69 ideas
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| Full Idea: The standard sense of a 'contextual definition' permits the eliminating of the defined expression, by transforming any sentence containing it into an equivalent one not containing it. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.11) | |
| A reaction: So the whole definition might be eliminated by a single word, which is not equivalent to the target word, which is embedded in the original expression. Clearly contextual definitions have some problems |
| 21616 | Truth and falsity apply to suppositions as well as to assertions [Williamson] |
| Full Idea: The notion of truth and falsity apply to suppositions as well as to assertions. | |
| From: Timothy Williamson (Vagueness [1994], 7.2) | |
| A reaction: This may not be obvious to those who emphasise pragmatics and ordinary language, but it is self-evident to anyone who emphasises logic. |
| 21623 | True and false are not symmetrical; false is more complex, involving negation [Williamson] |
| Full Idea: The concepts of truth and falsity are not symmetrical. The asymmetry is visible in the fundamental principles governing them, for F is essentially more complex than T, by its use of negation. | |
| From: Timothy Williamson (Vagueness [1994], 7.5) | |
| A reaction: If T and F are primitives, controlled by axioms, then they might be symmetrical in nature, but asymmetrical in use. However, if forced to choose just one primitive, I presume it would be T. |
| 21602 | Many-valued logics don't solve vagueness; its presence at the meta-level is ignored [Williamson] |
| Full Idea: It is an illusion that many-valued logic constitutes a well-motivated and rigorously worked out theory of vagueness. ...[top] There has been a reluctance to acknowledge higher-order vagueness, or to abandon classical logic in the meta-language. | |
| From: Timothy Williamson (Vagueness [1994], 4.12) |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| Full Idea: For sentential or first-order logic, the logical truths are represented by valid formulas; in higher-order logics, by sentences formulated in purely logical terms. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 3) |
| 21611 | Formal semantics defines validity as truth preserved in every model [Williamson] |
| Full Idea: An aim of formal semantics is to define in mathematical terms a set of models such that an argument is valid if and only if it preserves truth in every model in the set, for that will provide us with a precise standard of validity. | |
| From: Timothy Williamson (Vagueness [1994], 5.3) |
| 21606 | 'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false [Williamson] |
| Full Idea: The meta-logical law of excluded middle is the meta-linguistic principle that any statement 'A' in the object language is either truth or false; it is now known as the principle of 'bivalence'. | |
| From: Timothy Williamson (Vagueness [1994], 5.2) | |
| A reaction: [He cites Henryk Mehlberg 1958] See also Idea 21605. Without this way of distinguishing bivalence from excluded middle, most discussions of them strikes me as shockingly lacking in clarity. Personally I would cut the normativity from this one. |
| 21605 | Excluded Middle is 'A or not A' in the object language [Williamson] |
| Full Idea: The logical law of excluded middle (now the standard one) is the schema 'A or not A' in the object-language. | |
| From: Timothy Williamson (Vagueness [1994], 5.2) | |
| A reaction: [He cites Henryk Mehlberg 1958] See Idea 21606. The only sensible way to keep Excluded Middle and Bivalence distinct. I would say: (meta-) only T and F are available, and (object) each proposition must have one of them. Are they both normative? |
| 21612 | Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B' [Williamson] |
| Full Idea: Argument by Cases (or or-elimination) is the standard way of using disjunctive premises. If one can argue from A and some premises to C, and from B and some premises to C, one can argue from 'A or B' and the combined premises to C. | |
| From: Timothy Williamson (Vagueness [1994], 5.3) |
| 21599 | A sorites stops when it collides with an opposite sorites [Williamson] |
| Full Idea: A sorites paradox is stopped when it collides with a sorites paradox going in the opposite direction. That account will not strike a logician as solving the sorites paradox. | |
| From: Timothy Williamson (Vagueness [1994], 3.3) |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| Full Idea: A prime number is one which is measured by a unit alone. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 11) | |
| A reaction: We might say that the only way of 'reaching' or 'constructing' a prime is by incrementing by one till you reach it. That seems a pretty good definition. 64, for example, can be reached by a large number of different routes. |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| Full Idea: It is essential to a quantitative domain of any kind that there should be an operation of adding its elements; that this is more fundamental thaat that they should be linearly ordered by magnitude is apparent from cyclic domains like that of angles. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |
| 9895 | A number is a multitude composed of units [Dummett] |
| Full Idea: A number is a multitude composed of units. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 2) | |
| A reaction: This is outdated by the assumption that 0 and 1 are also numbers, but if we say one is really just the 'unit' which is preliminary to numbers, and 0 is as bogus a number as i is, we might stick with the original Greek distinction. |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| Full Idea: A child understands 'there are just as many nuts as apples' as easily by pairing them off as by counting them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: I find it very intriguing that you could know that two sets have the same number, without knowing any numbers. Is it like knowing two foreigners spoke the same words, without understanding them? Or is 'equinumerous' conceptually prior to 'number'? |
| 9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
| Full Idea: The identity of a mathematical object may sometimes be fixed by its relation to what lies outside the structure to which it belongs. It is more fundamental to '3' that if certain objects are counted, there are three of them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This strikes me as Dummett being pushed (by his dislike of the purely abstract picture given by structuralism) back to a rather empiricist and physical view of numbers, though he would totally deny that. |
| 9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
| Full Idea: The number 0 is not differentiated from 1 by its position in a progression, otherwise there would be no difference between starting with 0 and starting with 1. That is enough to show that numbers are not identifiable just as positions in structures. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This sounds conclusive, but doesn't feel right. If numbers are a structure, then where you 'start' seems unimportant. Where do you 'start' in St Paul's Cathedral? Starting sounds like a constructivist concept for number theory. |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| Full Idea: The two frequent modern objects to logicism are that set theory is not part of logic, or that it is of no interest to 'reduce' a mathematical theory to another, more complex, one. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Dummett says these are irrelevant (see context). The first one seems a good objection. The second one less so, because whether something is 'complex' is a quite different issue from whether it is ontologically more fundamental. |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| Full Idea: The distinction between concrete and abstract objects, or Frege's corresponding distinction between actual and non-actual objects, is not a sharp dichotomy, but resembles a scale upon which objects occupy a range of positions. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This might seem right if you live (as Dummett chooses to) in the fog of language, but it surely can't be right if you think about reality. Is the Equator supposed to be near the middle of his scale? Either there is an equator, or there isn't. |
| 9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
| Full Idea: Fully fledged realism depends on - indeed, may be identified with - an undiluted application to sentences of the relevant kind of straightforwards two-valued semantics. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: This is the sort of account you get from a whole-heartedly linguistic philosopher. Personally I would say that Dummett has got it precisely the wrong way round: I adopt a two-valued semantics because my metaphysics is realist. |
| 21596 | Vagueness undermines the stable references needed by logic [Williamson] |
| Full Idea: Logic requires expressions to have the same referents wherever they occur; vague natural languages violate this contraint. | |
| From: Timothy Williamson (Vagueness [1994], 2.2) | |
| A reaction: This doesn't mean that logic has to win. Maybe it is important for philosophers who see logic as central to be always aware of vagueness as the gulf between their precision and the mess of reality. Precision is worth trying for, though. |
| 21601 | A vague term can refer to very precise elements [Williamson] |
| Full Idea: Both 30° and 60° are clearly acute angles. 'Acute' is precise in all relevant respects. Nevertheless, 30° is acuter than 60°. | |
| From: Timothy Williamson (Vagueness [1994], 4.11) | |
| A reaction: A very nice example of something which is vague, despite involving precise ingredients. But then 'bald' is vague, while 'this is a hair on his head' is fairly precise. |
| 21589 | When bivalence is rejected because of vagueness, we lose classical logic [Williamson] |
| Full Idea: The principle of bivalence (that every statement is either true or false) has been rejected for vague languages. To reject bivalence is to reject classical logic or semantics. | |
| From: Timothy Williamson (Vagueness [1994], Intro) | |
| A reaction: His example is specifying a moment when Rembrandt became 'old'. This is the number one reason why the problem of vagueness is seen as important. Is the rejection of classical logic a loss of our grip on the world? |
| 21629 | Equally fuzzy objects can be identical, so fuzziness doesn't entail vagueness [Williamson] |
| Full Idea: Fuzzy boundaries do not in any way require vague identity. Objects are identical only if their boundaries have exactly the same fuzziness. | |
| From: Timothy Williamson (Vagueness [1994], 9.2) | |
| A reaction: This all rests on the Fregean idea that determinate existence requires the ability to participate in an identity statement. |
| 21591 | Vagueness is epistemic. Statements are true or false, but we often don't know which [Williamson] |
| Full Idea: My thesis is that vagueness is an epistemic phenomenon. In cases of unclarity, statements remain true or false, but speakers of the language have no way of knowing which. Higher-order vagueness consists in ignorance about ignorance. | |
| From: Timothy Williamson (Vagueness [1994], Intro) | |
| A reaction: He has plumped for the intuitively least plausible theory. It means that a hair dropping out of someone's head triggers a situation where they are 'bald', but none of us know when that was. And Rembrandt became 'old' in an instant. |
| 21619 | If a heap has a real boundary, omniscient speakers would agree where it is [Williamson] |
| Full Idea: If, in judging a heap as grains are removed, omniscient speakers all stop at the same point, it must does mark some sort of previously hidden boundary. ...If there is no hidden boundary, then different omniscient speakers would stop at different points. | |
| From: Timothy Williamson (Vagueness [1994], 7.3) | |
| A reaction: A very nice thought experiment, which obviously won't settle anything, but brings out nicely the view the vagueness is a sort of ignorance. God is never vague in the application of terms (though God might withhold the application if there is no boundary). |
| 21620 | The epistemic view says that the essence of vagueness is ignorance [Williamson] |
| Full Idea: The epistemic view is that ignorance is the real essence of the phenomenon ostensively identified as vagueness. ...[203] According to the epistemic view, I am either thin or not thin, ...and we have no idea how to find out out which. | |
| From: Timothy Williamson (Vagueness [1994], 7.4) | |
| A reaction: Presumably this implies that there is often a real border (of which we may be ignorant), but it doesn't seem to rule out cases where there just is no border. Where does the east Atlantic meet the west Atlantic? |
| 21622 | If there is a true borderline of which we are ignorant, this drives a wedge between meaning and use [Williamson] |
| Full Idea: A common complaint against the epistemic view is that to postulate a matter of fact in borderline cases is to suppose, incoherently, that the meanings of our words draw a line where our use of them does not. | |
| From: Timothy Williamson (Vagueness [1994], 7.5) | |
| A reaction: This doesn't necessarily seem to require the view that the meaning of words is their usage. Just that if there is one consensus on usage, it seems unlikely that there is a different underlying reality about the true meaning. Externalist meanings? |
| 9120 | Vagueness in a concept is its indiscriminability from other possible concepts [Williamson] |
| Full Idea: Vagueness in a concept is its indiscriminability from other possible concepts; this can be reconciled with our knowledge of vague terms. | |
| From: Timothy Williamson (Vagueness [1994], 8.1) | |
| A reaction: Sorensen objects that this makes vagueness too relative to members of a speech community. He prefers 'absolute borderline cases'. If you like the epistemic view, then Williamson seems more plausible. My 'vague' might differ from yours. |
| 21614 | The 'nihilist' view of vagueness says that 'heap' is not a legitimate concept [Williamson] |
| Full Idea: The 'nihilist' view is that no genuine distinction can be vaguely drawn; since vague expressions are not properly meaningful, there is nothing for sorites reasoning to betray; they are empty. | |
| From: Timothy Williamson (Vagueness [1994], 6.1) | |
| A reaction: He cites Frege as holding this view. The thought is that 'heap' is not a legitimate concept, so fussing over what qualifies as one is pointless. This seems to be a semantic view of vagueness, of which the main rival is the contextual view. |
| 21617 | We can say propositions are bivalent, but vague utterances don't express a proposition [Williamson] |
| Full Idea: A philosopher might endorse bivalence for propositions, while treating vagueness as the failure of an utterance to express a unique proposition. | |
| From: Timothy Williamson (Vagueness [1994], 7.2) | |
| A reaction: This idea jumps at out me as an extremely promising approach to vagueness, because I am a fan of propositions (and have written a paper on them). The whole point of propositions is that they are not ambiguous (and probably not vague). |
| 21618 | If the vague 'TW is thin' says nothing, what does 'TW is thin if his perfect twin is thin' say? [Williamson] |
| Full Idea: If vague utterances in borderline cases fail to say anything, then if 'TW is thin' is vague, and TW has a twin of identical dimensions, it still seems that 'If TW is thin then his twin is thin' must be true, and so it must have said something. | |
| From: Timothy Williamson (Vagueness [1994], 7.2 (d)) | |
| A reaction: This an objection to the Fregean 'nihilistic' view of Idea 21614. I am inclined to a solution based on the proposition expressed, rather than the sentence. The first question is whether you are willing to assert 'TW is thin'. |
| 21625 | The vagueness of 'heap' can remain even when the context is fixed [Williamson] |
| Full Idea: Vagueness remains even when the context is fixed. In principle, a vague word might exhibit no context dependence whatsoever. ...For example, a dispute over whether someone has left a 'heap' of sand on the floor. | |
| From: Timothy Williamson (Vagueness [1994], 7.7) | |
| A reaction: A fairly devastating rebuttal of what seems to be David Lewis's view. He talks of something being 'smooth' depending on context. |
| 21590 | Asking when someone is 'clearly' old is higher-order vagueness [Williamson] |
| Full Idea: Difficulties of vagueness are presented by the question 'When did Rembrandt become clearly old?', and the iterating question 'When did he become clearly clearly old?'. This is the phenomenon of higher-order vagueness. The language of vagueness is vague. | |
| From: Timothy Williamson (Vagueness [1994], Intro) | |
| A reaction: [compressed] I presume the bottom level is a question about Rembrandt, the second level is about this use of the word 'old', and the third level is about this particular application of the word 'clearly'. Meta-languages. |
| 21609 | Supervaluationism defines 'supertruth', but neglects it when defining 'valid' [Williamson] |
| Full Idea: Supervaluationists identify truth with 'supertruth'; since validity is necessary preservation of truth, they should identify it with necessary preservation of supertruth. But it plays no role in their definition of 'local' validity. | |
| From: Timothy Williamson (Vagueness [1994], 5.3) | |
| A reaction: [See text for 'local'] Generally Williamson's main concern with attempts to sort out vagueness is that higher-order and meta-language issues are neglected. |
| 21610 | Supervaluation adds a 'definitely' operator to classical logic [Williamson] |
| Full Idea: Supervaluation seems to inherit the power of classical logic, ...but also enables it to be extended. It makes room for a new operator 'definitely' to express supertruth in the object-language. | |
| From: Timothy Williamson (Vagueness [1994], 5.3) | |
| A reaction: Once you mention higher-order vagueness you can see a regress looming over the horizon. 'He is definitely definitely definitely bald'. [p.164 he says 'definitely' has no analysis, and is an uninteresting primitive] |
| 21613 | Supervaluationism cannot eliminate higher-order vagueness [Williamson] |
| Full Idea: Supervaluationism cannot eliminate higher-order vagueness. It must conduct its business in a vague meta-language. ...[162] All truth is at least disquotational, and supertruth is not. | |
| From: Timothy Williamson (Vagueness [1994], 5.6) | |
| A reaction: This is Williamson's final verdict on the supervaluation strategy for vagueness. Intuitively, it looks as if merely narrowing down the vagueness (by some sort of consensus) is no solution to the problem of vagueness. |
| 21592 | Supervaluation keeps classical logic, but changes the truth in classical semantics [Williamson] |
| Full Idea: Supervaluationism preserves almost all of classical logic, at the expense of classical semantics, but giving a non-standard account of truth. I argue that its treatment of higher-order vagueness undermines the non-standard account of truth. | |
| From: Timothy Williamson (Vagueness [1994], Intro) |
| 21603 | You can't give a precise description of a language which is intrinsically vague [Williamson] |
| Full Idea: If a vague language is made precise, its expressions change in meaning, so an accurate semantic description of the precise language is inaccurate as a description of the vague one. | |
| From: Timothy Williamson (Vagueness [1994], 5.1) | |
| A reaction: Kind of obvious, really, but it clarifies the nature of any project (starting with Leibniz) to produce a wholly precise language. That is usually seen as a specialist language for science. |
| 21604 | Supervaluation assigns truth when all the facts are respected [Williamson] |
| Full Idea: 'Admissible' interpretations respect all the theoretical and ostensive connections. ...'Supervaluation' is the assignment of truth to the statements true on all admissible valuations, falsity to the false one, and neither to the rest. | |
| From: Timothy Williamson (Vagueness [1994], 5.2) | |
| A reaction: So 'he is bald' is true if when faced with all observations and definitions it is acceptable. Prima facie, that doesn't sound like a solution to the problem. Supervaluation started in philosophy of science. [p.156 'Admissible seems vague'] |
| 21607 | Supervaluation has excluded middle but not bivalence; 'A or not-A' is true, even when A is undecided [Williamson] |
| Full Idea: The supervaluationist denies bivalence but accepts excluded middle. The statement 'A or not-A' is true on each admissible interpretation, and therefore true, even if 'A' (and hence 'not-A') are true and some and false on others, so neither T nor F. | |
| From: Timothy Williamson (Vagueness [1994], 5.2) | |
| A reaction: See Ideas 21605 and 21606 for the distinction being used here. Denying bivalence allows 'A' to be neither true nor false. It seems common sense that 'he is either bald or not-bald' is true, without being sure about the disjuncts. |
| 21608 | Truth-functionality for compound statements fails in supervaluation [Williamson] |
| Full Idea: A striking fearure of supervaluations is the failure of truth-functionality for compound statements. | |
| From: Timothy Williamson (Vagueness [1994], 5.3) | |
| A reaction: Supervaluations has the initial appearance of enhancing classical logic, but turns out to somewhat undermine it. Hence Williamson's lack of sympathy. But see Idea 21610. |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| Full Idea: The nominalist superstition is based ultimately on the myth of the unmediated presentation of genuine concrete objects to the mind. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Personally I am inclined to favour nominalism and a representative theory of perception, which acknowledges some 'mediation', but of a non-linguistic form. Any good theory here had better include animals, which seem to form concepts. |
| 21633 | Nominalists suspect that properties etc are our projections, and could have been different [Williamson] |
| Full Idea: The nominalist suspects that properties, relations and states of affairs are mere projections onto the world of our forms of speech. One source of the suspicion is a sense that we could just as well have classified things differently. | |
| From: Timothy Williamson (Vagueness [1994], 9.3) | |
| A reaction: I know it is very wicked to say so, but I'm afraid I have some sympathy with this view. But I like the primary/secondary distinction, so there is more 'projection' in the latter case. Classification is not random; it is a response to reality. |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| Full Idea: The existence of abstract objects is a pseudo-problem. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This remark follows after Idea 9884, which says the abstract/concrete distinction is a sliding scale. Personally I take the distinction to be fairly sharp, and it is therefore probably the single most important problem in the whole of human thought. |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| Full Idea: Objects which are objective but not actual are precisely what are now called abstract objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Why can there not be subjective abstract objects? 'My favourites are x, y and z'. 'I'll decide later what my favourites are'. 'I only buy my favourites - nothing else'. |
| 9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
| Full Idea: If someone argued that assuming the existence of the Equator explains nothing, and it has no causal powers, so everything would be the same if it didn't exist, so we needn't accept its existence, we should gape at the crudity of the misunderstanding. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Not me. I would gape if someone argued that latitude 55° 14' (and an infinity of other lines) exists for the same reasons (whatever they may be) that the Equator exists. A mode of description can't create an object. |
| 9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
| Full Idea: 'We've crossed the Equator' is judged true if we are nearer the other Pole, so it not for philosophers to deny that the Earth has an equator, and we see that the Equator is not a concept or relation or function, so it must be classified as an object. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: A lovely example of linguistic philosophy in action (and so much the worse for that, I would say). A useful label here, I suggest (unoriginally, I think), is that we should label such an item a 'semantic object', rather than a real object in our ontology. |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| Full Idea: To recognise that there is no objection in principle to abstract objects requires acknowledgement that some form of the context principle is correct, since abstract objects can neither be encountered nor presented. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: I take this to be an immensely important idea. I consider myself to be a philosopher of thought rather than a philosopher of language (Dummett's distinction, he being one of the latter). Thought connects to the world, but does it connect to abstracta? |
| 21630 | If fuzzy edges are fine, then why not fuzzy temporal, modal or mereological boundaries? [Williamson] |
| Full Idea: If objects can have fuzzy spatial boundaries, surely they can have fuzzy temporal, modal or mereological boundaries too. | |
| From: Timothy Williamson (Vagueness [1994], 9.2) | |
| A reaction: Fair point. I think there is a distinction between parts of the thing, such as its edges, being fuzzy, and the whole thing being fuzzy, in the temporal case. |
| 21632 | A river is not just event; it needs actual and counterfactual boundaries [Williamson] |
| Full Idea: A river is not just an event. One would need to specify counterfactual as well as actual boundaries. | |
| From: Timothy Williamson (Vagueness [1994], 9.3) | |
| A reaction: In other words the same river can change its course a bit, but it can't head off in the opposite direction. |
| 9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
| Full Idea: Husserl says the only ground for assuming the replaceability of one content by another is their identity; we are therefore not entitled to define their identity as consisting in their replaceability. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by Michael Dummett - Frege philosophy of mathematics Ch.12 | |
| A reaction: This is a direct challenge to Frege. Tricky to arbitrate, as it is an issue of conceptual priority. My intuition is with Husserl, but maybe the two are just benignly inerdefinable. |
| 9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
| Full Idea: In his middle period Frege rated identity indefinable, on the ground that every definition must take the form of an identity-statement. Frege introduced the notion of criterion of identity, which has been widely used by analytical philosophers. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.10) | |
| A reaction: The objection that attempts to define identity would be circular sounds quite plausible. It sounds right to seek a criterion for type-identity (in shared properties or predicates), but token-identity looks too fundamental to give clear criteria. |
| 21621 | We can't infer metaphysical necessities to be a priori knowable - or indeed knowable in any way [Williamson] |
| Full Idea: The inference from metaphysical necessity to a priori knowlability is, as Kripke has emphasized, fallacious. Indeed, metaphysical necessities cannot be assumed knowable in any way at all. | |
| From: Timothy Williamson (Vagueness [1994], 7.4) | |
| A reaction: The second sentence sounds like common sense. He cites Goldbach's Conjecture. A nice case of the procedural rule of keeping your ontology firmly separated from your epistemology. How is it? is not How do we know it? |
| 21627 | We have inexact knowledge when we include margins of error [Williamson] |
| Full Idea: Inexact knowledge is a widespread and easily recognised cognitive phenomenon, whose underlying nature turns out to be characterised by the holding of margin of error principles. | |
| From: Timothy Williamson (Vagueness [1994], 8.3) | |
| A reaction: Williamson is invoking this as a tool in developing his epistemic view of vagueness. It obviously invites the question of how it can be knowledge if error is a possibility. A very large margin of error would obviously invalidate it. |
| 21626 | Knowing you know (KK) is usually denied if the knowledge concept is missing, or not considered [Williamson] |
| Full Idea: The failure of the KK principle is not news. The standard counterexamples involve knowing subjects who lack the concept of knowledge, or have not reflected on their knowledge, and therefore do not know that they know. | |
| From: Timothy Williamson (Vagueness [1994], 8.2) | |
| A reaction: There is also the timid but knowledgeable pupil, who can't believe they know so much. The simplest case would be if we accept that animals know lots of things, but are largely devoid of any metathinking. |
| 21631 | To know, believe, hope or fear, one must grasp the thought, but not when you fail to do them [Williamson] |
| Full Idea: To know, believe, hope, or fear that A, one must grasp the thought that A. In contrast, to fail to know, believe, hope or fear that A, one need not grasp the thought that A. | |
| From: Timothy Williamson (Vagueness [1994], 9.3 c) | |
| A reaction: A simple point, which at least shows that propositional attitudes are a two-stage operation. |
| 21600 | 'Blue' is not a family resemblance, because all the blues resemble in some respect [Williamson] |
| Full Idea: 'Blue' is vague by some standards, for it has borderline cases, but that does not make it a family resemblance term, for all the shades of blue resemble each other in some respect. | |
| From: Timothy Williamson (Vagueness [1994], 3.3) | |
| A reaction: Presumably the point of family resemblance is that fringe members as still linked to the family, despite having lost the main features. A bit of essentialism seems needed here. |
| 9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
| Full Idea: One powerful argument for a thesis that one notion is conceptually prior to another is the possibility of defining the first without reference to the second. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: You'd better check whether you can't also define the second without reference to the first before you rank their priority. And maybe 'conceptual priority' is conceptually prior to 'definition' (i.e. definition needs a knowledge of priority). Help! |
| 9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
| Full Idea: An argument for conceptual priority is greater simplicity in explanation. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: One might still have to decide priority between two equally simple (or complex) concepts. I begin to wonder whether 'priority' has any other than an instrumental meaning (according to which direction you wish to travel - is London before Edinburgh?). |
| 9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
| Full Idea: To recognise abstract terms as perfectly proper items of a vocabulary depends upon allowing that all that is necessary for the lawful introduction of a range of expressions into the language is a coherent account of how they are to function in sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: Why can't the 'coherent account' of the sentences include the fact that there must be something there for the terms to refer to? How else are we to eliminate nonsense words which obey good syntactical rules? Cf. Idea 9872. |
| 9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
| Full Idea: Dummett uses the term 'logical abstraction' for the construction of the abstract objects as equivalence classes, but it is not clear why we should call this construction 'logical'. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by William W. Tait - Frege versus Cantor and Dedekind n 14 | |
| A reaction: This is a good objection, and Tait offers a much better notion of 'logical abstraction' (as involving preconditions for successful inference), in Idea 9981. |
| 9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
| Full Idea: We arrive at the concept of suicide by considering both occurrences in the sentence 'Cato killed Cato' of the proper name 'Cato' as simultaneously replaceable by another name, say 'Brutus', and so apprehending the pattern common to both sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.14) | |
| A reaction: This is intended to illustrate Frege's 'logical abstraction' technique, as opposed to wicked psychological abstraction. The concept of suicide is the pattern 'x killed x'. This is a crucial example if we are to understand abstraction... |
| 9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
| Full Idea: To get units by abstraction, units arrived at by abstraction from forks must the identical to that abstracted from spoons, with no trace of individuality. But if spoons can no longer be differentiated from forks, they can't differ from one another either. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: [compressed] Dummett makes the point better than Frege did. Can we 'think of a fork insofar as it is countable, ignoring its other features'? What are we left thinking of? Frege says it must still be the whole fork. 'Nice fork, apart from the colour'. |
| 21615 | References to the 'greatest prime number' have no reference, but are meaningful [Williamson] |
| Full Idea: The predicate 'is a prime number greater than all other prime numbers' is necessarily not true of anything, but it is not semantically defective, for it occurs in sentences that constitute a sound proof that there is no such number. | |
| From: Timothy Williamson (Vagueness [1994], 6.2) | |
| A reaction: One might reply that the description can be legitimately mentioned, but not legitimately used. |
| 18038 | The 't' and 'f' of formal semantics has no philosophical interest, and may not refer to true and false [Williamson] |
| Full Idea: In a formal semantics we can label two properties 't' and 'f' and suppose that some sentences have neither (or both). Such a manoeuvre shows nothing of philosophical interest. No connection has been made between 't' and 'f' and truth and falsity. | |
| From: Timothy Williamson (Vagueness [1994], 7.2) | |
| A reaction: This is right, and means there is a huge gulf between 'formal' semantics (which could be implemented on a computer), and seriously interesting semantics about how language refers to and describes the world. |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| Full Idea: A Fregean semantics assumes a domain already determinately articulated into individual objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: A more interesting criticism than most of Dummett's other challenges to the Frege/Davidson view. I am beginning to doubt whether the semantics and the ontology can ever be divorced from the psychology, of thought, interests, focus etc. |
| 21624 | It is known that there is a cognitive loss in identifying propositions with possible worlds [Williamson] |
| Full Idea: It is well known that when a proposition is identified with the set of possible worlds at which it is true, a region in the space of possible worlds, cognitively significant distinctions are lost. | |
| From: Timothy Williamson (Vagueness [1994], 7.6) | |
| A reaction: Alas, he doesn't specify which distinctions get lost, so this is just a pointer. It would seem likely that two propositions could have identical sets of possible worlds, while not actually saying the same thing. Equilateral/equiangular. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
| Full Idea: By what right do we assume that the limit of measurement is a point, and not an interval? | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |