17 ideas
| 10365 | We might use 'facta' to refer to the truth-makers for facts [Mellor, by Schaffer,J] |
| Full Idea: Mellor offers a distinction between 'facts' and 'facta' (the latter being the truth-makers for facts). | |
| From: report of D.H. Mellor (The Facts of Causation [1995]) by Jonathan Schaffer - The Metaphysics of Causation 1.1 | |
| A reaction: The idea is that 'facta' can do the work in causation, because 'facts' are not part of the world. This seems a very helpful terminology, which should be encouraged, since 'fact' is plainly ambiguous in current usage. |
| 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...' |
| 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'. |
| 19730 | Epistemic virtues: love of knowledge, courage, caution, autonomy, practical wisdom... [Kvanvig] |
| Full Idea: Virtue theorists may focus on the particular habits or virtues of successful cognizers, such as love of knowledge, firmness, courage and caution, humility, autonomy, generosity, and practical wisdom. | |
| From: Jonathan Kvanvig (Virtue Epistemology [2011], III) | |
| A reaction: [He cites Roberts and Wood 2007] It is interesting that most of these virtues do not merely concern cognition. How about diligence, self-criticism, flexibility...? |
| 19731 | If epistemic virtues are faculties or powers, that doesn't explain propositional knowledge [Kvanvig] |
| Full Idea: Conceiving of the virtues in terms of faculties or powers doesn't help at all with the problem of accounting for propositional knowledge. | |
| From: Jonathan Kvanvig (Virtue Epistemology [2011], IV B) | |
| A reaction: It always looks as if epistemic virtues are a little peripheral to the main business of knowledge, which is getting beliefs to be correct and well-founded. Given that epistemic saints make occasional mistakes, talk of virtues can't be enough. |
| 19732 | The value of good means of attaining truth are swamped by the value of the truth itself [Kvanvig] |
| Full Idea: The Swamping Problem is that the value of truth swamps the value of additional features of true beliefs which are only instrumentally related to them. True belief is no more valuable if one adds a feature valuable for getting one to the truth. | |
| From: Jonathan Kvanvig (Virtue Epistemology [2011], IV B) | |
| A reaction: His targets here are reliabilism and epistemic virtues. Kvanvig's implication is that the key to understanding the nature of knowledge is to pinpoint why we value it so much. |
| 4785 | Causal statements relate facts (which are whatever true propositions express) [Mellor, by Psillos] |
| Full Idea: Mellor argues that causal statements relate facts, where facts may be seen as whatever true propositions express. | |
| From: report of D.H. Mellor (The Facts of Causation [1995]) by Stathis Psillos - Causation and Explanation §2.6 | |
| A reaction: Choose between 'facts', 'objects', 'conserved quantities, 'events' (the usual one) or 'processes'. I rather like processes (Salmon) as they are a better prospect as the building blocks of an ontology. |
| 8408 | Probabilistic causation says C is a cause of E if it increases the chances of E occurring [Mellor, by Tooley] |
| Full Idea: The basic idea of probabilistic causation is that a sufficient condition of C's being a cause of E is that C and E are actual, individual events, and the objective chance of E's occurring is greater given the occurrence of C than it would be without C. | |
| From: report of D.H. Mellor (The Facts of Causation [1995]) by Michael Tooley - Causation and Supervenience 5.3 | |
| A reaction: Mellor has to include objective 'chances' in his ontology to support his theory. As it stands this looks like a weak theory, since the event might not occur despite C happening, and some less likely event might turn out to be the actual cause. |