39 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'. |
| 2730 | Because 'gold is malleable' is necessary does not mean that it is analytic [Audi,R] |
| Full Idea: Taking the proposition that gold is malleable to be necessary does not commit one to considering it analytic. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], IV p.116) |
| 2715 | Beliefs are based on perception, memory, introspection or reason [Audi,R] |
| Full Idea: The four basic kinds of belief are rooted in perception, memory, introspective consciousness, and reason. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], Intr.p.7) |
| 2735 | Could you have a single belief on its own? [Audi,R] |
| Full Idea: Could one have just a single belief? | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VII p.198) |
| 2736 | We can make certain of what we know, so knowing does not entail certainty [Audi,R] |
| Full Idea: The possibility of making certain of what we already know suggests that knowing a proposition does not entail its being certain. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VIII p.220) |
| 2721 | If you gradually remove a book's sensory properties, what is left at the end? [Audi,R] |
| Full Idea: If you imagine subtracting a book's sensory properties one by one, what is left of it? | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.42) |
| 2722 | Sense-data theory is indirect realism, but phenomenalism is direct irrealism [Audi,R] |
| Full Idea: Where the sense-datum theory is an indirect realism, phenomenalism is a direct irrealism. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.43) |
| 2728 | The concepts needed for a priori thought may come from experience [Audi,R] |
| Full Idea: I may well need experience to acquire the concepts needed for knowledge of the a priori, such as the concept of a colour. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], IV p.103) |
| 2727 | Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R] |
| Full Idea: The proposition that nothing is red and green all over at once is not analytic, but it is rationally graspable, so it seems to be an a priori synthetic proposition. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], IV p.100) |
| 2716 | To see something as a field, I obviously need the concept of a field [Audi,R] |
| Full Idea: The propositional belief which portrays what I see in front of me AS a field requires my having a concept of one. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.17) | |
| A reaction: To me this immediately invites the question of what a cow or horse experiences when they look at a familiar field. They know how to leave and enter it, and register its boundaries and qualities. Concepts? |
| 2717 | How could I see a field and believe nothing regarding it? [Audi,R] |
| Full Idea: How could I see a field and believe nothing regarding it? | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.20) |
| 2719 | Sense data imply representative realism, possibly only representing primary qualities [Audi,R] |
| Full Idea: A sense-datum theory might be called a representative realism because it conceives perception as a relation in which sense-data represent perceived external (hence real) objects to us. For Locke they were resemblances only of primary qualities. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.33) |
| 2720 | Sense-data (and the rival 'adverbial' theory) are to explain illusions and hallucinations [Audi,R] |
| Full Idea: The sense-datum theory is mainly to explain hallucinations and illusions, though there might be other theories, such as the 'adverbial' theory. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.36) |
| 2718 | Perception is first simple, then objectual (with concepts) and then propositional [Audi,R] |
| Full Idea: Simple perceiving gives rise to objectual perceiving (attaching concepts to the object), which gives rise to propositional perceiving. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.23) |
| 2729 | Virtually all rationalists assert that we can have knowledge of synthetic a priori truths [Audi,R] |
| Full Idea: Rationalists virtually always assert or imply that, in addition to knowledge of analytic truths, there is knowledge of synthetic a priori truths. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], IV p.105) |
| 2741 | The principles of justification have to be a priori [Audi,R] |
| Full Idea: The crucial principles of justification are a priori. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], X p.311) |
| 2725 | To remember something is to know it [Audi,R] |
| Full Idea: Remembering something is so entails knowing that it is so. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], II p.68) | |
| A reaction: Clearly I can say I "remember" x, but be wrong. Presumably we then say that I didn't really remember, which requires success, like "I know". It is true (as with "know") that as soon as I say that the something is false, I can't claim to remember it. |
| 2724 | I might remember someone I can't recall or image, by recognising them on meeting [Audi,R] |
| Full Idea: If I can neither recall nor image Jane I can still remember her, for on seeing her I might recognise her, and might remember, and even recall, our last meeting. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], II p.66) | |
| A reaction: Hm. I can hardly claim to remember her if I have no concept of her, and don't recall our last meeting. If seeing her triggers recognition, I would say that I NOW remember her, but I didn't before. Memory is more conscious than Audi claims. |
| 2731 | Justification is either unanchored (infinite or circular), or anchored (in knowledge or non-knowledge) [Audi,R] |
| Full Idea: There are four possible kinds of epistemic chain: infinite and unanchored, circular and unanchored, anchored in a belief which is not knowledge, and anchored in a belief which is bedrock knowledge. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VII p.183) | |
| A reaction: About right, though I don't think 'chain' is the right word for what is proposed if justification is to be coherent. The justifications float like lilies in the pond of reason, and a Self (Monet?) seems needed to assess the picture |
| 2739 | Internalism about justification implies that there is a right to believe something [Audi,R] |
| Full Idea: Internalists about justification tend to conceive of it as a matter of having a right to believe something. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VIII p.234) | |
| A reaction: I'm an internalist, but I don't understand this, unless it refers to the social aspect of justification. Can I grant myself internal rights? I can justify my belief to other people. |
| 2732 | Maths may be consistent with observations, but not coherent [Audi,R] |
| Full Idea: That 7+5=12 and that carrots are nourishing are mutually consistent, but do not exhibit coherence. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VII p.192) | |
| A reaction: This shows how difficult it would be to define 'coherent'. Is 'carrots are nourishing' coherent with 'fish are nourishing'? Is the battle of Hastings coherent with the battle of Waterloo? |
| 2733 | It is very hard to show how much coherence is needed for justification [Audi,R] |
| Full Idea: It is very difficult to specify when an explanatory relation generates enough coherence to create justification. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VII p.193) | |
| A reaction: I take coherence to be the key concept in epistemology, and quite impossible to define. This is why the 'space of reasons' is a useful concept. It is a courtroom, in which each case is different. |
| 2734 | A consistent madman could have a very coherent belief system [Audi,R] |
| Full Idea: A schizophrenic who thinks he is Napoleon, if he has a completely consistent story with enough interlocking details, may have a belief system that is superbly coherent. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VII p.194) | |
| A reaction: This is an exaggeration, but the fact is that one isolated lie is totally coherent, so coherence can only emerge when a system is large. Sense experience must be central to coherence. |
| 2738 | Consistent accurate prediction looks like knowledge without justified belief [Audi,R] |
| Full Idea: If someone consistently prophesied the winners of horse races, it appears that this man knows who will win the races, but surely he does not have justified beliefs as to who will win? | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VIII p.229) | |
| A reaction: This is where internalists and externalists (notably reliabilists) sharply part company. IF a reliable clairvoyant appeared, we would eventually accept them as a knower. But they DON'T appear, because knowledge needs justification! |
| 2740 | A reliability theory of knowledge seems to involve truth as correspondence [Audi,R] |
| Full Idea: If one favours a reliability theory of knowledge (which is externalist) the correspondence theory of truth seems the most appropriate. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VIII p.243) | |
| A reaction: Sounds right. Coherence implies some sort of internal assessment, whereas correspondence just needs to plugged into the facts. I like coherence justification and correspondence truth. |
| 2737 | 'Reliable' is a very imprecise term, and may even mean 'justified' [Audi,R] |
| Full Idea: Reliabilism cannot specify how reliable a process must be before it grounds knowledge, and it cannot specify what is reliable in the first place. 'Reliable' may become circular, and may mean 'justified'. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VIII p.225) | |
| A reaction: The first time you ever read an instrument, or talk to a stranger, you have no indication of reliability. Circularity looks like a big problem. Knowledge must precede reliability? |
| 2726 | We can be ignorant about ourselves, for example, our desires and motives [Audi,R] |
| Full Idea: We can have false beliefs, or some degree of ignorance, about our own mental lives. For example, about our own dispositions, such as not believing that we have a certain ignoble desire. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], III p.83) | |
| A reaction: This idea, that we don't know ourselves, has become a commonplace of recent philosophy, but I am unconvinced. Mostly we know only too well that we harbour a base desire, and we feel a creeping sense of shame. Total ignorance is very rare. |
| 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. |
| 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. |