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. |
| 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. |
| 10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
| Full Idea: Second-order logic raises doubts because of its ontological commitment to the set-theoretic hierarchy, and the allegedly problematic epistemic status of the second-order consequence relation. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §1) | |
| A reaction: The 'epistemic' problem is whether you can know the truths, given that the logic is incomplete, and so they cannot all be proved. Rossberg defends second-order logic against the second problem. A third problem is that it may be mathematics. |
| 10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
| Full Idea: Henkin semantics (for second-order logic) specifies a second domain of predicates and relations for the upper case constants and variables. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This second domain is restricted to predicates and relations which are actually instantiated in the model. Second-order logic is complete with this semantics. Cf. Idea 10756. |
| 10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
| Full Idea: In addition to standard and Henkin semantics for second-order logic, one might also employ substitutional or game-theoretical or topological semantics, or Boolos's plural interpretation, or even a semantics inspired by Lesniewski. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This is helpful in seeing the full picture of what is going on in these logical systems. |
| 10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
| Full Idea: Logical consequence is intuitively taken to be a semantic notion, ...and it is therefore the formal semantics, i.e. the model theory, that captures logical consequence. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: If you come at the issue from normal speech, this seems right, but if you start thinking about the necessity of logical consequence, that formal rules and proof-theory seem to be the foundation. |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| Full Idea: Deductive consequence, written Γ|-S, is loosely read as 'the sentence S can be deduced from the sentences Γ', and semantic consequence Γ|=S says 'all models that make Γ true make S true as well'. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: We might read |= as 'true in the same model as'. What is the relation, though, between the LHS and the RHS? They seem to be mutually related to some model, but not directly to one another. |
| 10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
| Full Idea: A proof-theorist could insist that the logical form of a sentence is exhibited by the logical constants that it contains. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: You have to first get to the formal logical constants, rather than the natural language ones. E.g. what is the truth table for 'but'? There is also the matter of the quantifiers and the domain, and distinguishing real objects and predicates from bogus. |
| 10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
| Full Idea: A standard model is a set of objects called the 'domain', and an interpretation function, assigning objects in the domain to names, subsets to predicate letters, subsets of the Cartesian product of the domain with itself to binary relation symbols etc. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: The model actually specifies which objects have which predicates, and which objects are in which relations. Tarski's account of truth in terms of 'satisfaction' seems to be just a description of those pre-decided facts. |
| 10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
| Full Idea: A mathematical theory is 'categorical' if, and only if, all of its models are isomorphic. Such a theory then essentially has just one model, the standard one. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: So the term 'categorical' is gradually replacing the much-used phrase 'up to isomorphism'. |
| 10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
| Full Idea: All that should be required to get a semantics relative to which a given deductive system is complete is a sufficiently cunning model-theorist. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §5) |
| 10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
| Full Idea: No deductive system is semantically incomplete in and of itself; rather a deductive system is incomplete with respect to a specified formal semantics. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This important point indicates that a system might be complete with one semantics and incomplete with another. E.g. second-order logic can be made complete by employing a 'Henkin semantics'. |
| 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. |
| 16718 | Primary qualities are the cause of all the other sensible qualities [Albertus Magnus] |
| Full Idea: The primary qualities of tangible things are the cause of all the other sensible qualities. | |
| From: Albertus Magnus (On 'Generation and Corruption' [1261], II.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 21.2 | |
| A reaction: This makes the primary qualities sound suspiciously like the essence. |
| 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. |