59 ideas
| 9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
| Full Idea: Most accounts of the concept of mathematical truth can be identified with serving one or another of either semantic theory (matching it to ordinary language), or with epistemology (meshing with a reasonable view) - always at the expense of the other. | |
| From: Paul Benacerraf (Mathematical Truth [1973], Intro) | |
| A reaction: The gist is that language pulls you towards platonism, and epistemology pulls you towards empiricism. He argues that the semantics must give ground. He's right. |
| 13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
| Full Idea: Not all numbers could possibly have been learned à la Frege-Russell, because we could not have performed that many distinct acts of abstraction. Somewhere along the line a rule had to come in to enable us to obtain more numbers, in the natural order. | |
| From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165) | |
| A reaction: Follows on from Idea 13411. I'm not sure how Russell would deal with this, though I am sure his account cannot be swept aside this easily. Nevertheless this seems powerful and convincing, approaching the problem through the epistemology. |
| 13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
| Full Idea: Both ordinalists and cardinalists, to account for our number words, have to account for the fact that we know so many of them, and that we can 'recognize' numbers which we've neither seen nor heard. | |
| From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166) | |
| A reaction: This seems an important contraint on any attempt to explain numbers. Benacerraf is an incipient structuralist, and here presses the importance of rules in our grasp of number. Faced with 42,578,645, we perform an act of deconstruction to grasp it. |
| 9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
| Full Idea: The fact that Zermelo and Von Neumann disagree on which particular sets the numbers are is fatal to the view that each number is some particular set. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], II) | |
| A reaction: I agree. A brilliantly simple argument. There is the possibility that one of the two accounts is correct (I would vote for Zermelo), but it is not actually possible to prove it. |
| 9912 | There are no such things as numbers [Benacerraf] |
| Full Idea: There are no such things as numbers. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: Mill said precisely the same (Idea 9794). I think I agree. There has been a classic error of reification. An abstract pattern is not an object. If I coin a word for all the three-digit numbers in our system, I haven't created a new 'object'. |
| 13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
| Full Idea: If we accept the Frege-Russell analysis of number (the natural numbers are the cardinals) as basic and correct, one thing which seems to follow is that one could know, say, three, seventeen, and eight, but no other numbers. | |
| From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164) | |
| A reaction: It seems possible that someone might only know those numbers, as the patterns of members of three neighbouring families (the only place where they apply number). That said, this is good support for the priority of ordinals. See Idea 13412. |
| 9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
| Full Idea: Benacerraf thinks of numbers as being defined by their natural ordering. | |
| From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §5 | |
| A reaction: My intuition is that cardinality is logically prior to ordinality, since that connects better with the experienced physical world of objects. Just as the fact that people have different heights must precede them being arranged in height order. |
| 13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
| Full Idea: Benacerraf claims that the concept of a progression is in some way the fundamental arithmetical notion, essential to understanding the idea of a finite cardinal, with a grasp of progressions sufficing for grasping finite cardinals. | |
| From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xv | |
| A reaction: He cites Dedekind (and hence the Peano Axioms) as the source of this. The interest is that progression seems to be fundamental to ordianls, but this claims it is also fundamental to cardinals. Note that in the first instance they are finite. |
| 17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
| Full Idea: Any set has k members if and only if it can be put into one-to-one correspondence with the set of numbers less than or equal to k. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], I) | |
| A reaction: This is 'Ernie's' view of things in the paper. This defines the finite cardinal numbers in terms of the finite ordinal numbers. He has already said that the set of numbers is well-ordered. |
| 17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
| Full Idea: I would disagree with Quine. The explanation of cardinality - i.e. of the use of numbers for 'transitive counting', as I have called it - is part and parcel of the explication of number. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], I n2) | |
| A reaction: Quine says numbers are just a progression, with transitive counting as a bonus. Interesting that Benacerraf identifies cardinality with transitive counting. I would have thought it was the possession of numerical quantity, not ascertaining it. |
| 9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
| Full Idea: Learning number words in the right order is counting 'intransitively'; using them as measures of sets is counting 'transitively'. ..It seems possible for someone to learn the former without learning the latter. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], I) | |
| A reaction: Scruton's nice question (Idea 3907) is whether you could be said to understand numbers if you could only count intransitively. I would have thought such a state contained no understanding at all of numbers. Benacerraf agrees. |
| 17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
| Full Idea: It seems that it is possible for someone to learn to count intransitively without learning to count transitively. But not vice versa. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], I) | |
| A reaction: Benacerraf favours the priority of the ordinals. It is doubtful whether you have grasped cardinality properly if you don't know how to count things. Could I understand 'he has 27 sheep', without understanding the system of natural numbers? |
| 9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
| Full Idea: The application of a system of numbers is counting and measurement. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], I) | |
| A reaction: A simple point, but it needs spelling out. Counting seems prior, in experience if not in logic. Measuring is a luxury you find you can indulge in (by imagining your quantity) split into parts, once you have mastered counting. |
| 9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
| Full Idea: Ernie's number progression is [φ],[φ,[φ]],[φ,[φ],[φ,[φ,[φ]]],..., whereas Johnny's is [φ],[[φ]],[[[φ]]],... For Ernie 3 belongs to 17, not for Johnny. For Ernie 17 has 17 members; for Johnny it has one. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], II) | |
| A reaction: Benacerraf's point is that there is no proof-theoretic way to choose between them, though I am willing to offer my intuition that Ernie (Zermelo) gives the right account. Seventeen pebbles 'contains' three pebbles; you must pass 3 to count to 17. |
| 9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
| Full Idea: For Ernie, the successor of a number x was the set consisting of x and all the members of x, while for Johnny the successor of x was simply [x], the unit set of x - the set whose only member is x. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], II) | |
| A reaction: See also Idea 9900. Benacerraf's famous point is that it doesn't seem to make any difference to arithmetic which version of set theory you choose as its basis. I take this to conclusively refute the idea that numbers ARE sets. |
| 8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
| Full Idea: If two children were brought up knowing two different set theories, they could entirely agree on how to do arithmetic, up to the point where they discuss ontology. There is no mathematical way to tell which is the true representation of numbers. | |
| From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: Benacerraf ends by proposing a structuralist approach. If mathematics is consistent with conflicting set theories, then those theories are not shedding light on mathematics. |
| 8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
| Full Idea: Hume's Principle can't tell us what a cardinal number is (this is one lesson of Benacerraf's well-known problem). An infinity of pairs of sets could actually be the number two (not just the simplest sets). | |
| From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by E.J. Lowe - The Possibility of Metaphysics 10.3 | |
| A reaction: The drift here is for numbers to end up as being basic, axiomatic, indefinable, universal entities. Since I favour patterns as the basis of numbers, I think the basis might be in a pre-verbal experience, which even a bird might have, viewing its eggs. |
| 9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
| Full Idea: If a particular set-theory is in a strong sense 'reducible to' the theory of ordinal numbers... then we can still ask, but which is really which? | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIB) | |
| A reaction: A nice question about all reductions. If we reduce mind to brain, does that mean that brain is really just mind. To have a direction (up/down?), reduction must lead to explanation in a single direction only. Do numbers explain sets? |
| 13415 | An adequate account of a number must relate it to its series [Benacerraf] |
| Full Idea: No account of an individual number is adequate unless it relates that number to the series of which it is a member. | |
| From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.169) | |
| A reaction: Thus it is not totally implausible to say that 2 is several different numbers or concepts, depending on whether you see it as a natural number, an integer, a rational, or a real. This idea is the beginning of modern structuralism. |
| 9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
| Full Idea: If any recursive sequence whatever would do to explain ordinal numbers suggests that what is important is not the individuality of each element, but the structure which they jointly exhibit. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: This sentence launched the whole modern theory of Structuralism in mathematics. It is hard to see what properties a number-as-object could have which would entail its place in an ordinal sequence. |
| 9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
| Full Idea: 'Objects' do not do the job of numbers singly; the whole system performs the job or nothing does. I therefore argue that numbers could not be objects at all. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: This thought is explored by structuralism - though it is a moot point where mere 'nodes' in a system (perhaps filled with old bits of furniture) will do the job either. No one ever explains the 'power' of numbers (felt when you do a sudoku). Causal? |
| 9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
| Full Idea: Any object can play the role of 3; that is, any object can be the third element in some progression. What is peculiar to 3 is that it defines that role, not by being a paradigm, but by representing the relation of any third member of a progression. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: An interesting early attempt to spell out the structuralist idea. I'm thinking that the role is spelled out by the intersection of patterns which involve threes. |
| 9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
| Full Idea: Questions of the identification of the referents of number words should be dismissed as misguided in just the way that a question about the referents of the parts of a ruler would be seen as misguided. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: What a very nice simple point. It would be very strange to insist that every single part of the continuum of a ruler should be regarded as an 'object'. |
| 8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
| Full Idea: Mathematical objects have no properties other than those relating them to other 'elements' of the same structure. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], p.285), quoted by Fraser MacBride - Structuralism Reconsidered §3 n13 | |
| A reaction: Suppose we only had one number - 13 - and we all cried with joy when we recognised it in a group of objects. Would that be a number, or just a pattern, or something hovering between the two? |
| 9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
| Full Idea: Benacerraf raises the question how numbers can be 'objects' if they have no properties except order in a particular ω-sequence. | |
| From: report of Paul Benacerraf (What Numbers Could Not Be [1965], p.301) by Hilary Putnam - Mathematics without Foundations | |
| A reaction: Frege certainly didn't think that order was their only property (see his 'borehole' metaphor in Grundlagen). It might be better to say that they are objects which only have relational properties. |
| 9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
| Full Idea: The identification of numbers with objects works wholesale but fails utterly object by object. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: This seems to be a glaring problem for platonists. You can stare at 1728 till you are blue in the face, but it only begins to have any properties at all once you examine its place in the system. This is unusual behaviour for an object. |
| 17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
| Full Idea: Benacerraf argues that realists about mathematical objects have a nice normal semantic but no epistemology, and anti-realists have a good epistemology but an unorthodox semantics. | |
| From: report of Paul Benacerraf (Mathematical Truth [1973]) by Mark Colyvan - Introduction to the Philosophy of Mathematics 1.2 |
| 9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
| Full Idea: The principle defect of the standard (platonist) account of mathematical truth is that it appears to violate the requirement that our account be susceptible to integration into our over-all account of knowledge. | |
| From: Paul Benacerraf (Mathematical Truth [1973], III) | |
| A reaction: Unfortunately he goes on to defend a causal theory of justification (fashionable at that time, but implausible now). Nevertheless, his general point is well made. Your theory of what mathematics is had better make it knowable. |
| 9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
| Full Idea: The unpredicative nature of number words can be seen by noting how different they are from, say, ordinary adjectives, which do function as predicates. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], II) | |
| A reaction: He points out that 'x is seventeen' is a rare construction in English, unlike 'x is happy/green/interesting', and that numbers outrank all other adjectives (having to appear first in any string of them). |
| 9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
| Full Idea: In no consistent theory is there a class of all classes with seventeen members. The existence of the paradoxes is a good reason to deny to 'seventeen' this univocal role of designating the class of all classes with seventeen members. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], II) | |
| A reaction: This was Frege's disaster, and seems to block any attempt to achieve logicism by translating numbers into sets. It now seems unclear whether set theory is logic, or mathematics, or sui generis. |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| Full Idea: Identity statements make sense only in contexts where there exist possible individuating conditions. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], III) | |
| A reaction: He is objecting to bizarre identifications involving numbers. An identity statement may be bizarre even if we can clearly individuate the two candidates. Winston Churchill is a Mars Bar. Identifying George Orwell with Eric Blair doesn't need a 'respect'. |
| 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) |
| 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) |
| 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) |
| 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) |
| 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? |
| 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) |
| 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) |
| 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) |
| 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? |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
| 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. |
| 20064 | Actions are not mere effects of reasons, but are under their control [Audi,R] |
| Full Idea: An action for a reason is one that is, in a special way, under the control of reason. It is a response to, not a mere effect of, a reason. | |
| From: Robert Audi (Action, Intention and Reason [1992], p.177), quoted by Rowland Stout - Action 6 'Alien' | |
| A reaction: This modifies Davidson's 'reasons are causes'. Audi has a deviant causal chain which causes trouble for his idea, but Stout says he is right to focus on causal 'processes' (an Aristotelian idea) rather than causal 'chains'. |