16 ideas
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
Full Idea: We should abandon the idea that the use of plural forms commits us to the existence of sets/classes… Entities are not to be multiplied beyond necessity. There are not two sorts of things in the world, individuals and collections. | |
From: George Boolos (To be is to be the value of a variable.. [1984]), quoted by Henry Laycock - Object | |
A reaction: The problem of quantifying over sets is notoriously difficult. Try http://plato.stanford.edu/entries/object/index.html. |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
Full Idea: Is there, in addition to the 200 Cheerios in a bowl, also a set of them all? And what about the vast number of subsets of Cheerios? It is haywire to think that when you have some Cheerios you are eating a set. What you are doing is: eating the Cheerios. | |
From: George Boolos (To be is to be the value of a variable.. [1984], p.72) | |
A reaction: In my case Boolos is preaching to the converted. I am particularly bewildered by someone (i.e. Quine) who believes that innumerable sets exist while 'having a taste for desert landscapes' in their ontology. |
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 |
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 Øystein 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 Øystein Linnebo - Plural Quantification Exposed p.74 |
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. |
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...' |
14592 | Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer] |
Full Idea: Many things that seem to be abstract also seem to have a beginning (and ending) in time, such as a language like Urdu. It may be tempting to say that such things exist in time but not in space, but where exactly? | |
From: Chris Swoyer (Abstract Entities [2008], 1.1) | |
A reaction: A few distinctions might be needed. Urdu-speaking is an ability of certain people. We abstract from that their 'language'. There is nothing there apart from that ability. It has no more abstract existence than the 'weather'. |
14594 | Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer] |
Full Idea: Four things philosophers often want to know about a given sort of entity are: its existence conditions, its identity conditions, its modal status, and its epistemic status. | |
From: Chris Swoyer (Abstract Entities [2008], 3) | |
A reaction: I prefer 'modal profile' to 'modal status'. The 'existence conditions' sound rather epistemic. Why does the existence of anything require 'conditions' other than just existing? I suspect identity is irrelevant if humans aren't around. |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
Full Idea: Ontological commitment is carried by first-order quantifiers; a second-order quantifier needn't be taken to be a first-order quantifier in disguise, having special items, collections, as its range. They are two ways of referring to the same things. | |
From: George Boolos (To be is to be the value of a variable.. [1984], p.72) | |
A reaction: If second-order quantifiers are just a way of referring, then we can see first-order quantifiers that way too, so we could deny 'objects'. |
14595 | Can properties exemplify other properties? [Swoyer] |
Full Idea: Can properties themselves exemplify properties? | |
From: Chris Swoyer (Abstract Entities [2008], 3) | |
A reaction: Since I espouse a rather strict causal view of true properties, and lump the rest into the category of 'predicates', I am inclined to answer 'no' to this. Most people would disagree. 'Bright red' seems to be an example. But it isn't. |
14593 | Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer] |
Full Idea: Quantum field theory strongly suggests that there are (at the fundamental level) no individual, particular things. | |
From: Chris Swoyer (Abstract Entities [2008], 2.1) | |
A reaction: When people introduce quantum theory into ontological discussions I reach for my shotgun, but it does rather look as if things turn to mush at the bottom level. |
22251 | Liberalism may fail because it neglects the shared nature of what we pursue and protect [Haldane] |
Full Idea: I am interested in the claim that liberalism fails inasmuch as it neglects, and cannot accommodate, the fact that some or all of the goods we pursue, and which a system of rights is concerned to protect, are goods possessed in common. | |
From: John Haldane (The Individual, the State, and the Common Good [1996], III) | |
A reaction: It depends how individualistic we take liberalism to be. Extreme individualism (Nozick) strikes me as crazy. If 'we' erect a statue to some dubious politicians, it might be presented as a common good, but actually be despised by many. |