27 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...' |
| 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'. |
| 23708 | Humeans see properties as having no more essential features and relations than their distinctness [Friend/Kimpton-Nye, by PG] |
| Full Idea: The Humean view says properties are 'quiddities', which individuates properties by nothing more than their distinctness from one another, so that dispositions are not essential to them, and there is no limit to possible property recombination. | |
| From: report of Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.3.1) by PG - Db (ideas) | |
| A reaction: [my summary] All of this is implied by Hume, rather than stated. David Lewis supports this view. The theory of basic powers is the view's main opponent. This quidditist view is not found in physics, where a property's modal profile matters. |
| 23709 | Dispositions are what individuate properties, and they constitute their essence [Friend/Kimpton-Nye] |
| Full Idea: Dispositions constitute the essences of properties, and hence the identity of a property is not primitive ('quidditism'), but is given in terms of its dispositional relations to other properties. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.3.1) | |
| A reaction: I like the picture that powers are basic, giving rise to dispositions, which combine to produce qualitative and active properties. Powers are precise and relatively few, and properties are ill-defined and very numerous. Being 'influential', for example. |
| 23707 | Powers are properties which necessitate dispositions [Friend/Kimpton-Nye] |
| Full Idea: In broad terms: powers are properties that necessitate dispositions. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.2) | |
| A reaction: If powers are properties then they must be properties 'of' something, which then seems to be more fundamental than the powers. Maybe our concept of an electron helps, which seems to be a bundle of a few properties, but no one even asks 'of' what. |
| 23714 | Dispositional essentialism (unlike the grounding view) says only fundamental properties are powers [Friend/Kimpton-Nye] |
| Full Idea: Dispositional essentialism yields the view that just fundamental properties and some evolved macro properties are powers. The grounding view, by contrast, seems to yield the result that all properties are powers. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.7) | |
| A reaction: For the second view, Mumford (for example) claims that the sphericity of a ball is a power, but that seems to miss the whole motivation for the powers ontology, which offers a fairly fundamental explanation of laws and modality. |
| 23711 | A power is a property which consists entirely of dispositions [Friend/Kimpton-Nye] |
| Full Idea: In the 'dispositional essentialist' account (the main view) …what it is to be a power is to be a property whose essence is exhaustively constituted by dispositions. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.4) | |
| A reaction: [compressed] Sounds wrong to me. A very complex property (such as 'stormy' weather) could be nothing more than a large bundle of dispositions, but that wouldn't make it a 'power', which has to be simpler and more basic. |
| 23712 | Powers are qualitative properties which fully ground dispositions [Friend/Kimpton-Nye] |
| Full Idea: In the 'grounding' view of powers …powers are qualitative, because their essence can be specified independently of any dispositions or relations, but they fully ground dispositions. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.4) | |
| A reaction: [compressed] They give this as the rival view to dispositional essentialism. It may be a mistake to call a power a property (which needs to be 'of' something). Not sure how powers can be both fundamental and qualitative. Don't they also ground qualities? |
| 23698 | Dispositions have directed behaviour which occurs if triggered [Friend/Kimpton-Nye] |
| Full Idea: The three platitudes about dispositions are that 1) they are directed towards some specific behaviour, 2) they can be triggered under specific conditions, and 3) their directedness is modal, meaning not 'when it is triggered' but 'it it were triggered'. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.1.1) | |
| A reaction: [PG summary] This is the preliminary to an attempt at a precise formal analysis, covering a number of hypothetical problem cases. 3) is the counterfactual rather than material conditional. Seems accurate. |
| 23699 | 'Masked' dispositions fail to react because something intervenes [Friend/Kimpton-Nye] |
| Full Idea: A disposition is 'masked' when it fails to manifest due to interference, such as a fragile vase packed in bubble wrap, or an antidote taken after some poison. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.1) | |
| A reaction: [compressed] The easiest account of these would be to say that the stimulus or trigger of the disposition never completely occurs. Poisons are only disposed to kill when they are fully ingested. Bubble wrapped vases can't be properly struck. |
