22 ideas
| 1564 | True and false statements can use exactly the same words [Anon (Diss)] |
| Full Idea: There is no difference between a true statement and a false statement, because they can use exactly the same words. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §4) |
| 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'. |
| 1559 | Thracians think tattooing adds to a girl's beauty, but elsewhere it is a punishment [Anon (Diss)] |
| Full Idea: Thracians think that tattooing enhances a girl's beauty, whereas for everyone else tattooing is a punishment for a crime. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §2) |
| 1561 | Anything can be acceptable in some circumstances and unacceptable in others [Anon (Diss)] |
| Full Idea: Anything can be acceptable under the right circumstances, and unacceptable under the wrong circumstances. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §2) |
| 1560 | Lydians prostitute their daughters to raise a dowery, but no Greek would marry such a girl [Anon (Diss)] |
| Full Idea: The Lydians find it acceptable for their daughters to work as prostitutes to raise money for getting married, but no one in Greece would be prepared to marry such a girl. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §2) |
| 1567 | How could someone who knows everything fail to act correctly? [Anon (Diss)] |
| Full Idea: If someone knows the nature of everything, how could he fail to be able also to act correctly in every case? | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §8) |
| 1563 | Every apparent crime can be right in certain circumstances [Anon (Diss), by PG] |
| Full Idea: It can be right, in certain circumstances, to steal, to break a solemn promise, to rob temples, and even (as Orestes did) to murder one's nearest and dearest. | |
| From: report of Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §3) by PG - Db (ideas) | |
| A reaction: Not sure about the last one! I suppose you can justify any hideousness if the fate of the universe depends on it. It must be better to die than the perform certain extreme deeds. |
| 1562 | It is right to lie to someone, to get them to take medicine they are reluctant to take [Anon (Diss)] |
| Full Idea: It is right to lie to your parents, in order to get them to take a good medicine they are reluctant to take. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §3) | |
| A reaction: I dread to think what the medicines were which convinced the writer of this. A rule such as this strikes me as dangerous. Justifiable in extreme cases. House on fire etc. |
| 1566 | The first priority in elections is to vote for people who support democracy [Anon (Diss)] |
| Full Idea: A lottery is not democratic, because every state contains people who are not democratic, and if the lottery chooses them they will destroy the democracy. People should elect those who are observed to favour democracy. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §7) |
| 1565 | We learn language, and we don't know who teaches us it [Anon (Diss)] |
| Full Idea: We learn language, and we don't know who teaches us it. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §6) |
| 8416 | Reductionists can't explain accidents, uninstantiated laws, probabilities, or the existence of any laws [Tooley] |
| Full Idea: Reductionist accounts of causation cannot distinguish laws from accidental uniformities, cannot allow for basic uninstantiated laws, can't explain probabilistic laws, and cannot even demonstrate the existence of laws. | |
| From: Michael Tooley (Causality: Reductionism versus Realism [1990], 2) | |
| A reaction: I am tempted to say that this is so much the worse for the idea of laws. Extensive regularities only occur for a reason. Probabilities aren't laws. Hypothetical facts will cover uninstantiated laws. Laws are just patterns. |
| 8418 | Quantum physics suggests that the basic laws of nature are probabilistic [Tooley] |
| Full Idea: Quantum physics seems to lend strong support to the idea that the basic laws of nature may well be probabilistic. | |
| From: Michael Tooley (Causality: Reductionism versus Realism [1990], 3.2.1) | |
| A reaction: Groan. Quantum physics should be outlawed from all philosophical discussions. The scientists don't understand it themselves. I'm certainly not going to build my worldview on it. I don't accept that these probabilities could count as 'laws'. |