23 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. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 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'. |
| 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. |
| 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. |
| 19355 | The soul doesn't understand many of its own actions, if perceptions are confused and desires buried [Leibniz] |
| Full Idea: The soul does many things without knowing how it does them - when it does them by means of confused perceptions and unconscious inclinations or appetites. | |
| From: Gottfried Leibniz (On Note L to Bayle's 'Rorarius' [1705], [L]) | |
| A reaction: This increasingly strikes me as a wonderful and important insight for its time. He's really paid attention to his own mind, and given up the simplistic view that derives from Descartes. Are birds conscious? Yes or no! Silly. |
| 19350 | We should say that body is mechanism and soul is immaterial, asserting their independence [Leibniz] |
| Full Idea: I think we should keep both sides: we should be more Democritean and make all actions of bodies mechanical and independent of souls, and we should also be more than Platonic and hold that all actions of souls are immaterial and independent of mechanism. | |
| From: Gottfried Leibniz (On Note L to Bayle's 'Rorarius' [1705], [C]) | |
| A reaction: This is about as dualist as it is possible to get. It certainly looks as if many of Leibniz's doctrines are rebellions against Spinoza (in this case his 'dual aspect monism'). I take Leibniz to be utterly but heroically wrong. |
| 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. |
| 19356 | Minds unconsciously count vibration beats in music, and enjoy it when they coincide [Leibniz] |
| Full Idea: In music, the soul counts the beats of the vibrating object which makes the sound, and when these beats regularly coincide at short intervals, it finds them pleasing. Thus it counts without knowing it. | |
| From: Gottfried Leibniz (On Note L to Bayle's 'Rorarius' [1705], [L]) | |
| A reaction: Only a mathematician would see music this way! He is defending his account of the unconscious mind. The proposal that we unconsciously count sounds highly implausible. He needs to recognise the patterns that ground mathematics. |