| 23700 | A disposition is 'altered' when the stimulus reverses the disposition [Friend/Kimpton-Nye] |
| Full Idea: A disposition is subject to 'altering' when the stimulus of the disposition influences whether (and to what degree) an object has that disposition. Either a live wire goes dead when it is touched, or a dead wire has a sensor making it live when touched. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.2) | |
| A reaction: The word 'fink' is used of such interference. Not much of a problem, I would say, because at the moment when the stimulus comes to do its job, there is no longer a disposition for it to trigger. No different from switching off a light. |
| 23701 | A disposition is 'mimicked' if a different cause produces that effect from that stimulus [Friend/Kimpton-Nye] |
| Full Idea: A disposition is 'mimicked' by objects without that disposition which behave as though they do have it. Styrofoam plates are not fragile, but make a horrible sound when stressed, causing some annoyed person to break them. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.3) | |
| A reaction: A rather strained example! It shouldn't be a problem if the same cause (stress) leads to the same effect (breaking), but by a different path which is not the same as fragility. A formal analysis must obviously cover this case. |
| 23702 | A 'trick' can look like a stimulus for a disposition which will happen without it [Friend/Kimpton-Nye] |
| Full Idea: A 'trick' can behave like a disposition, as when someone says 'abracadabra' over a hot cup of coffee, stimulating it (?) to gradually cool down. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.4) | |
| A reaction: This is like Humean constant conjunction which is obviously not a cause, such as night following day. Only a problem is this cup of coffee is seen in isolation from all other cups of coffee. Post hoc propter hoc does not apply to all stimuli! |
| 23703 | Some dispositions manifest themselves without a stimulus [Friend/Kimpton-Nye] |
| Full Idea: Some dispositions, such as loquaciousness or irascibility, are disposed to manifest whether they are provoked to do so. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.3.3) | |
| A reaction: We might surmise that such people have internal triggers that get them going, rather than overt ones. The Sun has a disposition to shine, without an external stimulus. The theory of powers says nature is active, rather than being disposed to activity. |
| 23704 | We could analyse dispositions as 'possibilities', with no mention of a stimulus [Friend/Kimpton-Nye] |
| Full Idea: We might abandon the relational analysis of dispositions (as stimulus-effect), and just say a disposition is a 'possibility', which simply can manifest, however that manifestation comes about. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.3.5) | |
| A reaction: [Compressed. He particularly cites Barbara Vetter] A mere 'possibility' seems to cover passive states as well as potentially active ones. A cushion can be dented, but I wouldn't say it was 'disposed' to dent. Radioactive decay is a disposition, though. |
| 23710 | Dispositionalism says modality is in the powers of this world, not outsourced to possible worlds [Friend/Kimpton-Nye] |
| Full Idea: Dispositionalism does not 'outsource' modality to other possible worlds, it roots modality in the powers of concrete individuals in this world. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.3.3) | |
| A reaction: Possible worlds are to abolish modality, by treating it as the non-modal facts of different worlds. I see the dispositional view as vastly superior, because the world is awash with vivid and undeniable potentialities, and one world is better ontology. |
| 3460 | Superactors and superspartans count against behaviourism [Putnam, by Searle] |
| Full Idea: Putnam proposed the superactor/superspartan objection to behaviourism. | |
| From: report of Hilary Putnam (Brains and Behaviour [1963]) by John Searle - The Rediscovery of the Mind Ch. 2.II | |
| A reaction: This is a beautiful compression of the obvious counterexamples, which are behaviour-wth-no-experience, and experience-with-no-behaviour. Presumably, though, Spartans are disposed to go 'aagh!' when they get home, and there are no 'super' actors. |
| 23706 | Hume's Dictum says no connections are necessary - so mass and spacetime warping could separate [Friend/Kimpton-Nye] |
| Full Idea: Hume's Dictum says there are no necessary connections between existences, …and also between the distinct properties that individuals instantiate. …It follows that an object's property of mass and its disposition to warp space-time could come apart. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.2) | |
| A reaction: [compressed] This nicely pinpoints the heart of the Humean view, to which scientific essentialists and fans of powers in nature object. The objectors include me. |