78 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| Full Idea: Philosophy says it is not right even to stretch out a finger without some reason. | |
| From: Epictetus (fragments/reports [c.57], 15) | |
| A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!). |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| Full Idea: Poincaré suggested that what is wrong with an impredicative definition is that it allows the set defined to alter its composition as more sets are added to the theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 10354 | Correspondence could be with other beliefs, rather than external facts [Kusch] |
| Full Idea: The correspondence theory of truth does not commit one to the view the reality is mind-independent. There is no reason why the 'facts' that correspond to true beliefs might not themselves be beliefs or ideas. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch.17) | |
| A reaction: This seems important, as it is very easy to assume that espousal of correspondence necessarily goes with realism about the external world. It is surprising to think that a full-blown Idealist might espouse the correspondence theory. |
| 10353 | Tarskians distinguish truth from falsehood by relations between members of sets [Kusch] |
| Full Idea: According to the Tarskians we separate out truths from falsehoods by tracing the relations between members of different sets. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch.16) |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| Full Idea: None of the classical ways of defining one logical constant in terms of others is available in intuitionist logic (and this includes the two quantifiers). | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| Full Idea: There is so far no agreed set of axioms for set theory which is categorical, i.e. which does pick just one structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: This contrasts with Peano Arithmetic, which is categorical in its second-order version. |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| Full Idea: A 'proper class' cannot be a member of anything, neither of a set nor of another proper class. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| Full Idea: We could add the axiom that all sets are constructible (V = L), making the universe of sets as small as possible, or add the axiom that there is a supercompact cardinal (SC), making the universe as large as we no know how to. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: Bostock says most mathematicians reject the first option, and are undecided about the second option. |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| Full Idea: The usual accounts of ZF are not restricted to subsets that we can describe, and that is what justifies the axiom of choice. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4 n36) | |
| A reaction: This contrasts interestingly with predicativism, which says we can only discuss things which we can describe or define. Something like verificationism hovers in the background. |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| Full Idea: The Axiom of Replacement (or the Axiom of Subsets, 'Aussonderung', Fraenkel 1922) in effect enforces the idea that 'limitation of size' is a crucial factor when deciding whether a proposed set or does not not exist. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| Full Idea: First-order logic is not decidable. That is, there is no test which can be applied to any arbitrary formula of that logic and which will tell one whether the formula is or is not valid (as proved by Church in 1936). | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| Full Idea: From the fact that the usual rules for first-level logic are complete (as proved by Gödel 1930), it follows that this logic is 'compact'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) | |
| A reaction: The point is that the completeness requires finite proofs. |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| Full Idea: Substitutional quantification and quantification understood in the usual 'ontological' way will coincide when every object in the (ontological) domain has a name. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.3 n23) |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| Full Idea: The Deduction Theorem is what licenses a system of 'natural deduction' in the first place. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| Full Idea: Berry's Paradox can be put in this form, by considering the alleged name 'The least number not named by this name'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| Full Idea: If you add to the ordinals you produce many different ordinals, each measuring the length of the sequence of ordinals less than it. They each have cardinality aleph-0. The cardinality eventually increases, but we can't say where this break comes. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| Full Idea: If we add ω onto the end of 0,1,2,3,4..., it then has a different length, of ω+1. It has a different ordinal (since it can't be matched with its first part), but the same cardinal (since adding 1 makes no difference). | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: [compressed] The ordinals and cardinals coincide up to ω, but this is the point at which they come apart. |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| Full Idea: It is the usual procedure these days to identify a cardinal number with the earliest ordinal number that has that number of predecessors. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: This sounds circular, since you need to know the cardinal in order to decide which ordinal is the one you want, but, hey, what do I know? |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| Full Idea: The cardinal aleph-1 is identified with the first ordinal to have more than aleph-0 members, and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) | |
| A reaction: That is, the succeeding infinite ordinals all have the same cardinal number of members (aleph-0), until the new total is triggered (at the number of the reals). This is Continuum Hypothesis territory. |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| Full Idea: In addition to cuts, or converging series, Cantor suggests we can simply lay down a set of axioms for the real numbers, and this can be done without any explicit mention of the rational numbers [note: the axioms are those for a complete ordered field]. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: It is interesting when axioms are best, and when not. Set theory depends entirely on axioms. Horsten and Halbach are now exploring treating truth as axiomatic. You don't give the 'nature' of the thing - just rules for its operation. |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| Full Idea: It is not difficult to show that the number of the real numbers is the same as the number of all the subsets of the natural numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: The Continuum Hypothesis is that this is the next infinite number after the number of natural numbers. Why can't there be a number which is 'most' of the subsets of the natural numbers? |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| Full Idea: As Eudoxus claimed, two distinct real numbers cannot both make the same cut in the rationals, for any two real numbers must be separated by a rational number. He did not say, though, that for every such cut there is a real number that makes it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: This is in Bostock's discussion of Dedekind's cuts. It seems that every cut is guaranteed to produce a real. Fine challenges the later assumption. |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| Full Idea: Non-standard natural numbers will yield non-standard rational and real numbers. These will include reciprocals which will be closer to 0 than any standard real number. These are like 'infinitesimals', so that notion is not actually a contradiction. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| Full Idea: A modern axiomatisation of geometry, such as Hilbert's (1899), does not need to claim the existence of real numbers anywhere in its axioms. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.ii) | |
| A reaction: This is despite the fact that geometry is reduced to algebra, and the real numbers are the equivalent of continuous lines. Bostock votes for a Greek theory of proportion in this role. |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| Full Idea: The Peano Axioms are categorical, meaning that they describe a unique structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4 n20) | |
| A reaction: So if you think there is nothing more to the natural numbers than their structure, then the Peano Axioms give the essence of arithmetic. If you think that 'objects' must exist to generate a structure, there must be more to the numbers. |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| Full Idea: Hume's Principle will not do as an implicit definition because it makes a positive claim about the size of the universe (which no mere definition can do), and because it does not by itself explain what the numbers are. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| Full Idea: Hume's Principle gives a criterion of identity for numbers, but it is obvious that many other things satisfy that criterion. The simplest example is probably the numerals (in any notation, decimal, binary etc.), giving many different interpretations. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| Full Idea: There is not just one way of giving a criterion of identity for numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| Full Idea: The Julius Caesar problem was one reason that led Frege to give an explicit definition of numbers as special sets. He does not appear to notice that the same problem affects his Axiom V for introducing sets (whether Caesar is or is not a set). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: The Julius Caesar problem is a sceptical acid that eats into everything in philosophy of mathematics. You give all sorts of wonderful accounts of numbers, but at what point do you know that you now have a number, and not something else? |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| Full Idea: There is no ground for saying that a number IS a position, if the truth is that there is nothing to determine which number is which position. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: If numbers lose touch with the empirical ability to count physical objects, they drift off into a mad world where they crumble away. |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| Full Idea: Structuralism begins from a false premise, namely that numbers have no properties other than their relations to other numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.5) | |
| A reaction: Well said. Describing anything purely relationally strikes me as doomed, because you have to say why those things relate in those ways. |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| Full Idea: Nominalism has two main versions, one which tries to 'reduce' the objects of mathematics to something simpler (Russell and Wittgenstein), and another which claims that such objects are mere 'fictions' which have no reality (Field). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9) |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| Full Idea: The style of nominalism which aims to reduce statements about numbers to statements about their applications does not work for the natural numbers, because they have many applications, and it is arbitrary to choose just one of them. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.iii) |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| Full Idea: We all know that in practice no physical measurement can be 100 per cent accurate, and so it cannot require the existence of a genuinely irrational number, rather than some of the rational numbers close to it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.3) |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| Full Idea: The basic use of the ordinal numbers is their use as ordinal adjectives, in phrases such as 'the first', 'the second' and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: That is because ordinals seem to attach to particulars, whereas cardinals seem to attach to groups. Then you say 'three is greater than four', it is not clear which type you are talking about. |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| Full Idea: The simple theory of types distinguishes sets into different 'levels', but this is quite different from the distinction into 'orders' which is imposed by the ramified theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) | |
| A reaction: The ramified theory has both levels and orders (p.235). Russell's terminology is, apparently, inconsistent. |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| Full Idea: The neo-logicists take up Frege's claim that Hume's Principle introduces a new concept (of a number), but unlike Frege they go on to claim that it by itself gives a complete account of that concept. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: So the big difference between Frege and neo-logicists is the Julius Caesar problem. |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| Full Idea: The response of neo-logicists to the Julius Caesar problem is to strengthen Hume's Principle in the hope of ensuring that only numbers will satisfy it. They say the criterion of identity provided by HP is essential to number, and not to anything else. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| Full Idea: If Hume's Principle is all we are given, by way of explanation of what the numbers are, the only conclusion to draw would seem to be the structuralists' conclusion, ...studying all systems that satisfy that principle. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: Any approach that implies a set of matching interpretations will always imply structuralism. To avoid it, you need to pin the target down uniquely. |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| Full Idea: Many of the crucial definitions in the logicist programme are in fact impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| Full Idea: If logic is neutral on the number of objects there are, then logicists can't construe numbers as objects, for arithmetic is certainly not neutral on the number of numbers there are. They must be treated in some other way, perhaps as numerical quantifiers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| Full Idea: In its higher reaches, which posit sets of huge cardinalities, set theory is just a fairy story. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: You can't say the higher reaches are fairy stories but the lower reaches aren't, if the higher is directly derived from the lower. The empty set and the singleton are fairy stories too. Bostock says the axiom of infinity triggers the fairy stories. |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| Full Idea: A common view is that although a fairy tale may provide very useful predictions, it cannot provide explanations for why things happen as they do. In order to do that a theory must also be true (or, at least, an approximation to the truth). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5) | |
| A reaction: Of course, fictionalism offers an explanation of mathematics as a whole, but not of the details (except as the implications of the initial fictional assumptions). |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| Full Idea: In my personal opinion, predicativism is the best version of conceptualism that we have yet discovered. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: Since conceptualism is a major player in the field, this makes predicativism a very important view. I won't vote Predicativist quite yet, but I'm tempted. |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| Full Idea: Three simple objections to conceptualism in mathematics are that we do not ascribe mathematical properties to our ideas, that our ideas are presumably finite, and we don't think mathematics lacks truthvalue before we thought of it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: [compressed; Bostock refers back to his Ch 2] Plus Idea 18134. On the whole I sympathise with conceptualism, so I will not allow myself to be impressed by any of these objections. (So, what's actually wrong with them.....?). |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| Full Idea: If an abstract object exists only when there is some suitable way of expressing it, then there are at most denumerably many abstract objects. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) | |
| A reaction: Fine by me. What an odd view, to think there are uncountably many abstract objects in existence, only a countable portion of which will ever be expressed! [ah! most people agree with me, p.243-4] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| Full Idea: Classical mathematicians say predicative mathematics omits areas of great interest, all concerning non-denumerable real numbers, such as claims about huge cardinals. There cannot be a predicative version of this theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I'm not sure that anyone will really miss huge cardinals if they are prohibited, though cryptography seems to flirt with such things. Are we ever allowed to say that some entity conjured up by mathematicians is actually impossible? |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| Full Idea: It has been claimed that only predicative mathematics has a justification through its usefulness to science (an empiricist approach). | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [compressed. Quine is the obvious candidate] I suppose predicativism gives your theory roots, whereas impredicativism is playing an abstract game. |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| Full Idea: If we accept the initial idea that we can think only of what we ourselves can describe, then something like the theory of predicativism quite naturally results | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I hate the idea that we can only talk of what falls under a sortal, but 'what we can describe' is much more plausible. Whether or not you agree with this approach (I'm pondering it), this makes predicativism important. |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| Full Idea: It is with the real numbers that the restrictions imposed by predicativity begin to make a real difference. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| Full Idea: The predicative approach cannot accept either the usual definition of identity or the usual definition of the natural numbers, for both of these definitions are impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [Bostock 237-8 gives details] |
| 10337 | We can have knowledge without belief, if others credit us with knowledge [Kusch] |
| Full Idea: We can have knowledge that p without believing that p. It is enough that others credit us with the knowledge. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 5) | |
| A reaction: [He is discussing Welbourne 1993] This is an extreme of the communitarian view. |
| 10357 | Methodological Solipsism assumes all ideas could be derived from one mind [Kusch] |
| Full Idea: 'Methodological solipsism' says merely that everyone can conceive of themselves as the only subject. Everyone can construct all referents of their thought and talk out of complexes of their very own experience. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch.19) | |
| A reaction: The possibility of this can be denied (e.g. by Putnam 1983, dating back to Wittgenstein). I too would doubt it, though finding a good argument seems a forlorn hope. |
| 10339 | Foundations seem utterly private, even from oneself at a later time [Kusch] |
| Full Idea: Foundationalists place the foundations of knowledge at a point where they are in principle accessible only to the individual knower. They cannot be 'shared' with another person, or with oneself at a later time. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 8) | |
| A reaction: Kusch is defending an extremely social view of knowledge. Being private to an individual may just he an unfortunate epistemological fact. Being unavailable even to one's later self seems a real problem for foundational certainty. |
| 10331 | Testimony is reliable if it coheres with evidence for a belief, and with other beliefs [Kusch] |
| Full Idea: Testimony must be reliable since its deliveries cohere both with input from other information routes in the formation of single beliefs, and with other types of beliefs in the formation of systems of belief. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 4) | |
| A reaction: Kusch criticises this view (credited to C.A.J. Coady 1992) as too individualistic , but it sounds to me dead right. I take a major appeal of the coherence account of justification to be its capacity to extend seamlessly out into external testimony. |
| 10338 | The coherentist restricts the space of reasons to the realm of beliefs [Kusch] |
| Full Idea: The coherentist restricts the space of reasons to the realm of beliefs. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 8) | |
| A reaction: I endorse this idea, which endorses Davidson's slogan on the subject. The key thought is that a 'pure' sensation is uninterpreted, and so cannot justify anything. It is only once it generates a proposition that it can justify. But McDowell 1994. |
| 10340 | Individualistic coherentism lacks access to all of my beliefs, or critical judgement of my assessment [Kusch] |
| Full Idea: Individualistic versions of coherentism assume that a belief is justified if it fits with all, or most, of my contemporaneous beliefs. But who has access to that totality? Who can judge my assessment? From what position could it be judged? | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 8) | |
| A reaction: [compressed] Though I agree with Kusch on the social aspect of coherence, I don't think these are major criticisms. Who can access, or critically evaluate a society's body of supposedly coherent beliefs? We just do our best. |
| 10345 | Individual coherentism cannot generate the necessary normativity [Kusch] |
| Full Idea: Standard forms of coherentism are unable to account for normativity, because of their common individualism. Normativity cannot be generated within the isolated individual, or in the causal interaction between world and individual mind. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch.10) | |
| A reaction: This thought leads to belief in rationalism and the a priori, not (as Kusch hopes) to the social dimension. How can social normativity get off the ground if there is none of it to be found in individuals? The criteria of coherence seem to be given. |
| 10350 | Cultures decide causal routes, and they can be critically assessed [Kusch] |
| Full Idea: Assessments of causal routes are specific to cultures, and thus not beyond dialectical justification. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch.11) | |
| A reaction: This is a good defence of the social and communitarian view against those who are trying to be thoroughly naturalistic and physicalist by relying entirely on causal processes for all explanation, even though I sympathise with such naturalism. |
| 10343 | Process reliabilism has been called 'virtue epistemology', resting on perception, memory, reason [Kusch] |
| Full Idea: Process reliabilism is sometimes subsumed under the label 'virtue epistemology', so that processes are 'epistemically virtuous' if they lead mostly to true beliefs. The 'intellectual virtues' here are perception, memory or reasoning. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 9) | |
| A reaction: I am shocked that 'intellectual virtue' should be hijacked by reliabilists, suggesting that it even applies to a good clock. I like the Aristotelian idea that sound knowledge rests on qualities of character in the knower - including social qualities. |
| 10341 | Justification depends on the audience and one's social role [Kusch] |
| Full Idea: How a claim (about an X-ray) needs to be justified depends on whether one is confronted by a group of laypersons, or of experts, and is prescribed by one's social role. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 8) | |
| A reaction: I think this is exactly right. I cannot think of any absolute criterion for justification which doesn't play straight into the hands of sceptics. Final and certain justification is an incoherent notion. But I am a little more individualistic than Kusch. |
| 10334 | Testimony is an area in which epistemology meets ethics [Kusch] |
| Full Idea: Testimony is an area in which epistemology meets ethics. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 5) | |
| A reaction: This is very thought-provoking. A key concept linking the two would be 'respect'. Consider also 'experts'. |
| 10336 | Powerless people are assumed to be unreliable, even about their own lives [Kusch] |
| Full Idea: The powerless in society are not usually taken to be trustworthy witnesses even when it comes to providing information about their own lives. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 5) | |
| A reaction: This is where epistemology shades off into politics and the writings of Foucault. |
| 10324 | Testimony does not just transmit knowledge between individuals - it actually generates knowledge [Kusch] |
| Full Idea: Testimony is not just a means of transmission of complete items of knowledge from and to an individual. Testimony is almost always generative of knowledge. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Intro) | |
| A reaction: I'm not clear how my testimony could fail to be knowledge for me, but become knowledge just because I pass it to you. I might understand what I say better than you did. When fools pool their testimony, presumably not much knowledge results. |
| 10327 | Some want to reduce testimony to foundations of perceptions, memories and inferences [Kusch] |
| Full Idea: Reductionalists about testimony are foundationalists by temperament. ...Their project amounts to justifying our testimonial beliefs in terms of perceptions, memories and inferences. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 4) | |
| A reaction: Kusch wants to claim that the sharing of testimony is the means by which knowledge is created. My line is something like knowledge being founded on a social coherence, which is an extension of internal individual coherence. |
| 10329 | Testimony won't reduce to perception, if perception depends on social concepts and categories [Kusch] |
| Full Idea: How can we hope to reduce testimony to perception if the way we perceive the world is to a considerable extent shaped by concepts and categories that we have learned from others? | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 4) | |
| A reaction: To me this sounds like good support for coherentism, the benign circle between my reason, my experience, and the testimony and reason of others. Asking how the circle could get started shows ignorance of biology. |
| 10330 | A foundation is what is intelligible, hence from a rational source, and tending towards truth [Kusch] |
| Full Idea: It can be argued that testimony is non-reductive because it relies on the fact that whatever is intelligible is likely to come from a rational source, and that rational sources, by their very nature, tend towards the truth. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 4 n7) | |
| A reaction: [He cites Tyler Burge 1993, 1997] If this makes testimony non-reductive, how would one assess whether the testimony is 'intelligible'? |
| 10325 | Vindicating testimony is an expression of individualism [Kusch] |
| Full Idea: To believe that testimony needs a general vindication is itself an expression of individualism. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Intro) | |
| A reaction: Kusch is a spokesman for Communitarian Epistemology. Surely we are allowed to identify the criteria for what makes a good witness? Ask a policeman. |
| 10335 | Myths about lonely genius are based on epistemological individualism [Kusch] |
| Full Idea: Many myths about the lonely scientific genius underwrite epistemological individualism. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 5) | |
| A reaction: They all actually say that they 'stood on the shoulders of giants', and they are invariably immersed in the contemporary researches of teams of like-minded people. How surprised were the really expert contemporaries by Newton, Einstein, Gödel? |
| 10323 | Communitarian Epistemology says 'knowledge' is a social status granted to groups of people [Kusch] |
| Full Idea: I propose 'communitarian epistemology' - claiming first that the term 'knowledge' marks a social status, and is dependent on the existence of communities, and second that this social status is typically granted to groups of people. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Intro) | |
| A reaction: I find this very congenial, though Kusch goes a little far when he claims that knowledge is largely created by social groups. He allows that Robinson Crusoe might have knowledge of his island, but can't give a decent account of it. |
| 10348 | Private justification is justification to imagined other people [Kusch] |
| Full Idea: Coming to convince myself is actually to form a pretend communal belief with pretend others, ..which is clearly parasitic on the case where the others are real. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch.11) | |
| A reaction: This slightly desperate move is a way for 'communitarian' epistemologists to deal with Robinson Crusoe cases. I think Kusch is right, but it is a bit hard to prove that this is what is 'actually' going on. |
| 10349 | To be considered 'an individual' is performed by a society [Kusch] |
| Full Idea: One cannot even have the social status of 'being an individual' unless it has been conferred on one by a communal performative belief. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch.11) | |
| A reaction: This sounds crazy until you think of the mentality of a tenth generation slave in a fully slave-owning society. |
| 10344 | Our experience may be conceptual, but surely not the world itself? [Kusch] |
| Full Idea: I am unconvinced by McDowell's arguments in favour of treating the world as itself conceptual. Granted that our experience is conceptual in quality; it still does not follow that the world itself is conceptual. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 9) | |
| A reaction: I would take Kusch's point to be a given in any discussion of concepts, and McDowell as a non-starter on this one. I am inclined to believe that we do have non-conceptual experiences, but I take them to be epistemologically useless. |
| 10358 | Often socialising people is the only way to persuade them [Kusch] |
| Full Idea: Often we can convince members of other cultures only by socializing them into our culture. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch.19) | |
| A reaction: This looks both true and interesting, and is good support for Kusch's communitarian epistemology. What actually persuades certainly doesn't have to be reasons, and may be almost entirely social. |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| Full Idea: In Modus Ponens where the first premise is 'P' and the second 'P→Q', in the first premise P is asserted but in the second it is not. Yet it must mean the same in both premises, or it would be guilty of the fallacy of equivocation. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) | |
| A reaction: This is Geach's thought (leading to an objection to expressivism in ethics, that P means the same even if it is not expressed). |
| 10333 | Communitarianism in epistemology sees the community as the primary knower [Kusch] |
| Full Idea: Communitarianism in epistemology sees the community as the primary knower. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 5) | |
| A reaction: This thought offers an account of epistemology which could fit in with communitarian political views. See the ideas of Martin Kusch in this database. |
| 10351 | Natural kinds are social institutions [Kusch] |
| Full Idea: Natural kinds are social institutions. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch.11) | |
| A reaction: I can see what he means, but I take this to be deeply wrong. A clarification of what exactly is meant by a 'natural kind' is needed before we can make any progress with this one. Is a village a natural kind? Or a poodle? Or a shoal? |
| 10332 | Omniscience is incoherent, since knowledge is a social concept [Kusch] |
| Full Idea: The very idea of omniscience is dubious, at least for the communitarian epistemologist, since knowing is a social state, and knowledge is a social status, needing a position in a social network. | |
| From: Martin Kusch (Knowledge by Agreement [2002], Ch. 4) | |
| A reaction: A nice test case. Would an omniscient mind have evidence for its beliefs? Would it continually check for coherence? Is it open to criticism? Does it even entertain the possibility of error? Could another 'omniscient' mind challenge it? |