66 ideas
| 3593 | The only way to specify the corresponding fact is asserting the sentence [Williams,M] |
| Full Idea: The trouble with appeal to facts in the correspondence theory is that, in general, we have no way of indicating what fact a sentence, when true, corresponds to other than asserting the sentence. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.12) |
| 3584 | Justification needs coherence, while truth might be ideal coherence [Williams,M] |
| Full Idea: Contemporary coherence theorists are advancing a theory of justification, not of truth, …with those who argue that truth is also coherence explaining it in terms of ideal coherence, or coherence at the limit of enquiry. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.10) |
| 3585 | Coherence needs positive links, not just absence of conflict [Williams,M] |
| Full Idea: It is often claimed that coherence is more than 'absence of conflict' between beliefs; it also involves 'positive connections'. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.10) |
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| Full Idea: The logic of ZF Set Theory is classical first-order predicate logic with identity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.121) | |
| A reaction: This logic seems to be unable to deal with very large cardinals, precisely those that are implied by set theory, so there is some sort of major problem hovering here. Boolos is fairly neutral. |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| Full Idea: Maybe the axioms of extensionality and the pair set axiom 'force themselves on us' (Gödel's phrase), but I am not convinced about the axioms of infinity, union, power or replacement. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.130) | |
| A reaction: Boolos is perfectly happy with basic set theory, but rather dubious when very large cardinals come into the picture. |
| 18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
| Full Idea: For Boolos, the Replacement Axioms go beyond the iterative conception. | |
| From: report of George Boolos (The iterative conception of Set [1971]) by Penelope Maddy - Naturalism in Mathematics I.3 |
| 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. |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| Full Idea: The naïve view of set theory (that any zero or more things form a set) is natural, but inconsistent: the things that do not belong to themselves are some things that do not form a set. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.127) | |
| A reaction: As clear a summary of Russell's Paradox as you could ever hope for. |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| Full Idea: According to the iterative conception, every set is formed at some stage. There is a relation among stages, 'earlier than', which is transitive. A set is formed at a stage if and only if its members are all formed before that stage. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.126) | |
| A reaction: He gives examples of the early stages, and says the conception is supposed to 'justify' Zermelo set theory. It is also supposed to make the axioms 'natural', rather than just being selected for convenience. And it is consistent. |
| 13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
| Full Idea: Weak Limitation of Size: If there are no more Fs than Gs and the Gs form a collection, then Fs form a collection. Strong Limitation of Size: A property F fails to be collectivising iff there are as many Fs as there are objects. | |
| From: report of George Boolos (Iteration Again [1989]) by Michael Potter - Set Theory and Its Philosophy 13.5 |
| 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. |
| 3599 | Deduction shows entailments, not what to believe [Williams,M] |
| Full Idea: The rules of deduction are rules of entailment, not rules of inference. They tell us what follows from what, not what to believe on the basis of what. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.18) |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth. | |
| From: George Boolos (On Second-Order Logic [1975], p.45) | |
| A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification. |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5 | |
| A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?). |
| 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 |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts. | |
| From: George Boolos (On Second-Order Logic [1975], p.44) | |
| A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction? |
| 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. |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed. | |
| From: George Boolos (On Second-Order Logic [1975], p.46) | |
| A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain. |
| 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...' |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
| From: George Boolos (On Second-Order Logic [1975], p.52) | |
| A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| Full Idea: The existence of infinitely many natural numbers seems to me no more troubling than that of infinitely many computer programs or sentences of English. There is, for example, no longest sentence, since any number of 'very's can be inserted. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: If you really resisted an infinity of natural numbers, presumably you would also resist an actual infinity of 'very's. The fact that it is unclear what could ever stop a process doesn't guarantee that the process is actually endless. |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| Full Idea: To the best of my knowledge nothing in mathematics or science requires the existence of very high orders of infinity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.122) | |
| A reaction: He is referring to particular high orders of infinity implied by set theory. Personally I want to wield Ockham's Razor. Is being implied by set theory a sufficient reason to accept such outrageous entities into our ontology? |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| Full Idea: The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity. | |
| From: George Boolos (On Second-Order Logic [1975], p.48) |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| Full Idea: It is no surprise that we should be able to reason mathematically about many of the things we experience, for they are already 'abstract'. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: He has just given a list of exemplary abstract objects (Idea 10489), but I think there is a more interesting idea here - that our experience of actual physical objects is to some extent abstract, as soon as it is conceptualised. |
| 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'. |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| Full Idea: It's a kind of lunacy to think that sound scientific philosophy demands that we think that we see ink-tracks but not words, i.e. word-types. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: This seems to link him with Armstrong's mockery of 'ostrich nominalism'. There seems to be some ambiguity with the word 'see' in this disagreement. When we look at very ancient scratches on stones, why don't we always 'see' if it is words? |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| Full Idea: I am rather a fan of abstract objects, and confident of their existence. Smaller numbers, sets and functions don't offend my sense of reality. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: The great Boolos is rather hard to disagree with, but I disagree. Logicians love abstract objects, indeed they would almost be out of a job without them. It seems to me they smuggle them into our ontology by redefining either 'object' or 'exists'. |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| Full Idea: We twentieth century city dwellers deal with abstract objects all the time, such as bank balances, radio programs, software, newspaper articles, poems, mistakes, triangles. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: I find this claim to be totally question-begging, and typical of a logician. The word 'object' gets horribly stretched in these discussions. We can create concepts which have all the logical properties of objects. Maybe they just 'subsist'? |
| 3591 | We could never pin down how many beliefs we have [Williams,M] |
| Full Idea: Asking how many beliefs I have is like asking how many drops of water there are in a bucket. If I believe my dog is in the garden, do I also believe he is not in the house, or in Siberia? | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.11) |
| 3582 | Propositions make error possible, so basic experiential knowledge is impossible [Williams,M] |
| Full Idea: Propositional content is inseparable from possible error. Therefore no judgement, however modest, is indubitable. So if basic experiential knowledge has to be indubitable, there is no such knowledge. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 8) |
| 3592 | Phenomenalism is a form of idealism [Williams,M] |
| Full Idea: Phenomenalism is a form of idealism. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.12) |
| 3579 | Sense data avoid the danger of misrepresenting the world [Williams,M] |
| Full Idea: The point of insisting on the absolute immediacy of sense data is that representation always seems to involve the possibility of misrepresentation. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 8) |
| 3581 | Sense data can't give us knowledge if they are non-propositional [Williams,M] |
| Full Idea: Acquaintance with sense data is supposed to be a form of non-propositional knowledge, but how can something be non-propositional and yet knowledge? | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 8) |
| 3564 | Is it people who are justified, or propositions? [Williams,M] |
| Full Idea: What exactly is supposed to be 'justified': a person's believing some particular proposition, or the proposition that he believes? | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 1) | |
| A reaction: A key distinction. See my comment on Idea 3752. What would justify a sign saying 'treasure buried here'? People can be justified in believing falsehoods. How could a false proposition be justified? |
| 8851 | Coherentists say that regress problems are assuming 'linear' justification [Williams,M] |
| Full Idea: From the point of view of the coherentist, Agrippa's Dilemma fails because it presupposes a 'linear' conception of justifying inference. | |
| From: Michael Williams (Without Immediate Justification [2005], §2) | |
| A reaction: [He cites Bonjour 1985 for this view] Since a belief may have several justifications, and one belief could justify a host of others, there certainly isn't a simple line of justifications. I agree with the coherentist picture here. |
| 3595 | What works always takes precedence over theories [Williams,M] |
| Full Idea: A theory that represents working practices as unworkable is a bad theory. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.13) | |
| A reaction: Good point. There's a lot of this about in epistemology, especially accusations of circularity or infinite regress, which (if true) don't somehow seem to worry the cove on the Clapham omnibus. |
| 8849 | Traditional foundationalism is radically internalist [Williams,M] |
| Full Idea: Traditional foundationalism is radically internalist. The justification-making factors for beliefs, basic and otherwise, are all open to view, and perhaps even actual objects of awareness. I am always in a position to know that I know. | |
| From: Michael Williams (Without Immediate Justification [2005], §1) | |
| A reaction: This is a helpful if one is trying to draw a map of the debate. An externalist foundationalism would have to terminate in the external fact which was the object of knowledge (via some reliable channel), but that is the truth, not the justification. |
| 8853 | Basic judgements are immune from error because they have no content [Williams,M] |
| Full Idea: Basic judgements threaten to buy their immunity from error at the cost of being drained of descriptive content altogether. | |
| From: Michael Williams (Without Immediate Justification [2005], §4) | |
| A reaction: This is probably the key objection to foundationalism. As you import sufficient content into basic experiences to enable them to actually justify a set of beliefs, you find you have imported all sorts of comparisons and classifications as well. |
| 3580 | Experience must be meaningful to act as foundations [Williams,M] |
| Full Idea: If we are to treat experience as the foundation of knowledge, then experience must itself be understood to involve propositional content. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 8) | |
| A reaction: This sounds right, but since pure 'experience' obviously doesn't have propositional content, because it needs interpretation and evaluation, then this strategy won't work. |
| 8855 | Sensory experience may be fixed, but it can still be misdescribed [Williams,M] |
| Full Idea: The fact that experiential contents cannot be other than they are, as far as sensory awareness goes, does not imply that we cannot misdescribe them, as in misreporting the number of speckles on a speckled hen (Chisholm's example). | |
| From: Michael Williams (Without Immediate Justification [2005], §4) | |
| A reaction: [Chisholm 1942 is cited] Such experiences couldn't be basic beliefs if there was a conflict between their intrinsic nature and the description I used in discussing them. |
| 3578 | Are empirical foundations judgements or experiences? [Williams,M] |
| Full Idea: Empirical foundationists must decide whether knowledge ultimately rests on either beliefs or judgements about experience, or on the experiences or sensations themselves. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 8) | |
| A reaction: This clarifies the key issue very nicely, and I firmly vote for the former option. The simplest point is that error is possible about what sensations are taken to be of, so they won't do on their own. |
| 3576 | Foundationalists are torn between adequacy and security [Williams,M] |
| Full Idea: The foundationalists dilemma is to define a basis for knowledge modest enough to be secure but rich enough to be adequate. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 7) | |
| A reaction: ..And that is just what they are unable to do, precisely because adequate support would have to have enough content to be defeasibe or fallible. |
| 3577 | Strong justification eliminates error, but also reduces our true beliefs [Williams,M] |
| Full Idea: A strongly justificationist view of rationality may not be so rational; we want the truth, but avoiding all errors and maximising our number of true beliefs are not the same thing. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 7) | |
| A reaction: An interesting dilemma - to avoid all errors, believing nothing; to maximise true belief, believe everything. It is rational to follow intuition, guesses, and a wing and a prayer - once you are experienced and educated. |
| 3590 | Coherence theory must give a foundational status to coherence itself [Williams,M] |
| Full Idea: Coherence theory implicitly assigns the criteria of coherence a special status. …In so far as this status is assigned a priori, the coherence theory represents a rationalistic variant of foundationalism. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.11) | |
| A reaction: Nice move, to accuse coherence theorists of foundationalism! Wrong, though, because the a priori principles of coherence are not basic beliefs, but evolved pragmatic procedures (or something...). |
| 3589 | Why should diverse parts of our knowledge be connected? [Williams,M] |
| Full Idea: Why should political theory ever have much to do with quantum physics, or pet care with parliamentary history? | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.11) | |
| A reaction: This hardly demolishes the coherence account of justification, since your views on pet care had better be coherent, for your pet's sake. It's a pity people can make their politics cohere with their ethics. |
| 3571 | Externalism does not require knowing that you know [Williams,M] |
| Full Idea: From an externalist point of view, knowing about one's reliability is not required for 'first-order' knowledge. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 2) | |
| A reaction: Ah. 'First-order knowledge' - what's that? What we used to call 'true belief', I would say. Adequate for animals, and a good guide to daily life, but uncritical and unjustifiable. |
| 3574 | Externalism ignores the social aspect of knowledge [Williams,M] |
| Full Idea: A problem with pure externalism is that it ignores the social dimension of knowledge. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 2) | |
| A reaction: This seems to be contradicted by Idea 3573, which allows a social dimension to agreement over what is reliable. I am inclined to take knowledge as an entirely social concept. |
| 3567 | How could there be causal relations to mathematical facts? [Williams,M] |
| Full Idea: It is not clear what would even be meant by supposing that there are causal relations to mathematical facts. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 2) | |
| A reaction: I agree, though platonists seem to be willing to entertain the possibility that there are causal relations, for which no further explanation can be given. Better is knowledge without a causal relation. |
| 3569 | In the causal theory of knowledge the facts must cause the belief [Williams,M] |
| Full Idea: According to Goldman's early causal theory of knowledge, my belief that p counts as knowledge if and only if it is caused by the fact that p. This is sufficient as well as necessary, and so does not involve justification. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 2) | |
| A reaction: I take his theory simply to be false because what causes a belief is not what justifies it. I expect my mother to ring; the phone rings; I 'know' it is my mother (and it is), because I strongly expect it. |
| 3586 | Only a belief can justify a belief [Williams,M] |
| Full Idea: Justification requires logical rather than causal connections. That is the point of the slogan that only a belief can justify a belief. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.10) | |
| A reaction: It seems better to talk of 'rational' connections, rather than 'logical' connections. It isn't 'logical' to believe that someone despises me because their lip is faintly curled. |
| 3573 | Externalist reliability refers to a range of conventional conditions [Williams,M] |
| Full Idea: The radical externalists' key notion is 'reliability', which is a normative condition governing adequate performance, involving reference to a range of conditions which we decide rather than discover. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 2) | |
| A reaction: If we can decide whether a source is reliable, we can also decide whether a reliable source has performed well on this occasion, and that will always take precedence. |
| 3565 | Sometimes I ought to distrust sources which are actually reliable [Williams,M] |
| Full Idea: I may reach a belief using a procedure that is in fact reliable, but which I ought to distrust. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 1) | |
| A reaction: The tramp on the park bench who gives good share tips. The clock that is finally working, but has been going haywire for weeks. Reliabilism is a bad theory. |
| 3566 | We control our beliefs by virtue of how we enquire [Williams,M] |
| Full Idea: We control our beliefs by virtue of how we enquire. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 1) |
| 8852 | In the context of scepticism, externalism does not seem to be an option [Williams,M] |
| Full Idea: In the peculiar context of the skeptical challenge, it is easy to persuade oneself that externalism is not an option. | |
| From: Michael Williams (Without Immediate Justification [2005], §3) | |
| A reaction: This is because externalism sees justification as largely non-conscious, but when faced with scepticism, the justifications need to be spelled out, and therefore internalised. So are sceptical discussions basic, or freakish anomalies? |
| 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 |
| 3594 | Scepticism just reveals our limited ability to explain things [Williams,M] |
| Full Idea: All the sceptic's arguments show is that there are limits to our capacity to give reasons or cite evidence. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.13) |
| 3575 | Scepticism can involve discrepancy, relativity, infinity, assumption and circularity [Williams,M] |
| Full Idea: The classical Five Modes of Scepticism are Discrepancy (people always disagree), Relativity ('according to you'), Infinity (infinite regress of questions), Assumption (ending in dogma) and Circularity (end up where you started). | |
| From: Michael Williams (Problems of Knowledge [2001], Ch. 5) | |
| A reaction: I take Relativity to be different from scepticism (because, roughly, it says there is nothing to know), and the others go with Agrippa's Trilemma of justification, which may have solutions. |
| 3587 | Seeing electrons in a cloud chamber requires theory [Williams,M] |
| Full Idea: Armed with enough theory, we can see electrons in a cloud chamber. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.10) |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| Full Idea: Hume's Principle has a structure Boolos calls an 'abstraction principle'. Within the scope of two universal quantifiers, a biconditional connects an identity between two things and an equivalence relation. It says we don't care about other differences. | |
| From: George Boolos (Is Hume's Principle analytic? [1997]), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 3.7 | |
| A reaction: This seems to be the traditional principle of abstraction by ignoring some properties, but dressed up in the clothes of formal logic. Frege tries to eliminate psychology, but Boolos implies that what we 'care about' is relevant. |
| 3588 | Foundationalists base meaning in words, coherentists base it in sentences [Williams,M] |
| Full Idea: In the foundationalist picture the meaning of individual words (defined ostensively) is primary, and that of sentences is derivative. For coherentists sentences come first, with meaning understood functionally or inferentially. | |
| From: Michael Williams (Problems of Knowledge [2001], Ch.10) | |
| A reaction: Coherentism about language doesn't imply coherentism about justification. On language I vote for foundationalism, because I am impressed by the phenomenon of compositionality. |