25 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. |
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| Full Idea: The logic of ZF Set Theory is classical first-order predicate logic with identity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.121) | |
| A reaction: This logic seems to be unable to deal with very large cardinals, precisely those that are implied by set theory, so there is some sort of major problem hovering here. Boolos is fairly neutral. |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| Full Idea: Maybe the axioms of extensionality and the pair set axiom 'force themselves on us' (Gödel's phrase), but I am not convinced about the axioms of infinity, union, power or replacement. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.130) | |
| A reaction: Boolos is perfectly happy with basic set theory, but rather dubious when very large cardinals come into the picture. |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| Full Idea: The naïve view of set theory (that any zero or more things form a set) is natural, but inconsistent: the things that do not belong to themselves are some things that do not form a set. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.127) | |
| A reaction: As clear a summary of Russell's Paradox as you could ever hope for. |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| Full Idea: According to the iterative conception, every set is formed at some stage. There is a relation among stages, 'earlier than', which is transitive. A set is formed at a stage if and only if its members are all formed before that stage. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.126) | |
| A reaction: He gives examples of the early stages, and says the conception is supposed to 'justify' Zermelo set theory. It is also supposed to make the axioms 'natural', rather than just being selected for convenience. And it is consistent. |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| Full Idea: The existence of infinitely many natural numbers seems to me no more troubling than that of infinitely many computer programs or sentences of English. There is, for example, no longest sentence, since any number of 'very's can be inserted. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: If you really resisted an infinity of natural numbers, presumably you would also resist an actual infinity of 'very's. The fact that it is unclear what could ever stop a process doesn't guarantee that the process is actually endless. |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| Full Idea: To the best of my knowledge nothing in mathematics or science requires the existence of very high orders of infinity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.122) | |
| A reaction: He is referring to particular high orders of infinity implied by set theory. Personally I want to wield Ockham's Razor. Is being implied by set theory a sufficient reason to accept such outrageous entities into our ontology? |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| Full Idea: It is no surprise that we should be able to reason mathematically about many of the things we experience, for they are already 'abstract'. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: He has just given a list of exemplary abstract objects (Idea 10489), but I think there is a more interesting idea here - that our experience of actual physical objects is to some extent abstract, as soon as it is conceptualised. |
| 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'. |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| Full Idea: It's a kind of lunacy to think that sound scientific philosophy demands that we think that we see ink-tracks but not words, i.e. word-types. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: This seems to link him with Armstrong's mockery of 'ostrich nominalism'. There seems to be some ambiguity with the word 'see' in this disagreement. When we look at very ancient scratches on stones, why don't we always 'see' if it is words? |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| Full Idea: I am rather a fan of abstract objects, and confident of their existence. Smaller numbers, sets and functions don't offend my sense of reality. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: The great Boolos is rather hard to disagree with, but I disagree. Logicians love abstract objects, indeed they would almost be out of a job without them. It seems to me they smuggle them into our ontology by redefining either 'object' or 'exists'. |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| Full Idea: We twentieth century city dwellers deal with abstract objects all the time, such as bank balances, radio programs, software, newspaper articles, poems, mistakes, triangles. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: I find this claim to be totally question-begging, and typical of a logician. The word 'object' gets horribly stretched in these discussions. We can create concepts which have all the logical properties of objects. Maybe they just 'subsist'? |
| 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. |
| 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. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |