24 ideas
| 14519 | It is a great good to show reverence for a wise man [Epicurus] |
| Full Idea: To show reverence for a wise man is itself a great good for him who reveres [the wise man]. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 32) | |
| A reaction: It is characteristic of Epicurus to move up a level in his thinking, and not merely respect wisdom, but ask after the value of his own respect. Compare Idea 14517. Nice. |
| 14518 | In the study of philosophy, pleasure and knowledge arrive simultaneously [Epicurus] |
| Full Idea: In philosophy the pleasure accompanies the knowledge. For the enjoyment does not come after the learning but the learning and the enjoyment are simultaneous. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 27) |
| 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'. |
| 14524 | Bodies are combinations of shape, size, resistance and weight [Epicurus] |
| Full Idea: Epicurus said that body was conceived as an aggregate of shape and size and resistance and weight. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE]) | |
| A reaction: [Source Sextus 'Adversus Mathematicos' 10.257] Note that this is how we 'conceive' them. They might be intrinsically different, except that Epicurus is pretty much a phenomenalist. |
| 14521 | If everything is by necessity, then even denials of necessity are by necessity [Epicurus] |
| Full Idea: He who claims that everything occurs by necessity has no complaint against him who claims that everything does not occur by necessity. For he makes the very claim in question by necessity. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 40) |
| 14522 | What happens to me if I obtain all my desires, and what if I fail? [Epicurus] |
| Full Idea: One should bring this question to bear on all one's desires: what will happen to me if what is sought by desire is achieved, and what will happen if it is not? | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 71) | |
| A reaction: Yet another example of Epicurus moving up a level in his thinking about ethical issues, as in Idea 14517 and Idea 14519. The mark of a true philosopher. This seems to be a key idea for wisdom - to think further ahead than merely what you desire. |
| 3563 | Pleasure and virtue entail one another [Epicurus] |
| Full Idea: It is not possible to live pleasantly without living intelligently and finely and justly, nor to live intelligently and finely and justly without living pleasantly. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 5), quoted by Julia Annas - The Morality of Happiness Ch.16 | |
| A reaction: A person with all these virtues might still suffer from depression. And I don't see why having limited intelligence should stop someone from living pleasantly. Just be warm-hearted. |
| 3560 | Justice is merely a contract about not harming or being harmed [Epicurus] |
| Full Idea: There is no such things as justice in itself; in people's relations with one another in any place and at any time it is a contract about not harming or being harmed. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 33), quoted by Julia Annas - The Morality of Happiness 13.2 |
| 14517 | We value our own character, whatever it is, and we should respect the characters of others [Epicurus] |
| Full Idea: We value our characters as our own personal possessions, whether they are good and envied by men or not. We must regard our neighbours' characters thus too, if they are respectable. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 15) | |
| A reaction: I like this because it introduces a metaethical dimension to the whole problem of virtue. We should value our own character - so should we try to improve it? Should we improve so much as to become unrecognisable? |
| 14513 | Justice is a pledge of mutual protection [Epicurus] |
| Full Idea: The justice of nature is a pledge of reciprocal usefulness, neither to harm one another nor to be harmed. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 31) | |
| A reaction: Notice that justice is not just reciprocal usefulness, but a 'pledge' to that effect. This implies a metaethical value of trust and honesty in keeping the pledge. Is it better to live by the pledge, or to be always spontaneously useful? |
| 14515 | A law is not just if it is not useful in mutual associations [Epicurus] |
| Full Idea: If someone passes a law and it does not turn out to be in accord with what is useful in mutual associations, this no longer possesses the nature of justice. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 37) |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 14520 | It is small-minded to find many good reasons for suicide [Epicurus] |
| Full Idea: He is utterly small-minded for whom there are many plausible reasons for committing suicide. | |
| From: Epicurus (Principle Doctrines ('Kuriai Doxai') (frags) [c.290 BCE], 38) | |
| A reaction: It is a pity that the insult of 'small-minded' has slipped out of philosophy. The Greeks use it all the time, and know exactly what it means. We all recognise small-mindedness, and it is a great (and subtle) vice. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |