial reference to Neptune has to be by description, but you could still give a baptismal account once it is discovered. The direct contact now takes precedence. Suppose another similar planet was found nearby... |
| 9171 | The function of names is simply to refer [Kripke] |
| Full Idea: The function of names is simply to refer. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.167) | |
| A reaction: This is Kripke reverting to the John Stuart Mill view of names. If I say "you are a right Casanova" I don't simply refer to Casanova. In notorious examples like 'Homer' reference is fine, but the object of reference is a bit elusive. |
| 10428 | Proper names must have referents, because they are not descriptive [Kripke, by Sainsbury] |
| Full Idea: A common source of the view that proper names must have referents is that they are not descriptive (as expressed by Kripke). | |
| From: report of Saul A. Kripke (Naming and Necessity lectures [1970]) by Mark Sainsbury - The Essence of Reference 18.2 | |
| A reaction: Sainsbury observes that there might be some other way for a name to be intelligible, with describing or referring. |
| 4959 | A name's reference is not fixed by any marks or properties of the referent [Kripke] |
| Full Idea: It is in general not the case that the reference of a name is determined by some uniquely identifying marks, some unique properties satisfied by the referent and known or believed to be true of that referent by the speaker. | |
| From: Saul A. Kripke (Naming and Necessity lectures [1970], Lecture 3) | |
| A reaction: He is proposing, instead, his historical/causal theory. There does seem to be a problem with objects which have a historical 'baptism', and then entirely change their properties. Kripke us desperate for a simple account of reference. |
| 16982 | A man has two names if the historical chains are different - even if they are the same! [Kripke] |
| Full Idea: Two totally distinct 'historical chains' that be sheer accident assign the same name to the same man should probably count as creating distinct names despite the identity of the referents. | |
| From: Saul A. Kripke (Naming and Necessity preface [1980], p.08 n9) | |
| A reaction: A nice puzzle for his own theory. 'What's you name?' 'Alice, and Alice!' |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed. | |
| From: George Boolos (On Second-Order Logic [1975], p.46) | |
| A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain. |
| 10792 | The substitutional quantifier is not in competition with the standard interpretation [Kripke, by Marcus (Barcan)] |
| Full Idea: Kripke proposes that the substitutional quantifier is not a replacement for, or in competition with, the standard interpretation. | |
| From: report of Saul A. Kripke (A Problem about Substitutional Quantification? [1976]) by Ruth Barcan Marcus - Nominalism and Substitutional Quantifiers p.165 |
| 13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
| Full Idea: Boolos proposes that second-order quantifiers be regarded as 'plural quantifiers' are in ordinary language, and has developed a semantics along those lines. In this way they introduce no new ontology. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by Stewart Shapiro - Foundations without Foundationalism 7 n32 | |
| A reaction: This presumably has to treat simple predicates and relations as simply groups of objects, rather than having platonic existence, or something. |
| 10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
| Full Idea: Standard second-order existential quantifiers pick out a class or a property, but Boolos suggests that they be understood as a plural quantifier, like 'there are objects' or 'there are people'. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by Stewart Shapiro - Philosophy of Mathematics 7.4 | |
| A reaction: This idea has potential application to mathematics, and Lewis (1991, 1993) 'invokes it to develop an eliminative structuralism' (Shapiro). |
| 10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
| Full Idea: Abandon the idea that use of plural forms must always be understood to commit one to the existence of sets of those things to which the corresponding singular forms apply. | |
| From: George Boolos (To be is to be the value of a variable.. [1984], p.66) | |
| A reaction: It seems to be an open question whether plural quantification is first- or second-order, but it looks as if it is a rewriting of the first-order. |
| 7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
| Full Idea: Boolos virtually patented the new device of plural quantification. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by José A. Benardete - Logic and Ontology | |
| A reaction: This would be 'there are some things such that...' |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
| From: George Boolos (On Second-Order Logic [1975], p.52) | |
| A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |