78 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| Full Idea: We are all post-Kantians, ...because Kant set an agenda for philosophy that we are still working through. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Hart says that the main agenda is set by Kant's desire to defend the principle of sufficient reason against Hume's attack on causation. I would take it more generally to be the assessment of metaphysics, and of a priori knowledge. |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| Full Idea: The real monuments of philosophy are its problems. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Presumably he means '....rather than its solutions'. No other subject would be very happy with that sort of claim. Compare Idea 8243. A complaint against analytic philosophy is that it has achieved no consensus at all. |
| 16241 | The metaphysics of nature should focus on physics [Maudlin] |
| Full Idea: Metaphysics, insofar as it is concerned with the natural world, can do no better than to reflect on physics. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: I suppose so. Physics only works at one level of description. Metaphysics often works with concepts which only emerge at a more general level than physics. There are also many metaphysical problems which are of no interest to most physicists. |
| 16257 | Kant survives in seeing metaphysics as analysing our conceptual system, which is a priori [Maudlin] |
| Full Idea: The Kantian strain survives in the notion that metaphysics is not about the world, but about our 'conceptual system', especially as what structures our thought about the world. This keeps it a priori, and so not about the world itself. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3) | |
| A reaction: Strawson would embody this view, I suppose. I take our conceptual system to be largely a reflection of (and even creation of) the world, and not just an arbitrary conventional attempt to grasp the world. Analysing concepts partly analyses the world. |
| 16276 | Wide metaphysical possibility may reduce metaphysics to analysis of fantasies [Maudlin] |
| Full Idea: If metaphysical possibility extends more widely than physical possibility, this may make metaphysics out to be nothing but the analysis of fantastical descriptions produced by philosophers. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 7 Epilogue) | |
| A reaction: Maudlin wants metaphysics to be firmly constrained in its possibilities by what scientific undestanding permits, and he is right. Metaphysics must integrate into science, or wither away on the margins. |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| Full Idea: By now, no education in abstract pursuits is adequate without some familiarity with sets. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: A heart-sinking observation for those who aspire to study metaphysics and modality. The question is, what will count as 'some' familiarity? Are only professional logicians now allowed to be proper philosophers? |
| 16244 | If the universe is profligate, the Razor leads us astray [Maudlin] |
| Full Idea: If the universe has been profligate, then Ockham's Razor will lead us astray. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: That is, there may be a vast number of entities which exist beyond what seems to be 'necessary'. |
| 16255 | The Razor rightly prefers one cause of multiple events to coincidences of causes [Maudlin] |
| Full Idea: The Razor is good when it councils higher credence to explanations which posit a single cause to multiple events that occur in a striking pattern, over explanations involving coincidental multiple causes. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 2.5) | |
| A reaction: This is in the context of Maudlin warning against embracing the Razor too strongly. Presumably inductive success suggests that the world supports this particular use of the Razor. |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| Full Idea: It is an ancient and honourable view that truth is correspondence to fact; Tarski showed us how to do without facts here. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This is a very interesting spin on Tarski, who certainly seems to endorse the correspondence theory, even while apparently inventing a new 'semantic' theory of truth. It is controversial how far Tarski's theory really is a 'correspondence' theory. |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| Full Idea: We explain truth for sentences in terms of satisfaction of formulae. The crux here is that for a sentence, either all sequences satisfy it or none do (with no middle ground). For formulae, some sequences may satisfy it and others not. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This is the hardest part of Tarski's theory of truth to grasp. |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| Full Idea: In any first-order language, there are infinitely many T-sentences. Since definitions should be finite, the agglomeration of all the T-sentences is not a definition of truth. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This may be a warning shot aimed at Davidson's extensive use of Tarski's formal account in his own views on meaning in natural language. |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| Full Idea: A 'conditional proof' licenses inferences to a conditional from a deduction of its consequent from its antecedent. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: That is, a proof can be enshrined in an arrow. |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| Full Idea: When a quantifier is attached to a variable, as in '∃(y)....', then it should be read as 'There exists an individual, call it y, such that....'. One should not read it as 'There exists a y such that...', which would attach predicate to quantifier. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: The point is to make clear that in classical logic the predicates attach to the objects, and not to some formal component like a quantifier. |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| Full Idea: It is set theory, and more specifically the theory of relations, that articulates order. | |
| From: William D. Hart (The Evolution of Logic [2010]) | |
| A reaction: It would seem that we mainly need set theory in order to talk accurately about order, and about infinity. The two come together in the study of the ordinal numbers. |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| Full Idea: The theory of types is a thing of the past. There is now nothing to choose between ZFC and NBG (Neumann-Bernays-Gödel). NF (Quine's) is a more specialized taste, but is a place to look if you want the universe. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| Full Idea: ∈ relates across layers (Plato is a member of his unit set and the set of people), while ⊆ relates within layers (the singleton of Plato is a subset of the set of people). This distinction only became clear in the 19th century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: Getting these two clear may be the most important distinction needed to understand how set theory works. |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| Full Idea: Without the empty set, disjoint sets would have no intersection, and we could not form a∩b without checking that a and b meet. This is an example of the utility of the empty set. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: A novice might plausibly ask why there should be an intersection for every pair of sets, if they have nothing in common except for containing this little puff of nothingness. But then what do novices know? |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| Full Idea: In the second half of the twentieth century there emerged the opinion that foundation is the heart of the way to do set theory. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: It is foundation which is the central axiom of the iterative conception of sets, where each level of sets is built on previous levels, and they are all 'well-founded'. |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| Full Idea: The usual statement of Foundation is that any nonempty set has a member disjoint from it. This phrasing is ordinal-free and closer to the primitives of ZFC. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| Full Idea: When a set is finite, we can prove it has a choice function (∀x x∈A → f(x)∈A), but we need an axiom when A is infinite and the members opaque. From infinite shoes we can pick a left one, but from socks we need the axiom of choice. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The socks example in from Russell 1919:126. |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| Full Idea: It follows from the Axiom of Choice that every set can be well-ordered. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: For 'well-ordered' see Idea 13460. Every set can be ordered with a least member. |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| Full Idea: It has been said (by Burt Dreben) that the only reason set theorists do not generally buy the view that V = L is that it would put them out of business by settling their open questions. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: Hart says V=L breaks with the interative conception of sets at level ω+1, which is countable is the constructible view, but has continuum many in the cumulative (iterative) hierarch. The constructible V=L view is anti-platonist. |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| Full Idea: 'Comprehension' is the assumption that every predicate has an extension. Naïve set theory is the theory whose axioms are extensionality and comprehension, and comprehension is thought to be its naivety. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: This doesn't, of course, mean that there couldn't be a more modest version of comprehension. The notorious difficulty come with the discovery of self-referring predicates which can't possibly have extensions. |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| Full Idea: That the iterative sets suffice for most of ZFC does not show they are necessary, nor is it evident that the set of operations has no fixed points (as 0 is a fixed point for square-of), and no infinitely descending chains (like negative integers). | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: People don't seem to worry that they aren't 'necessary', and further measures are possible to block infinitely descending chains. |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| Full Idea: We say that a binary relation R 'partially orders' a field A just in case R is irreflexive (so that nothing bears R to itself) and transitive. When the set is {a,b}, its subsets {a} and {b} are incomparable in a partial ordering. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| Full Idea: A partial ordering is a 'total ordering' just in case any two members of its field are comparable, that is, either a is R to b, or b is R to a, or a is b. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: See Idea 13457 for 'partial ordering'. The three conditions are known as the 'trichotomy' condition. |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| Full Idea: A total order 'well-orders' its field just in case any nonempty subset B of its field has an R-least member, that is, there is a b in B such that for any a in B different from b, b bears R to a. So less-than well-orders natural numbers, but not integers. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The natural numbers have a starting point, but the integers are infinite in both directions. In plain English, an order is 'well-ordered' if there is a starting point. |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| Full Idea: One of the glories of Von Neumann's theory of numbers is to define α < β to mean that α ∈ β. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| Full Idea: Some have claimed that sets should be rethought in terms of still more basic things, categories. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: [He cites F.William Lawvere 1966] It appears to the the context of foundations for mathematics that he has in mind. |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| Full Idea: All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain? |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| Full Idea: The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| Full Idea: Modern model theory investigates which set theoretic structures are models for which collections of sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: So first you must choose your set theory (see Idea 13497). Then you presumably look at how to formalise sentences, and then look at the really tricky ones, many of which will involve various degrees of infinity. |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| Full Idea: There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| Full Idea: Models are ways the world might be from a first-order point of view. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| Full Idea: Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea. |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'. |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| Full Idea: We can show (using the axiom of choice) that the less-than relation, <, well-orders the ordinals, ...and that it partially orders the ordinals, ...and that it totally orders the ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| Full Idea: The axiom of infinity with separation yields a least limit ordinal, which is called ω. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| Full Idea: Since we can map the transfinite ordinals one-one into the infinite cardinals, there are at least as many infinite cardinals as transfinite ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| Full Idea: It is easier to generalize von Neumann's finite ordinals into the transfinite. All Zermelo's nonzero finite ordinals are singletons, but if ω were a singleton it is hard to see how if could fail to be the successor of its member and so not a limit. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| Full Idea: The real numbers were not isolated from geometry until the arithmetization of analysis during the nineteenth century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| Full Idea: Mathematical induction is a way to establish truths about the infinity of natural numbers by a finite proof. | |
| From: William D. Hart (The Evolution of Logic [2010], 5) | |
| A reaction: If there are truths about infinities, it is very tempting to infer that the infinities must therefore 'exist'. A nice, and large, question in philosophy is whether there can be truths without corresponding implications of existence. |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| Full Idea: There is a familiar comparison between Euclid (unique parallel) and 'spherical' geometry (no parallel) and 'saddle' geometry (several parallels). | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 16243 | The Humean view is wrong; laws and direction of time are primitive, and atoms are decided by physics [Maudlin] |
| Full Idea: The Humean project is unjustified, in that both the laws of nature and the direction of time require no analysis, and is misconceived, in that the atoms it employs do not correspond to present physical ontology. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: I certainly find it strange, or excessively empirical, that Lewis thinks our account of reality should rest on 'qualities'. Maudlin's whole books is an implicit attack on David Lewis. |
| 16271 | Lewis says it supervenes on the Mosaic, but actually thinks the Mosaic is all there is [Maudlin] |
| Full Idea: At base it is not merely, as Lewis says, that everything else supervenes on the Mosaic; but rather that anything that exists at all is just a feature or element or generic property of the Mosaic. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 6) | |
| A reaction: [Maudlin has just quoted Idea 16210] Correct about Lewis, but Lewis just has a normal view of supervenience. Only 'emergentists' would think the supervenience allowed anything more, and they are deeply misguided, and in need of help. |
| 16273 | If the Humean Mosaic is ontological bedrock, there can be no explanation of its structure [Maudlin] |
| Full Idea: The Humean Mosaic appears to admit of no further explanation. Since it is the ontological bedrock, …none of the further things can account for the structure of the Mosaic itself. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 6) | |
| A reaction: A very nice point, reminiscent of Popper's objection to essentialism, that he thought it blocked further enquiry, when actually further enquiry was possible. Lewis and Hume seem too mesmerised by epistemology. They need best explanation. |
| 16275 | The 'spinning disc' is just impossible, because there cannot be 'homogeneous matter' [Maudlin] |
| Full Idea: The 'spinning disc' is not metaphysically possible. We have every reason to believe that there is no such thing as 'perfectly homogeneous matter'. The atomic theory of matter is as well established as any scientific theory is likely to be. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 7 Epilogue) | |
| A reaction: This is a key case for Maudlin, and his contempt for metaphysics which is not scientifically informed. I agree with him. Extreme thought experiments are worth considering, but impossible ones are pointless. |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| Full Idea: Jespersen calls a noun a mass word when it has no plural, does not take numerical adjectives, and does not take 'fewer'. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: Jespersen was a great linguistics expert. |
| 16258 | To get an ontology from ontological commitment, just add that some theory is actually true [Maudlin] |
| Full Idea: The doctrine of ontological commitment becomes a central element in a theory of ontology if one merely adds that a particular theory is, in fact, true | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.1) | |
| A reaction: Helpful. I don't think the truth of a theory entails the actual existence of every component mentioned in the theory, as some of them may be generalisations, abstractions, vague, or even convenient linking fictions. |
| 16259 | Naïve translation from natural to formal language can hide or multiply the ontology [Maudlin] |
| Full Idea: Naïve translation from natural language into formal language can obscure necessary ontology as easily as it can create superfluous ontological commitment. …The lion's share of metaphysical work is done when settling on the right translation. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.1) | |
| A reaction: I suspect this is more than a mere problem of 'naivety', but may be endemic to the whole enterprise. If you hammer a square peg into a round hole, you expect to lose something. Language is subtle, logic is crude. |
| 16253 | A property is fundamental if two objects can differ in only that respect [Maudlin] |
| Full Idea: Fragility is not a fundamental physical property, in that two pieces of glass cannot be physically identical save for their fragility. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 2.5) | |
| A reaction: Nice. The best idea I have found in Maudlin, so far! This gives a very nice test for picking out the fundamental physical and intrinsic properties. |
| 16263 | Fundamental physics seems to suggest there are no such things as properties [Maudlin] |
| Full Idea: If one believes that fundamental physics is the place to look for the truths about universals (or tropes or natural sets), then one may find that physics is telling us there are no such things. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.2) | |
| A reaction: His prior discussion of quantum chromodynamics suggests, to me, merely that properties can be described in terms of vectors etc., and remains neutral on the ontology - but then I am blinded by science. |
| 16260 | Existence of universals may just be decided by acceptance, or not, of second-order logic [Maudlin] |
| Full Idea: On one line of thought, the question of whether universals exist seems to reduce to the question of the utility, or necessity, of using second-order rather than first-order logic. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.1) | |
| A reaction: Second-order logic quantifies over properties, where first-order logic just quantifies over objects. This is an extreme example of doing your metaphysics largely through logic. Not my approach. |
| 16277 | Logically impossible is metaphysically impossible, but logically possible is not metaphysically possible [Maudlin] |
| Full Idea: While logical impossibility is a species of metaphysical impossibility, logical possibility is not a species of metaphysical possibility. The logically impeccable description 'Cicero was not Tully' describes a metaphysically impossible situation. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 7 Epilogue) | |
| A reaction: The context of this is Maudlin attack on daft notions of metaphysical possibility that are at variance with the limits set by science, but he is still conceding that there are types of metaphysical modality. |
| 16249 | A counterfactual antecedent commands the redescription of a selected moment [Maudlin] |
| Full Idea: The purpose of the antecedent of a counterfactual is to provide instructions on how to pick a Cauchy surface (pick a moment in time) and how to generate an altered description of that moment. It is more of a command than an indicative sentence. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.5) | |
| A reaction: Quite plausible, but the antecedent might contain no description. 'If things had gone differently, we wouldn't be in this mess'. The antecedent might be timeless. 'If pigs had wings, they still wouldn't fly'. |
| 16285 | A possible world can be seen as a complete and consistent novel [Jeffrey] |
| Full Idea: A novel describes a possible world in as much detail as is possible without exceeding the resources of the agent's language. But if talk of possible worlds seems dangerously metaphysical, focus on the novels themselves, when complete and consistent. | |
| From: Richard Jeffrey (The Logic of Decision [1965], 12.8), quoted by David Lewis - On the Plurality of Worlds | |
| A reaction: Lewis seems to cite this remark from Jeffrey as the source of the idea that ersatz linguistic worlds are like novels. Why won't a novel with one tiny inconsistency count as a possible world? People seem to live in it. |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| Full Idea: The conception of Frege is that self-evidence is an intrinsic property of the basic truths, rules, and thoughts expressed by definitions. | |
| From: William D. Hart (The Evolution of Logic [2010], p.350) | |
| A reaction: The problem is always that what appears to be self-evident may turn out to be wrong. Presumably the effort of arriving at a definition ought to clarify and support the self-evident ingredient. |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| Full Idea: In the case of the parallels postulate, Euclid's fifth axiom (the whole is greater than the part), and comprehension, saying was believing for a while, but what was said was false. This should make a shrewd philosopher sceptical about a priori knowledge. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Euclid's fifth is challenged by infinite numbers, and comprehension is challenged by Russell's paradox. I can't see a defender of the a priori being greatly worried about these cases. No one ever said we would be right - in doing arithmetic, for example. |
| 16254 | Induction leaps into the unknown, but usually lands safely [Maudlin] |
| Full Idea: Induction is always a leap beyond the known, but we are constantly assured by later experience that we have landed safely. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 2.5) | |
| A reaction: Not philosophically very interesting, but a nice remark for capturing the lived aspect of inductive thought, as practised by the humblest of animals. |
| 19155 | Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey, by Davidson] |
| Full Idea: Jeffrey produced a version of Bayesianism that made no direct use of gambling (as Ramsey had), but treats the objects of preference ...as propositions. | |
| From: report of Richard Jeffrey (The Logic of Decision [1965]) by Donald Davidson - Truth and Predication 3 | |
| A reaction: I'm guessing that Jeffreys launched modern Bayesian theory with this idea. It suggest that one can consider degrees of truth, rather than mere winning or losing. |
| 16245 | Laws should help explain the things they govern, or that manifest them [Maudlin] |
| Full Idea: A law ought to be capable of playing some role in explaining the phenomena that are governed by or are manifestations of it. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.2) | |
| A reaction: I find this attitude bewildering. 'Why do electrons have spin?' 'Because they all do!' The word 'governed' is the clue. What on earth is a law, if it can 'govern' nature? What is its ontological status? Natures of things are basic, not 'laws'. |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| Full Idea: A Fregean concept is a function that assigns to each object a truth value. So instead of the colour green, the concept GREEN assigns truth to each green thing, but falsity to anything else. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This would seem to immediately hit the renate/cordate problem, if there was a world in which all and only the green things happened to be square. How could Frege then distinguish the green from the square? Compare Idea 8245. |
| 16248 | Evaluating counterfactuals involves context and interests [Maudlin] |
| Full Idea: The evaluation of counterfactual claims is widely recognised as being influenced by context and interest. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.5) | |
| A reaction: Such evaluation certainly seems to involve imagination, and so the pragmatics can creep in there. I don't quite see why it should be deeply contextual. |
| 16250 | We don't pick a similar world from many - we construct one possibility from the description [Maudlin] |
| Full Idea: It seems unlikely the psychological process could mirror Lewis's semantics: people don't imagine a multiplicity of worlds and the pick out the most similar. Rather we construct representations of possible worlds from counterfactual descriptions. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.5) | |
| A reaction: I approve of fitting such theories into a psychology, but this may be unfair to Lewis, who aims for a logical model, not an account of how we actually approach the problem. |
| 16268 | The counterfactual is ruined if some other cause steps in when the antecedent fails [Maudlin] |
| Full Idea: A counterexample to the counterfactual approach is that perhaps the effect would have occurred despite the absence of the cause since another cause would have stepped in to bring it about. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5) | |
| A reaction: …Hence you cannot say 'if C had not occurred, E would definitely not have occurred'. You have to add 'ceteris paribus', which ruins the neatness of the theory. |
| 16267 | If we know the cause of an event, we seem to assent to the counterfactual [Maudlin] |
| Full Idea: When we think we know the cause of an event, we typically assent to the corresponding Hume counterfactual. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5) | |
| A reaction: This is the correct grounding of the counterfactual approach - not that we think counterfactuals are causation, but that knowledge of causation will map neatly onto a network of counterfactuals, thus providing a logic for the whole process. |
| 16269 | If the effect hadn't occurred the cause wouldn't have happened, so counterfactuals are two-way [Maudlin] |
| Full Idea: If Kennedy had still been President in Dec 1963, he would not have been assassinated in Nov 1963, so the counterfactual goes both ways (where the cause seems to only go one way). | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5) | |
| A reaction: Maudlin says a lot of fine-tuning has sort of addressed these problems, but that counterfactual causation is basically wrong-headed anyway, and I incline to agree, though one must understand what the theory is (and is not) trying to do. |
| 16247 | Laws are primitive, so two indiscernible worlds could have the same laws [Maudlin] |
| Full Idea: Laws are ontologically primitives at least in that two worlds could differ in their laws but not in any observable respect. ….[21] I take content of the laws to be expressed by equations. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.4) | |
| A reaction: At least that spells out his view fairly dramatically, but I am baffled as to what he thinks a law could be. He is arguing against the Lewis regularity-axioms view, and the Armstrong universal-relations view. He ignores the essentialist view. |
| 16272 | Fundamental laws say how nature will, or might, evolve from some initial state [Maudlin] |
| Full Idea: The fundamental laws of nature appear to be laws of temporal evolution: they specify how the state of the universe will, or might, evolve from a given intial state. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 6) | |
| A reaction: Maudlin takes both laws of nature and the passage of time to be primitive facts, and this is how they are connected. I think (this week) that I take time and causation to be primitive, but not laws. |
| 16242 | Laws of nature are ontological bedrock, and beyond analysis [Maudlin] |
| Full Idea: The laws of nature stand in no need of 'philosophical analysis'; they ought to be posited as ontological bedrock. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: This is Maudlin's most basic principle, and I don't agree with it. The notion that laws are more deeply embedded in reality than the physical stuff they control is a sort of 'law-mysticism' that needs to be challenged. |
| 16251 | 'Humans with prime house numbers are mortal' is not a law, because not a natural kind [Maudlin] |
| Full Idea: 'All humans who live in houses with prime house numbers are mortal' is not a law because the class referred to is not a natural kind. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.6) | |
| A reaction: Maudlin wants laws to be primitive, but he now needs a primitive notion of a natural kind to make it work. If kinds generate laws, you can ditch the laws, and build your theory on the kinds. He also says no death is explained by 'all humans are mortal'. |
| 16270 | If laws are just regularities, then there have to be laws [Maudlin] |
| Full Idea: On the Mill-Ramsey-Lewis account of laws, I take it that if the world is extensive and variegated enough, then there must be laws. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5.2) | |
| A reaction: A nice point. If there is any sort of pattern discernible in the surface waves on the sea, then there must be a law to cover it, not matter how vague or complex. |
| 16264 | I believe the passing of time is a fundamental fact about the world [Maudlin] |
| Full Idea: I believe that it is a fundamental, irreducible fact about the spatio-temporal structure of the world that time passes. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 4) | |
| A reaction: Worth quoting because it comes from a philosopher fully informed about, and heavily committed to, the physicist's approach to reality. One fears that physicists steeped in Einstein are all B-series Eternalists. Get a life! |
| 16265 | If time passes, presumably it passes at one second per second [Maudlin] |
| Full Idea: It is necessary and, I suppose, a priori that if time passes at all it passes at one second per second. …Similarly, the fair exchange rate for a dollar must be a dollar. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 4.1) | |
| A reaction: [He is discussing Huw Price on time] This is a reply to the claim that if time passes it has to pass at some rate, and 'one second per second' is ridiculous. Not very convincing, even with the dollar analogy. |
| 16266 | There is one ordered B series, but an infinitude of A series, depending on when the present is [Maudlin] |
| Full Idea: Given events ordered in a B series, one defines an infinitude of different A series that correspond to taking different events as 'now' or 'present'. McTaggart talks of 'the A series' when there is an infinitude of such. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 4.3 n11) | |
| A reaction: This strikes me as a rather mathematical (and distorted) claim about the A series view. The A-series is one dynamic happening. Not an infinity of static times lines, each focused on a different 'now'. |