19 ideas
| 15549 | If it were true that nothing at all existed, would that have a truthmaker? [Lewis] |
| Full Idea: If there was absolutely nothing at all, then it would have been true that there was nothing. Would there have been a truthmaker for this truth? | |
| From: David Lewis (A world of truthmakers? [1998], p.220) | |
| A reaction: This is a problem for Lewis's own claim that 'truth supervenes on being', as well as the more restricted truthmakers invoked by Armstrong. |
| 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'. |
| 6237 | Fear of God is not conscience, which is a natural feeling of offence at bad behaviour [Shaftesbury] |
| Full Idea: Conscience is to find horribly offensive the reflection of any unjust action or behaviour; to have awe and terror of the Deity, does not, of itself, imply conscience; …thus religious conscience supposes moral or natural conscience. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], II.II.I) | |
| A reaction: The reply from religion would be that the Deity has implanted natural conscience in each creature, though this seems to deny our freedom of moral judgment. Personally I am inclined to think that values are just observations of the world - such as health. |
| 6234 | If an irrational creature with kind feelings was suddenly given reason, its reason would approve of kind feelings [Shaftesbury] |
| Full Idea: If a creature wanting reason has many good qualities and affections, it is certain that if you give this creature a reflecting faculty, it will at the same instant approve of gratitude, kindness and pity. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], I.III.III) | |
| A reaction: A wonderful denunciation of the authority of reason, which must have influenced David Hume. I think, though, that the inverse of this case must be considered (if suddenly given feelings, they would fall in line with reasoning). We reason about feelings. |
| 6233 | A person isn't good if only tying their hands prevents their mischief, so the affections decide a person's morality [Shaftesbury] |
| Full Idea: We do not say that he is a good man when, having his hands tied up, he is hindered from doing the mischief he designs; …hence it is by affection merely that a creature is esteemed good or ill, natural or unnatural. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], I.II.I) | |
| A reaction: Note that he more or less equates being morally 'ill' with being 'unnatural'. We tend to reserve 'unnatural' for extreme or perverse crimes. Personally I would place more emphasis on evil judgements, and less on evil feelings. |
| 6236 | People more obviously enjoy social pleasures than they do eating and drinking [Shaftesbury] |
| Full Idea: How much the social pleasures are superior to any other may be known by visible tokens and effects; the marks and signs which attend this sort of joy are more intense and clear than those which attend the satisfaction of thirst and hunger. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], II.II.I) | |
| A reaction: He presumably refers to smiles and laughter, but they could be misleading as they are partly a means of social communication. You should ask people whether they would prefer a nice conversation or a good pork chop. Nice point, though. |
| 6235 | Self-interest is not intrinsically good, but its absence is evil, as public good needs it [Shaftesbury] |
| Full Idea: Though no creature can be called good merely for possessing the self-preserving affections, it is impossible that public good can be preserved without them; so that a creature wanting in them is wanting in natural rectitude, and may be esteemed vicious. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], II.I.III) | |
| A reaction: Aristotle held a similar view (Idea 92). I think maybe Shaftesbury was the last call of the Aristotelians, before being engulfed by utilitarians and Kantians. This idea is at the core of capitalism. |
| 6232 | Every creature has a right and a wrong state which guide its actions, so there must be a natural end [Shaftesbury] |
| Full Idea: We know there is a right and a wrong state of every creature; and that his right one is by nature forwarded, and by himself affectionately sought. There being therefore in every creature a certain interest or good; there must also be a natural end. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], I.II.I) | |
| A reaction: This is an early modern statement of Aristotelian teleology, just at the point where it was falling out of fashion. The underlying concept is that of right function. I agree with Shaftesbury, but you can't stop someone damaging their health. |
| 5642 | For Shaftesbury, we must already have a conscience to be motivated to religious obedience [Shaftesbury, by Scruton] |
| Full Idea: Shaftesbury argued that no morality could be founded in religious obedience, or piety. On the contrary, a man is motivated to such obedience only because conscience tells him that the divine being is worthy of it. | |
| From: report of 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699]) by Roger Scruton - Short History of Modern Philosophy Ch.8 | |
| A reaction: This seems to me a good argument. The only alternative is that we are brought to God by a conscience which was planted in us by God, but then how would you know you were being obedient to the right hypnotist? |