24 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. |
13407 | All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau] |
Full Idea: I would say that all worthwhile philosophy consists of synthetic theorizing, evaluated against experience. | |
From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §1) | |
A reaction: This is the view that philosophy is just science at a high level of abstraction, and he explicitly rejects 'conceptual analysis' as a fruitful activity. I need to take a stance on this one, but find I am in a state of paralysis. Welcome to philosophy... |
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. |
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
A reaction: Each expansion brings a limitation, but then you can expand again. |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
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'. |
13409 | Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau] |
Full Idea: Our empirically best-supported theories may commit us to certain abstract mathematical entities, but this does not necessarily mean that this is what justifies our commitment. That we are committed doesn't explain why we should be. | |
From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §4) | |
A reaction: A nice point. It is only a slightly gormless scientism which would say that we have to accept whatever scientists demand. Who's in charge here - scientists, mathematicians or philosophers? Don't answer that... |
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. |
13406 | A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau] |
Full Idea: I am a fully paid up-naturalist, but I see no reason to deny that a priori knowledge is possible. My view is that a priori knowledge is unimportant (esp to philosophy). If there is a priori knowledge, it is analytic, true by the structure of our concepts. | |
From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §1) | |
A reaction: It is one thing to say it is the structure of our concepts, and another to infer that it is unimportant. I take the structure of our concepts to be a shadow cast by the structure of the world. E.g. the structure of numbers reveals the world. |
13408 | Intuition and thought-experiments embody substantial information about the world [Papineau] |
Full Idea: Naturalists can allow for thought-experiments in philosophy. Intuitions play an important role, but only because they embody substantial information about the world. | |
From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §3) | |
A reaction: In this sense, intuitions are just memories which are too complex for us to articulate. They are not the intuitions of 'pure reason'. It is hard to connect the intuitive spotting of a proof with memories of the physical world. |
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. |
13410 | Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau] |
Full Idea: Verificationism about concepts implies that thinkers will not share concepts with adherents of theories they reject. Those who reject the phlogiston theory will not possess the same concept as adherents, so cannot say 'there is no phlogiston'. | |
From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §6) | |
A reaction: The point seems to be more general - that it is hard to see how you can have a concept of anything which doesn't actually exist, if the concept is meant to rest on some sort of empirical verification. |
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. |