45 ideas
| 9593 | Progress in philosophy is incremental, not an immature seeking after drama [Williamson] |
| Full Idea: The incremental progress which I envisage for philosophy lacks the drama after which some philosophers still hanker, and that hankering is itself a symptom of the intellectual immaturity that helps hold philosophy back. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], Intro) | |
| A reaction: This could stand as a motto for the whole current profession of analytical philosophy. It means that if anyone attempts to be dramatic they can make their own way out. They'll find Kripke out there, smoking behind the dustbins. |
| 15169 | Metaphysics is clarifying how we speak and think (and possibly improving it) [Sidelle] |
| Full Idea: Metaphysics, for the conventionalist, is not a matter of trying to see deeply into the structure of mind-independent reality, but of trying to clarify the way we actually speak and think, and perhaps negotiating ways of doing this to our best advantage. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1) | |
| A reaction: Note that he is still allowing space for 'revisionary' as well as for 'descriptive' metaphysics. I can't wholly accept this, as I really do think we can have some deep insights into reality, but Sidelle is articulating a large part of the truth. |
| 15164 | We seem to base necessities on thought experiments and imagination [Sidelle] |
| Full Idea: Judgments of necessity seem always to be based on thought experiments and appeals to what we can imagine. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1) | |
| A reaction: That is, the denial of this thing seems inconceivable. I would say that they are also based on coherence. The idea that we can think without imagination is nonsense. |
| 9594 | Correspondence to the facts is a bad account of analytic truth [Williamson] |
| Full Idea: Even if talk of truth as correspondence to the facts is metaphorical, it is a bad metaphor for analytic truth in a way that it is not for synthetic truth. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], 3.1) | |
| A reaction: A very simple and rather powerful point. Maybe the word 'truth' should be withheld from such cases. You might say that accepted analytic truths are 'conventional'. If that is wrong, then they correspond to natural facts at a high level of abstraction. |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| Full Idea: The empty set is usually derived via Zermelo's axiom of separation. But the axiom of separation is conditional: it requires the existence of a set in order to generate others as subsets of it. The original set has to come from the axiom of infinity. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: They charge that this leads to circularity, as Infinity depends on the empty set. |
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| Full Idea: Some authors need to be told loud and clear: if there is an empty set, it is something, not nothing. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: I'm inclined to think of a null set as a pair of brackets, so maybe that puts it into a metalanguage. |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| Full Idea: The empty set is said to be useful to express non-existence, but saying 'there are no Us', or ¬∃xUx are no less concise, and certainly less roundabout. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| Full Idea: Suppose we introduce Ω not as a term standing for a supposed empty set, but as a paradigm of an empty term, not standing for anything. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: This proposal, which they go on to explore, seems to mean that Ω (i.e. the traditional empty set symbol) is no longer part of set theory but is part of semantics. |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| Full Idea: Thomason says with no unit sets we couldn't call {1,2}∩{2,3} a set - but so what? Why shouldn't the intersection be the number 2? However, we then have to distinguish three different cases of intersection (common subset or member, or disjoint). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 2.2) |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| Full Idea: A 'singularist', who refers to objects one at a time, must resort to the language of sets in order to replace plural reference to members ('Henry VIII's wives') by singular reference to a set ('the set of Henry VIII's wives'). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: A simple and illuminating point about the motivation for plural reference. Null sets and singletons give me the creeps, so I would personally prefer to avoid set theory when dealing with ontology. |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| Full Idea: Plurals earn their keep in set theory, to answer Skolem's remark that 'in order to treat of 'sets', we must begin with 'domains' that are constituted in a certain way'. We can speak in the plural of 'the objects', not a 'domain' of objects. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: [Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it. |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| Full Idea: Logical truths should be true no matter what exists, so true even if nothing exists. The classical predicate calculus, however, makes it logically true that something exists. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| Full Idea: If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) | |
| A reaction: Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application. |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| Full Idea: Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2) | |
| A reaction: Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated. |
| 9601 | The realist/anti-realist debate is notoriously obscure and fruitless [Williamson] |
| Full Idea: The debate between realism and anti-realism has become notorious in the rest of philosophy for its obscurity, convolution, and lack of progress. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], After) | |
| A reaction: I find this reassuring, because fairly early on I decided that this problem was not of great interest, and quietly tiptoed away. I take the central issue to be whether nature has 'joints', to which the answer appears to be 'yes'. End of story. |
| 9599 | There cannot be vague objects, so there may be no such thing as a mountain [Williamson] |
| Full Idea: It is sometimes argued that if there is such a thing as a mountain it would be a vague object, but it is logically impossible for an object to be vague, so there is no such thing as a mountain. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], 7.2) | |
| A reaction: I don't take this to be a daft view. No one is denying the existence of the solid rock that is involved, but allowing such a vague object may be a slippery slope to the acceptance of almost anything as an 'object'. |
| 15180 | There doesn't seem to be anything in the actual world that can determine modal facts [Sidelle] |
| Full Idea: Metaphysically, nothing in the actual world seems to be a candidate for determining what is necessarily the case. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.4) | |
| A reaction: I file this under 'Dispositions' to show what is at stake in the debate about dispositional and categorical properties. I take a commitment to dispositions to be a commitment to modal facts about the actual world. |
| 9602 | Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson] |
| Full Idea: The constraints of common sense and classical logic are often simultaneously abandoned in debates on vagueness. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], After) | |
| A reaction: Wiliamson has described himself (in my hearing) as a 'rottweiller realist', but presumably the problem of vagueness interests a lot of people precisely because it pushes us away from common sense and classical logic. |
| 15184 | Causal reference presupposes essentialism if it refers to modally extended entities [Sidelle] |
| Full Idea: Even if the causal theory of reference proper does not presuppose essentialism, it does presuppose essentialism if it is to be an account of reference to modally extended entities. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.6) |
| 15172 | Clearly, essential predications express necessary properties [Sidelle] |
| Full Idea: It is clear, of course, that if there are true essential predications, then they express necessary properties. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.2) | |
| A reaction: I would certainly want to ask whether essences have to be analysed as properties, and also (more boldly) whether there might not be contingent essences. |
| 15181 | Being a deepest explanatory feature is an actual, not a modal property [Sidelle] |
| Full Idea: The property of being a deepest explanatory feature is a nonmodal property: it's an actual property. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.4) | |
| A reaction: I don't accept the existence of properties of the form 'being-F'. The possibility of securing a door may be the deepest explanatory feature of a lock. [To be fair to Sidelle, see context - just for once!] Dispositions are actual. |
| 15173 | That the essence of water is its microstructure is a convention, not a discovery [Sidelle] |
| Full Idea: The necessity to water of whatever is found out to be the water's microstructure is given by convention, and is not something which is discovered. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.2) | |
| A reaction: A powerful point. It shows the authority of science that we accept the microstructure as the essence. The essences of statues and people are definitely not their microstructures. One H2O molecule isn't water. Why not? Macro-properties count too! |
| 15185 | We aren't clear about 'same stuff as this', so a principle of individuation is needed to identify it [Sidelle] |
| Full Idea: Independent of conventions, no definite sense can be given to the notion of 'the same stuff as this'. So reference-fixing must include some principle of individuation to determine the aspects of sameness for the identity referred to. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.6) | |
| A reaction: Is he really saying that we don't understand 'same stuff as this'? Surely animals can manage that, and they are not famous for their conventions. Sidelle has fallen into the sortalist trap, I think. |
| 15175 | Evaluation of de dicto modalities does not depend on the identity of its objects [Sidelle] |
| Full Idea: In the evaluation of de dicto modal statements, whether some possible state of affairs is relevant to its truth does not depend on the identity of its objects, as in 'Necessarily, the President of the USA is male'. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.3) | |
| A reaction: This is a more clear-cut and easy to grasp criterion than most that are on offer. |
| 15032 | Necessary a posteriori is conventional for necessity and nonmodal for a posteriority [Sidelle, by Sider] |
| Full Idea: Sidelle defends conventionalism against a posteriori necessities by 'factoring' a necessary a posteriori truth into an analytic component and a nonmodal component. The modal force then comes from the analytic part, and the a posteriority from the other. | |
| From: report of Alan Sidelle (Necessity, Essence and Individuation [1989]) by Theodore Sider - Writing the Book of the World 12.8 | |
| A reaction: [I note that Sidelle refers, it seems, to the nonmodal component as a 'deep explanatory feature', which is exactly what I take an essence to be]. |
| 15179 | To know empirical necessities, we need empirical facts, plus conventions about which are necessary [Sidelle] |
| Full Idea: What we need to know, in order to know what is empirically necessary, is some empirical fact plus our conventions that tell us which truths are necessary given which empirical facts. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.4) | |
| A reaction: I take this attack on a posteriori necessities to be the most persuasive part of Sidelle's case, but you can't just put all of our truths down to convention. There are stabilities in the world, as well as in our conventions. |
| 9598 | Modal thinking isn't a special intuition; it is part of ordinary counterfactual thinking [Williamson] |
| Full Idea: The epistemology of metaphysical modality requires no dedicated faculty of intuition. It is simply a special case of the epistemology of counterfactual thinking, a kind of thinking tightly integrated with our thinking about the spatio-temporal world. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], 5.6) | |
| A reaction: This seems to me to be spot-on, though it puts the focus increasingly on the faculty of imagination, as arguably an even more extraordinary feature of brains than the much-vaunted normal consciousness. |
| 15171 | The necessary a posteriori is statements either of identity or of essence [Sidelle] |
| Full Idea: The necessary a posteriori crudely divides into two groups - (synthetic) identity statements (between rigid designators), and statements of essential properties. The latter is either statements of property identity, or of the essences of natural kinds. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.2) | |
| A reaction: He cites Kripke's examples (Hesperus,Cicero,Truman,water,gold), and divides them into the two groups. Helpful. |
| 16536 | Williamson can't base metaphysical necessity on the psychology of causal counterfactuals [Lowe on Williamson] |
| Full Idea: The psychological mechanism that Williamson proposes as the supposedly reliable source of our knowledge of necessities only seems applicable to counterfactuals that are distinctively causal, not metaphysical, in character. | |
| From: comment on Timothy Williamson (The Philosophy of Philosophy [2007]) by E.J. Lowe - What is the Source of Knowledge of Modal Truths? 5 | |
| A reaction: My rough impression of Williamson's account is that it is correct but unilluminating. We have to assess necessities by counterfactual thinking, because nothing else is available (apart from evaluating the coherence of the findings). |
| 9596 | We scorn imagination as a test of possibility, forgetting its role in counterfactuals [Williamson] |
| Full Idea: The epistemology of modality often focuses on (and pours scorn on) imagination or conceivability as a test of possibility, while ignoring the role of the imagination in the assessment of mundane counterfactuals. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], 5.4) | |
| A reaction: Good point. I've been guilty of this easy scorn myself. Williamson gives our modal capacities an evolutionary context. What is needed is well-informed imagination, rather than wild fantasy. |
| 15167 | Empiricism explores necessities and concept-limits by imagining negations of truths [Sidelle] |
| Full Idea: In the traditional empiricist picture, we go about modal enquiry by trying to see whether we can imagine a situation in which it would be correct to assert the negation of a proposed necessary truth. Thus we can find out the limits of our concepts. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1) |
| 15177 | Contradictoriness limits what is possible and what is imaginable [Sidelle] |
| Full Idea: Contradictoriness is the boundary both of what is possible and also of what is imaginable. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.4) | |
| A reaction: Of course we may see contradictions where there are none, and fail to grasp real hidden contradictions, so the two do not coincide in the practice. I think I would say it is 'a' boundary, not 'the' boundary. |
| 15176 | The individuals and kinds involved in modality are also a matter of convention [Sidelle] |
| Full Idea: It is not merely the modal facts that result from our conventions, but the individuals and kinds that are modally involved. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.3) | |
| A reaction: I am beginning to find Sidelle's views very sympathetic - going over to the Dark Side, I'm afraid. But conventions won't work at all if they don't correspond closely to reality. |
| 15174 | A thing doesn't need transworld identity prior to rigid reference - that could be a convention of the reference [Sidelle] |
| Full Idea: For a term to be rigid, it is said there must be real transworld identity prior to our use of the rigid term, ..but this may only be because we have conventional principles for individuating across worlds. 'Let's call him Fred' - perhaps explicitly rigid. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.3) | |
| A reaction: This seems right. An example might be a comic book character, who retains a perfect identity in all the comics, with no scars, weight change, or ageing. |
| 15183 | 'Dthat' operates to make a singular term into a rigid term [Sidelle] |
| Full Idea: 'Dthat' is Kaplan's indexical operator; it operates on a given singular term, φ, and makes it into a rigid designator of whatever φ designates in the original context. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.6 n11) | |
| A reaction: I like this idea a lot, because it strikes me that referring to something rigidly is a clear step beyond referring to it in actuality. I refer to 'whoever turns up each week', but that is hardly rigid. The germ of 2-D semantics is here. |
| 9597 | There are 'armchair' truths which are not a priori, because experience was involved [Williamson] |
| Full Idea: There is extensive 'armchair knowledge' in which experience plays no strictly evidential role, but it may not fit the stereotype of the a priori, because the contribution of experience was more than enabling, such as armchair truths about our environment. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], 5.5) | |
| A reaction: Once this point is conceded we have no idea where to draw the line. Does 'if it is red it can't be green' derive from experience? I think it might. |
| 15165 | A priori knowledge is entirely of analytic truths [Sidelle] |
| Full Idea: The a priori method yields a priori knowledge, and the objects of this knowledge are not facts about the world, but analytic truths. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1) | |
| A reaction: Are we not allowed any insights at all into how the world must be, independent of how we happen to conceptualise it? |
| 9592 | Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson] |
| Full Idea: Crude rationalists postulate a special knowledge-generating faculty of rational intuition. Crude empiricists regard intuition as an obscurantist term of folk psychology. Linguistic/conceptual philosophy says it reveals linguistic or conceptual competence. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], Intro) | |
| A reaction: Kripke seems to think that it is the basis of logical competence. I would use it as a blank term for any insight in which we have considerable confidence, and yet are unable to articulate its basis; roughly, for rational thought that evades logic. |
| 20181 | When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson] |
| Full Idea: 'Intuition' plays a major role in contemporary analytic philosophy's self-understanding. ...When contemporary analytic philosophers run out of arguments, they appeal to intuitions. ...Thus intuitions are presented as our evidence in philosophy. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], p.214-5), quoted by Herman Cappelen - Philosophy without Intuitions 01.1 | |
| A reaction: Williamson says we must investigate this 'scandal', but Cappelen's book says analytic philosophy does not rely on intuition. |
| 15168 | That water is essentially H2O in some way concerns how we use 'water' [Sidelle] |
| Full Idea: If water is essentially H2O, this is going to have something to do with our intentions in using 'water'. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1) | |
| A reaction: This very simple point looks to be correct, and raises very important questions about the whole Twin Earth thing. When new discoveries are made, words shift their meanings. We're not quite sure what 'jade' means any more. |
| 9595 | You might know that the word 'gob' meant 'mouth', but not be competent to use it [Williamson] |
| Full Idea: Someone who acquires the word 'gob' just by being reliably told that it is synonymous with 'mouth' knows what 'gob' means without being fully competent to use it. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], 4.7) | |
| A reaction: Not exactly an argument against meaning-as-use, but a very nice cautionary example to show that 'knowing the meaning' of a word may be a rather limited, and dangerous, achievement. |
| 15166 | Causal reference seems to get directly at the object, thus leaving its nature open [Sidelle] |
| Full Idea: The causal theory of reference appears to give us a way to get at an object while leaving it undetermined what its essence or necessary features might be. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.1) | |
| A reaction: This pinpoints why the direct/causal theory of reference seems to open the doors to scientific essentialism. Sidelle, of course, opposes the whole programme. |
| 15182 | Because some entities overlap, reference must have analytic individuation principles [Sidelle] |
| Full Idea: The phenomenon of overlapping entities requires that if our reference is to be determinate (as determinate as it is), then there must be analytic principles of individuation. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.5) | |
| A reaction: His point is that there is something inescapably conventional about the way in which our reference works. It isn't just some bald realist baptism. |
| 9600 | If languages are intertranslatable, and cognition is innate, then cultures are all similar [Williamson] |
| Full Idea: Given empirical evidence for the approximate intertranslatability of all human languages, and a universal innate basis of human cognition, we may wonder how 'other' any human culture really is. | |
| From: Timothy Williamson (The Philosophy of Philosophy [2007], 8.1) | |
| A reaction: This seems to be a fairly accurate account of the situation. In recent centuries people seem to have been over-impressed by superficial differences in cultural behaviour, but we increasingly see the underlying identity. |
| 15178 | Can anything in science reveal the necessity of what it discovers? [Sidelle] |
| Full Idea: Is there anything in the procedures of scientists that could reveal to them that water is necessarily H2O or that gold necessarily has atomic number 79. | |
| From: Alan Sidelle (Necessity, Essence and Individuation [1989], Ch.4) | |
| A reaction: This is Leibniz's is view, that empirical evidence can never reveal necessities. Given that we know some necessities, you have an argument for rationalism. |