32 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'. |
| 14703 | Superficial necessity is true in all worlds; deep necessity is thus true, no matter which world is actual [Schroeter] |
| Full Idea: If we have a 'fixedly' operator F, then a sentence is fixedly actually true if it is true no matter which world is designated as actual (which 'he actually won in 2008' fails to be). Maybe '□' is superficial necessity, and FA is 'deep' necessity. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.2.2) | |
| A reaction: Gareth Evans distinguishes 'deep' from 'superficial' necessity. Humberstone and others introduced 'F'. Presumably FA is deeper because it has to pass a tougher test. |
| 14714 | Contradictory claims about a necessary god both seem apriori coherent [Schroeter] |
| Full Idea: It seems apriori coherent that there could be a necessarily existing god, and that there could be no such god - but they can't both be true. Other examples include unprovable mathematical necessities | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.4) |
| 14704 | 2D semantics gives us apriori knowledge of our own meanings [Schroeter] |
| Full Idea: Generalized 2D semantics is meant to vindicate the traditional idea that we have apriori access to our own meanings through armchair reflection. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.1) | |
| A reaction: The idea is to split meaning in two, so that we know one part of it a priori. It is an unfashionably internalist view of meaning (which doesn't make it wrong!). |
| 3158 | Theories of intentionality presuppose rationality, so can't explain it [Dennett] |
| Full Idea: Intentional theory is vacuous as psychology because it presupposes and does not explain rationality or intelligence. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.15?) | |
| A reaction: Virtually every philosophical theory seems to founder because it presupposes something like the thing it is meant to explain. I agree that 'intentionality' is a slightly airy concept that would probably reduce to something better. |
| 3159 | Beliefs and desires aren't real; they are prediction techniques [Dennett] |
| Full Idea: Intentional systems don't really have beliefs and desires, but one can explain and predict their behaviour by ascribing beliefs and desires to them. This strategy is pragmatic, not right or wrong. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.7?) | |
| A reaction: If the ascription of beliefs and desires explains behaviour, then that is good grounds for thinking they might be real features of the brain, and even if that is not so, they are real enough as abstractions from brain events, like the 'economic climate'. |
| 14706 | Your view of water depends on whether you start from the actual Earth or its counterfactual Twin [Schroeter] |
| Full Idea: Your verdicts about whether the stuff on Twin Earth counts as water depends on whether you think of Twin Earth as a hypothesis about your actual environment or as a purely counterfactual possibility. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.2.3) | |
| A reaction: This is the 'two-dimensional semantics' approach to the Twin Earth problem, which splits meaning into two components. Whether you start from the actual world or from Twin Earth, you will rigidly designate the local wet stuff as 'water'. |
| 14711 | Rationalists say knowing an expression is identifying its extension using an internal cognitive state [Schroeter] |
| Full Idea: In rationalist views of meaning, based on the 'golden triangle', to be competent with an expression is to be in an internal cognitive state that puts one in a position to identify its extension in any possible world based only on apriori reflection. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.1) | |
| A reaction: This looks like a proper fight-back against modern rampant externalism about meaning. All my intuitions are with internalism, which I think points to a more coherent overall philosophy. Well done, David Chalmers! Even if he is wrong. |
| 14717 | Internalist meaning is about understanding; externalist meaning is about embedding in a situation [Schroeter] |
| Full Idea: Internalists take the notion of meaning to capture an aspect of an individual's current state of understanding, while externalists take the notion of meaning to reflect how an individual is embedded within her social and physical environment. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.4.3) | |
| A reaction: This idea also occurs in discussions of concepts (filed here under 'Thought'). |
| 14720 | Semantic theory assigns meanings to expressions, and metasemantics explains how this works [Schroeter] |
| Full Idea: A semantic theory assigns semantic values (meanings) to particular expressions of the language. In contrast, a metasemantic theory explains why expressions have those semantic values, appealing to facts about speakers and communities. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 3.4) | |
| A reaction: Presumably some people only want the metasemantic version. I assume that the two are entangled, but I would vote for both. |
| 14695 | Semantic theories show how truth of sentences depends on rules for interpreting and joining their parts [Schroeter] |
| Full Idea: Semantic theories explain how the truth or falsity of whole sentences depends on the meanings of their parts by stating rules governing the interpretation of subsentential expressions and their modes of combination. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: Somehow it looks as if the mystery of the whole business will still be missing if this project is ever successfully completed. Also one suspects that such a theory would be a fiction, rather than a description of actuality, which is too complex. |
| 14696 | Simple semantics assigns extensions to names and to predicates [Schroeter] |
| Full Idea: The simplest semantic frameworks assign extensions as semantic values of particular expressions. The extension of a name is the thing, of 'cool' is the set of cool things, and sets of ordered pairs for 2-place predicates. The sentence has T or F. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: The immediate well-known problem is different predicates with the same extensions, such as 'renate' and 'cordate'. Possible worlds semantics is supposed to be an improvement to cover this, and to give a semantics for modal talk as well. Sounds good. |
| 14697 | 'Federer' and 'best tennis player' can't mean the same, despite having the same extension [Schroeter] |
| Full Idea: A simple extensional semantics will assign the same semantic value to 'Roger Federer' and 'world's best tennis player', but they clearly differ in meaning, and if events had unfolded differently they would pick out different people. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: You would think that this would be too obvious to need pointing out, but it is clearly a view that had a lot of popularity before the arrival of possible worlds. |
| 14698 | Possible worlds semantics uses 'intensions' - functions which assign extensions at each world [Schroeter] |
| Full Idea: In standard possible worlds semantics, the semantic value of an expression is an 'intension', a function that assigns an extension to the expression 'at' every possible world. ...It keeps track of the 'modal profiles' of objects, kinds and properties. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: Personally I just don't buy a semantics which is entirely based on extensions, even if this has sorted out some more obvious problems of extensionality. When I say someone is 'my hero', I don't just mean to pick out a particular person. |
| 14699 | Possible worlds make 'I' and that person's name synonymous, but they have different meanings [Schroeter] |
| Full Idea: In standard possible worlds semantics the semantic value of Hllary Clinton's utterance of 'I' will be the same as her utterance of 'Hillary Clinton'. But clearly the English word 'I' is not synonymous with the name 'Hillary Clinton'. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.1) | |
| A reaction: This problem was spotted by Kaplan, and it has been a chief motivator for the creation of two-dimensional semantics, which some people have then extended into a complete semantic theory. No purely extensional semantics can be right. |
| 14709 | Possible worlds semantics implies a constitutive connection between meanings and modal claims [Schroeter] |
| Full Idea: In standard possible world semantics an expression's intension reflects the modal profile of an object, kind or property, which would establish an important constitutive connection between meanings and modal claims. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.1) | |
| A reaction: The central question becomes 'do you need to know a thing's modal profile in order to have a decent understanding of it?', but if you express it that way (my way), then what counts as 'decent' will be relative to all sorts of things. |
| 14719 | In the possible worlds account all necessary truths are same (because they all map to the True) [Schroeter] |
| Full Idea: A problem for a standard possible worlds analysis is that all necessary truths have precisely the same content (the function mapping every world to the True). Hesperus=Phosphorus has the same content as Hesperus=Hesperus-and-2+2=4. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 3.3) | |
| A reaction: If this is supposed to be a theory of meaning then it has gone very badly wrong indeed. Has modern semantics taken a wrong turning somewhere? Two-dimensionalism is meant to address some of these problems. |
| 14701 | Array worlds along the horizontal, and contexts (world,person,time) along the vertical [Schroeter] |
| Full Idea: In a two-dimensional matrix we array possible circumstances of evaluation (worlds) along the horizontal axis, and possible contexts of utterance (world, person, time) along the vertical axis. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.1.2) | |
| A reaction: This is due to Stalnaker 1978, and is clearest in operation when applied to an indexical such as 'I' in 'I am President'. 'I' is a rigid designator, but depends on context. The grid is filled in with T or F for each utterance in each world. |
| 14702 | If we introduce 'actually' into modal talk, we need possible worlds twice to express this [Schroeter] |
| Full Idea: At first glance necessity and possibility can be fully expressed by quantifying over all possible worlds, but this cannot capture 'Possibly everything actually red is also shiny'. This needs a double-indexed framework, with worlds playing two roles. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 1.2.1) | |
| A reaction: She points out that this also applies to tense logic, for the notion of 'now'. The point is that we not only need a set of possible worlds, but we also need a procedure (the 'Actuality' operator A or @) for picking out one of the worlds as special. |
| 14705 | Do we know apriori how we refer to names and natural kinds, but their modal profiles only a posteriori? [Schroeter] |
| Full Idea: Perhaps our best way of understanding names and natural kind terms is that we have apriori access to currently associated reference-fixing criterion, but only a posteriori access to the associated modal profile. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.1) | |
| A reaction: This is the 'generalized' view of 2D semantics (covering everything, not just modals and indexicals). I know apriori what something is, but only study will reveal its possibilities. The actual world is easy to talk about, but possible worlds are harder. |
| 14715 | 2D fans defend it for conceptual analysis, for meaning, and for internalist reference [Schroeter] |
| Full Idea: Supporters of generalized two-dimensional semantics agree to defend apriori conceptual analysis in metaphysics, and that 2D captures meaning and not just belief-patterns, and it gives a broadly internalist approach to reference determination. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.3.4) | |
| A reaction: I'm not sure I can evaluate this, but I sort of like conceptual analysis, and the concept of meaning, and fairly internalist views of reference, so I am ripe for the picking. |
| 14716 | 2D semantics can't respond to contingent apriori claims, since there is no single proposition involved [Schroeter] |
| Full Idea: It is objected to 2D semantics that it cannot explain Kripke's cases of contingent apriori truths, for there is no single proposition (construed as a set of possible worlds) that is both apriori and contingent. | |
| From: Laura Schroeter (Two-Dimensional Semantics [2010], 2.4.2) | |
| A reaction: This sounds like a rather large objection to the whole 2D plan, if it implies that when we say something there is no single proposition that is being expressed. |