19 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'. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 20937 | The state should produce higher civilisations for all, in tune with the economic apparatus [Gramsci] |
| Full Idea: The role of the State is always that of creating new and higher types of civilisation; of adapting the 'civilisation' and the morality of the broades popular masses to the necessities of the continuous development of the economic apparatus of production. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Collective') | |
| A reaction: This makes education virtually the prime role of the state. Reminiscent of Sir John Reith's original dream, in the 1930s, for the BBC. Many marxists feel that the economy is in direct conflict with morality and civilisation. |
| 20935 | Eventually political parties lose touch with the class they represent, which is dangerous [Gramsci] |
| Full Idea: At a certain point in their lives, social classes become detached from their traditional parties. In that particular form ...the parties are no longer recognised by their class as its exopression. ...The field is then open for violent solutions. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Parties') | |
| A reaction: Left wing parties pursue ideologies that don't connect with the actual current interests of the working class, and righ wing parties are taken over by rich elites who don't value safe traditonal communities. (This thought is resonant in the 2018 UK). |
| 20936 | Caesarism emerges when two forces in society are paralysed in conflict [Gramsci] |
| Full Idea: Caesarism (as the emergence of a 'heroic' personality) expresses a situation in which the forces in conflict balance each other in a catastrophic manner ...which can only terminate in their reciprocal destruction. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Caesarism') | |
| A reaction: He goes on to distinguish progressive and reactionary versions of Caesarism. Gramsci's interest is in the circumstances that throw up such people. Marx had identified 'Bonapartism'. |
| 20941 | Totalitarian parties cut their members off from other cultural organisations [Gramsci] |
| Full Idea: A totalitarian party ensures that members find in that particular party all the satisfactions that they formerly found in a multiplicity of organisations. They break the threads that bind them to extraneous cultural organisms. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Organisation') | |
| A reaction: British parties traditionally had a 'club house', where you could do most of your socialising. Presumably Nazis left the church, and various interest groups. |
| 20939 | What is the function of a parliament? Does it even constitute a part of the State structure? [Gramsci] |
| Full Idea: The question has to be asked: do parliaments, even in fact constitute a part of the State structure? In other words, what is the real function? | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Parliament') | |
| A reaction: Nice question. In the UK it is only the cabinet which has active power. Backbench MPs are usually very frustrated, especially if their party has a comfortable majority, and their vote is not precious. They are privileged lobbyists. |
| 20938 | Liberalism's weakness is its powerful rigid bureaucracy [Gramsci] |
| Full Idea: Liberalism's weakness is the bureacracy - the crystallisation of the leading personnel - which exercises power, and at a certain point it becomes a caste. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Hegemony') | |
| A reaction: This sounds more like what is called 'the Establishment' in Britain, which is the hidden controllers of power, rather than the administrators (whose role is only despised by right-wingers). |
| 20940 | Perfect political equality requires economic equality [Gramsci] |
| Full Idea: The idea that complete and perfect political equality cannot exist without economic equality ...remains correct. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'The State') | |
| A reaction: In the west we are living in a period (2018) when the top 0.1% of the wealthy are racing away, creating huge inequality. Their wealth controls the media, and it seems unrestrainable. The belief that we live in a 'democracy' is an illusion. |