22 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'. |
| 14329 | Some dispositional properties (such as mental ones) may have no categorical base [Price,HH] |
| Full Idea: There is no a priori necessity for supposing that all disposition properties must have a 'categorical base'. In particular, there may be some mental dispositions which are ultimate. | |
| From: H.H. Price (Thinking and Experience [1953], Ch.XI) | |
| A reaction: I take the notion that mental dispositions could be ultimate as rather old-fashioned, but I agree with the notion that dispositions might be more fundamental that categorical (actual) properties. Personally I like 'powers'. |
| 9032 | Before we can abstract from an instance of violet, we must first recognise it [Price,HH] |
| Full Idea: Abstraction is preceded by an earlier stage, in which we learn to recognize instances; before I can conceive of the colour violet in abstracto, I must learn to recognize instances of this colour when I see them. | |
| From: H.H. Price (Thinking and Experience [1953], Ch.II) | |
| A reaction: The problem here might be one of circularity. If you are actually going to identify something as violet, you seem to need the abstract concept of 'violet' in advance. See Idea 9034 for Price's attempt to deal with the problem. |
| 9035 | If judgement of a characteristic is possible, that part of abstraction must be complete [Price,HH] |
| Full Idea: If we are to 'judge' - rightly or not - that this object has a specific characteristic, it would seem that so far as the characteristic is concerned the process of abstraction must already be completed. | |
| From: H.H. Price (Thinking and Experience [1953], Ch.III) | |
| A reaction: Personally I think Price is right, despite the vicious attack from Geach that looms. We all know the experiences of familiarity, recognition, and identification that go on when see a person or picture. 'What animal is that, in the distance?' |
| 9034 | There may be degrees of abstraction which allow recognition by signs, without full concepts [Price,HH] |
| Full Idea: If abstraction is a matter of degree, and the first faint beginnings of it are already present as soon as anything has begun to feel familiar to us, then recognition by means of signs can occur long before the process of abstraction has been completed. | |
| From: H.H. Price (Thinking and Experience [1953], Ch.III) | |
| A reaction: I like this, even though it is unscientific introspective psychology, for which no proper evidence can be adduced - because it is right. Neuroscience confirms that hardly any mental life has an all-or-nothing form. |
| 9036 | There is pre-verbal sign-based abstraction, as when ice actually looks cold [Price,HH] |
| Full Idea: We must still insist that some degree of abstraction, and even a very considerable degree of it, is present in sign-cognition, pre-verbal as it is. ...To us, who are familiar with northern winters, the ice actually looks cold. | |
| From: H.H. Price (Thinking and Experience [1953], Ch.IV) | |
| A reaction: Price may be in the weak position of doing armchair psychology, but something like his proposal strikes me as correct. I'm much happier with accounts of thought that talk of 'degrees' of an activity, than with all-or-nothing cut-and-dried pictures. |
| 9037 | Intelligent behaviour, even in animals, has something abstract about it [Price,HH] |
| Full Idea: Though it may sound odd to say so, intelligent behaviour has something abstract about it no less than intelligent cognition; and indeed at the animal level it is unrealistic to separate the two. | |
| From: H.H. Price (Thinking and Experience [1953], Ch.IV) | |
| A reaction: This elusive thought strikes me as being a key one for understanding human existence. To think is to abstract. Brains are abstraction machines. Resemblance and recognition require abstaction. |
| 9033 | Recognition must precede the acquisition of basic concepts, so it is the fundamental intellectual process [Price,HH] |
| Full Idea: Recognition is the first stage towards the acquisition of a primary or basic concept. It is, therefore, the most fundamental of all intellectual processes. | |
| From: H.H. Price (Thinking and Experience [1953], Ch.II) | |
| A reaction: An interesting question is whether it is an 'intellectual' process. Animals evidently recognise things, though it is a moot point whether slugs 'recognise' tasty leaves. |
| 9030 | Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item [Price,HH] |
| Full Idea: An abstract idea may have a dispositional as well as an occurrent interpretation. ..A man who possesses the concept Dog, when he is actually perceiving a dog can recognize that it is one, and can think about dogs when he is not perceiving any dog. | |
| From: H.H. Price (Thinking and Experience [1953], Ch.IX) | |
| A reaction: Ryle had just popularised the 'dispositional' account of mental events. Price is obviously right. The man may also be able to use the word 'dog' in sentences, but presumably dogs recognise dogs, and probably dream about dogs too. |
| 9029 | If ideas have to be images, then abstract ideas become a paradoxical problem [Price,HH] |
| Full Idea: There used to be a 'problem of Abstract Ideas' because it was assumed that an idea ought, somehow, to be a mental image; if some of our ideas appeared not to be images, this was a paradox and some solution must be found. | |
| From: H.H. Price (Thinking and Experience [1953], Ch.VIII) | |
| A reaction: Berkeley in particular seems to be struck by the fact that we are incapable of thinking of a general triangle, simply because there is no image related to it. Most conversations go too fast for images to form even of very visual things. |
| 9031 | The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH] |
| Full Idea: Basic concepts are acquired by direct abstraction from instances; unless there were some concepts acquired in this way by direct abstraction, there would be no conceptual cognition at all. | |
| From: H.H. Price (Thinking and Experience [1953], Ch.II) | |
| A reaction: This seems to me to be correct. A key point is that not only will I acquire the concept of 'dog' in this direct way, from instances, but also the concept of 'my dog Spot' - that is I can acquire the abstract concept of an instance from an instance. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |