31 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. |
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'. |
16648 | Accidents must have formal being, if they are principles of real action, and of mental action and thought [Duns Scotus] |
Full Idea: Accidents are principles of acting and principles of cognizing substance, and are the per se objects of the senses. But it is ridiculous to say that something is a principle of acting (either real or intentional) and yet does not have any formal being. | |
From: John Duns Scotus (Ordinatio [1302], IV.12.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 10.5 | |
A reaction: Pasnau cites this as the key scholastic argument for accidental properties having some independent and real existence (as required for Transubstantiation). Rival views say accidents are just 'modes' of a thing's existence. Aquinas compromised. |
15386 | If only the singular exists, science is impossible, as that relies on true generalities [Duns Scotus, by Panaccio] |
Full Idea: Scotus argued that if everything is singular, with no objective common feature, science would be impossible, as it proceeds from general concepts. General is the opposite of singular, so it would be inadequate to understand a singular reality. | |
From: report of John Duns Scotus (Ordinatio [1302]) by Claude Panaccio - Medieval Problem of Universals 'John Duns' | |
A reaction: [compressed] It is a fact that if you generalise about 'tigers', you are glossing over the individuality of each singular tiger. That is OK for 'electron', if they really are identical, but our general predicates may be imposing identity on electrons. |
15387 | If things were singular they would only differ numerically, but horse and tulip differ more than that [Duns Scotus, by Panaccio] |
Full Idea: Scotus argued that there must be some non-singular aspects of things, since there are some 'less than numerical differences' among them. A horse and a tulip differ more from each other than do two horses. | |
From: report of John Duns Scotus (Ordinatio [1302]) by Claude Panaccio - Medieval Problem of Universals 'John Duns' | |
A reaction: This seems to treat being 'singular' as if it were being a singularity. Presumably he is contemplating a thing being nothing but its Scotist haecceity. A neat argument, but I don't buy it. |
16632 | We distinguish one thing from another by contradiction, because this is, and that is not [Duns Scotus] |
Full Idea: What is it [that establishes distinctness of things]? It is, to be sure, that which is universally the reason for distinguishing one thing from another: namely, a contradiction…..If this is, and that is not, then they are not the same entity in being. | |
From: John Duns Scotus (Ordinatio [1302], IV.11.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 08.2 | |
A reaction: This is a remarkably intellectualist view of such things. John Wycliff, apparently, enquired about how animals were going to manage all this sort of thing. It should appeal to the modern logical approach to metaphysics. |
13094 | The haecceity is the featureless thing which gives ultimate individuality to a substance [Duns Scotus, by Cover/O'Leary-Hawthorne] |
Full Idea: For Scotus, the haecceity of an individual was a positive non-quidditative entity which, together with a common nature from which it was formally distinct, played the role of the ultimate differentia, thus individuating the substance. | |
From: report of John Duns Scotus (Ordinatio [1302]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 6.1.3 | |
A reaction: Most thinkers seem to agree (with me) that this is a non-starter, an implausible postulate designed to fill a gap in a metaphysic that hasn't been properly worked out. Leibniz is the hero who faces the problem and works around it. |
16770 | It is absurd that there is no difference between a genuinely unified thing, and a mere aggregate [Duns Scotus] |
Full Idea: It seems absurd …that there should be no difference between a whole that is one thing per se, and a whole that is one thing by aggregation, like a cloud or a heap. | |
From: John Duns Scotus (Ordinatio [1302], III.2.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 25.5 | |
A reaction: Leibniz invented monads because he was driven crazy by the quest for 'true unity' in things. Objective unity may be bogus, but I suspect that imposing plausible unity on things is the only way we can grasp the 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. |
10919 | What prevents a stone from being divided into parts which are still the stone? [Duns Scotus] |
Full Idea: What is it in this stone, by which ...it is absolutely incompatible with the stone for it to be divided into several parts each of which is this stone, the kind of division that is proper to a universal whole as divided into its subjective parts? | |
From: John Duns Scotus (Ordinatio [1302], II d3 p1 q2 n48) | |
A reaction: This is the origin of the concept of haecceity, when Scotus wants to know what exactly individuates each separate entity. He may have been mistaken in thinking that such a question has an answer. |
16768 | Two things are different if something is true of one and not of the other [Duns Scotus] |
Full Idea: If this is, and that is not, then they are not the same entity in being. | |
From: John Duns Scotus (Ordinatio [1302], IV.11.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 25.3 | |
A reaction: This is the contrapositive of the indiscernibility of identicals, expressed in terms of what is true about a thing, rather than what properties pertain to it. |
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. |
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. |
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. |
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. |
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. |
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. |