99 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. |
| 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? |
| 14782 | Philosophy is an experimental science, resting on common experience [Peirce] |
| Full Idea: Philosophy, although it uses no microscopes or other apparatus of special observation, is really an experimental science, resting on that experience which is common to us all. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], I) | |
| A reaction: The 'experimental' either implies that thought-experiments are central to the subject, or that philosophers are discussing the findings of scientists, but at a high level of theory and abstraction. Peirce probably means the latter. I can't disagree. |
| 14787 | Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce] |
| Full Idea: It is an anacoluthon to say that a proposition is impossible because it is self-contradictory. It rather is thought so to appear self-contradictory because the ideal induction has shown it to be impossible. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], III) |
| 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. |
| 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) |
| 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. |
| 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. |
| 14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
| Full Idea: Mathematics is purely hypothetical: it produces nothing but conditional propositions. Logic, on the contrary, is categorical in its assertions. True, it is a normative science, and not a mere discovery of what really is. It discovers ends from means. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], II) |
| 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? |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 14788 | Mathematics is close to logic, but is even more abstract [Peirce] |
| Full Idea: The whole of the theory of numbers belongs to logic; or rather, it would do so, were it not, as pure mathematics, pre-logical, that is, even more abstract than logic. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], IV) | |
| A reaction: Peirce seems to flirt with logicism, but rejects in favour of some subtler relationship. I just don't believe that numbers are purely logical entities. |
| 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) |
| 14562 | A process is unified as an expression of a collection of causal powers [Mumford/Anjum] |
| Full Idea: A process has a unity to it that comes from being the expression of a collection of causal powers. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 5.5 1) | |
| A reaction: I would be happier with this if I had a clear notion of what counts as a 'collection' of causal powers. We are back with the Leibnizian anguish over what constitutes a 'unity'. Processes need more attention, I'm thinking. |
| 14541 | Events are essentially changes; property exemplifications are just states of affairs [Mumford/Anjum] |
| Full Idea: Events are to be understood essentially as changes, rather than as property exemplifications. A particular exemplifying a property (as in Kim 1973 and Lewis 1986) would be better understood as a state of affairs. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 2.3) | |
| A reaction: I agree entirely with this. I've never been able to make sense of events as such static relations. It resembles the dubious Russellian view of motion as just being at one place and then at another. |
| 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. |
| 14553 | Weak emergence is just unexpected, and strong emergence is beyond all deduction [Mumford/Anjum] |
| Full Idea: We can say that a phenomenon is 'weakly emergent' when it is unexpected, and 'strongly emergent' when it is not deducible even in principle. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 4.3) | |
| A reaction: [compression of Chalmers 2006:244] I don't find emergence very interesting, since weak emergence surrounds us all day long, and is the glory of the world, and strong emergence is (I believe) nonsense. |
| 14538 | Powers explain properties, causes, modality, events, and perhaps even particulars [Mumford/Anjum] |
| Full Idea: Properties, causes, modality, events, and perhaps even particulars, can all be explained in terms of powers. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 1.2) | |
| A reaction: I love powers, but this may be optimistic. I take the concept of causation to be 'more' primitive than powers; how else could you even say what a power is? I presume something must exist to have the power, which gives you particulars. |
| 14555 | Powers offer no more explanation of nature than laws do [Mumford/Anjum] |
| Full Idea: In respect of explanation the powers view does little better than the laws view. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 4.3c) | |
| A reaction: Quite so. Powers are primitive, so they offer no elucidation of nature, but constitute the building blocks for explanations. Essences are, I think, clusters of powers, and the way in which they cluster is where we find the explanations. |
| 14557 | Powers are not just basic forces, since they combine to make new powers [Mumford/Anjum] |
| Full Idea: Powers are not necessarily reducible to forces. ...That new powers can be found when others combine is a regular part of common sense. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 4.4) | |
| A reaction: [first bit p.102] Hm. I've always thought of powers as basic components of ontology. This idea implies that a herd of buffalo has a single power to flatten a tented village. An extra buffalo creates a completely new power. An awful lot of vague powers. |
| 14583 | Dispositionality is a natural selection function, picking outcomes from the range of possibilities [Mumford/Anjum] |
| Full Idea: Dispositionality can be understood as a sort of selection function - a natural one in this case - and picks out a limited number of outcomes from all the ones that the disposition is for. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 8.9) | |
| A reaction: Functions should strictly have one output. This sounds wrong. The disposition pushes its powers into the environment, but it is the surrounding contextual powers which do the selecting, in concert. No disposition does any selecting |
| 14536 | We say 'power' and 'disposition' are equivalent, but some say dispositions are manifestable [Mumford/Anjum] |
| Full Idea: We use the terms 'power' and 'disposition' as equivalent, but some reserve the term 'disposition' for powers that tend to be manifested. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 1.1) | |
| A reaction: [For the latter they cite Fara 2005] There is some point to the latter distinction, as separating those powers that relate to the actual world from those powers that could never be triggered in actuality. I would say a power produces a disposition. |
| 14584 | The simple conditional analysis of dispositions doesn't allow for possible prevention [Mumford/Anjum] |
| Full Idea: The most obvious inadequacy of the simple conditional account of dispositions is that it fails to accommodate the possibility of prevention. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 8.10) | |
| A reaction: [They cite Ryle 1949 for the original idea] The point is obviously correct, since the simple analysis assumes that the outcome occurred [∀x(Dx → (Sx → Mx)]. If the outcome was blocked (by finks or antidotes) the disposition would remain. |
| 14582 | Might dispositions be reduced to normativity, or to intentionality? [Mumford/Anjum] |
| Full Idea: There have been attempts to reduce dispositionality to normativity (by Lowe 1989) and to intentionality (by Molnar 1998). | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 8.8) | |
| A reaction: I don't really believe in something called 'normativity', and I think it is better to explain intentionality in terms of dispositions, rather than Molnar's way round (though intentionality of mind reveals the nature of powers rather well). |
| 14542 | If statue and clay fall and crush someone, the event is not overdetermined [Mumford/Anjum] |
| Full Idea: If both the statue and the clay fall on someone and crush them to death, we would not say that the death is overdetermined. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 2.7) | |
| A reaction: I don't need many reasons to give up the idea that the statue and the clay are two objects, but this will do nicely as one of them. |
| 14535 | Pandispositionalists say structures are clusters of causal powers [Mumford/Anjum] |
| Full Idea: A pandispositionalist has to defend the view that even a property such as sphericity is in reality a cluster of causal powers. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 1.1) | |
| A reaction: Is sphericity even a 'property'? I think 'feature' might be the best word for it. 'Quality' is quite good, but is too suggestive of qualia and secondary qualities. 'Mode' is not bad. Things have 'modes of existence' and 'powers'? Powers create modes. |
| 14561 | Perdurantism imposes no order on temporal parts, so sequences of events are contingent [Mumford/Anjum] |
| Full Idea: Perdurantism tends to go with the view that it is essentially contingent what follows what, because it is no part of the essence of temporal parts that they be arranged in any particular order. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 5.5 1) | |
| A reaction: Nice. There is nothing illogical, then, in elderly me intervening between childish me and middle-aged me. Essentialists like me must clearly oppose this view. Elderly me must be preceded and caused by middle-aged me. |
| 14579 | Dispositionality is the core modality, with possibility and necessity as its extreme cases [Mumford/Anjum] |
| Full Idea: We think dispositionality is the core modality from which the other two standard modal operators draw their sense as being limiting cases on a spectrum. ...This gives a very this-worldly account of possibility and necessity. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 8.5) | |
| A reaction: I'm strongly in favour of this-worldly accounts of modal truths, so I like this. They take dispositions to hover somewhere between what is barely possible and what is absolutely necessary. But is modality actually part of the physical world? |
| 14580 | Dispositions may suggest modality to us - as what might not have been, and what could have been [Mumford/Anjum] |
| Full Idea: Dispositionality could be what gives us the idea of there being modality in the first place: that what is might not be, and what is not could be. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 8.5) | |
| A reaction: Compare Williamson's suggestion that counterfactual thinking is the source of such things, which is a similar thought. I take it to be exactly correct. |
| 14552 | Relations are naturally necessary when they are generated by the essential mechanisms of the world [Mumford/Anjum] |
| Full Idea: The relationship between co-existing properties or successive events or states is naturally necessary when they are understood by scientists to be related in fact by generative mechanisms, whose structures constitute the essential nature of things. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 7.3) | |
| A reaction: This is the view I espouse. It doesn't follow that those mechanisms have necessary existence. Given those mechanisms, they can only behave in that way, because behaving in some way is precisely what they are. |
| 14578 | Possibility might be non-contradiction, or recombinations of the actual, or truth in possible worlds [Mumford/Anjum] |
| Full Idea: Possibility could be just logical possibility (as involving no formal contradictions), or recombinations of all the existing elements (Armstrong), or truth in other concrete worlds (Lewis). | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 8.4) | |
| A reaction: All wrong, I would say. Well, avoiding contradiction is obviously a sense of 'possible'. Armstrong is wrong. It rules out new 'elements' being possible, and implies impossible combinations of the current ones. As for Lewis... |
| 14786 | Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce] |
| Full Idea: Many say everything is logically possible which involves no contradiction. In this sense two contradictory propositions may be severally possible. In the substantive sense, the contradictory of a possible proposition is impossible (if we were omniscient). | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], III) |
| 14549 | Maybe truths are necessitated by the facts which are their truthmakers [Mumford/Anjum] |
| Full Idea: Some truthmaker theorists are truthmaker necessitarians, believing that the way facts in the world make certain propositions true is by necessitating them. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 3.10) | |
| A reaction: [The cite Armstrong 2007:5-6] I don't believe in this sort of proposition (which turns out, on close inspection, to be just another way of referring to 'the facts'). Propositions are our attempts to express facts, so they can't be necessitated. |
| 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. |
| 14585 | We have more than five senses; balance and proprioception, for example [Mumford/Anjum] |
| Full Idea: The myth of the fivefold division of the sense needs to be overturned. In the experience of causation the senses of balance and proprioception are more important. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 9.1) | |
| A reaction: Thinking is a sensual experience too, especially in its emotional dimension. David Hume always based his empiricism on 'experience', not on the mere five external senses. |
| 14789 | Experience is indeed our only source of knowledge, provided we include inner experience [Peirce] |
| Full Idea: If Mill says that experience is the only source of any kind of knowledge, I grant it at once, provided only that by experience he means personal history, life. But if he wants me to admit that inner experience is nothing, he asks what cannot be granted. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898]) | |
| A reaction: Notice from Idea 14785 that Peirce has ideas in mind, and not just inner experiences like hunger. Empiricism certainly begins to look more plausible if we expand the notion of experience. It must include what we learned from prior experience. |
| 14785 | The world is one of experience, but experiences are always located among our ideas [Peirce] |
| Full Idea: The real world is the world of sensible experience, and it is part of the process of sensible experience to locate its facts in the world of ideas. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], III) | |
| A reaction: This is the neatest demolition of the sharp dividing line between empiricism and rationalism that I have ever encountered. |
| 14576 | Smoking disposes towards cancer; smokers without cancer do not falsify this claim [Mumford/Anjum] |
| Full Idea: Smoking disposes towards cancer, and has its way in many instances. The existence of some smokers without cancer, however, does nothing to falsify this dispositional claim. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 7.5) | |
| A reaction: Indeed, falsification by one instance will only work against absolute and universal claims, and nature contains hardly any of those. |
| 14551 | If causation were necessary, the past would fix the future, and induction would be simple [Mumford/Anjum] |
| Full Idea: If there were necessity to be found in causation, then the problem of induction would seem to be dissolved. The future would indeed proceed like the past if it were for all time necessitated what caused what. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 3.14) | |
| A reaction: My working hypothesis is that the essences of nature necessitate their interactions, and that the problem of induction is solved in that way. We can allow causation to be a process in this action, the transmitter of necessities. Or it could drop out. |
| 14571 | The only full uniformities in nature occur from the essences of fundamental things [Mumford/Anjum] |
| Full Idea: There is indeed natural uniformity in the negative charge of electrons, but the reason for this is that it is an essential property of being an electron that something be negatively charged. It would not be an electron otherwise. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.6) | |
| A reaction: See Idea 14570 for the first part of this thought. This doesn't feel right. The behaviour of gravity according to the inverse square law, or General Relativity, seems to be a uniformity that extends beyond the essences of the ingredients. |
| 14570 | Nature is not completely uniform, and some regular causes sometimes fail to produce their effects [Mumford/Anjum] |
| Full Idea: The uniformity of nature principle, if it means absolute regularity, is simply false; not everyone who smokes gets cancer, not all bread nourishes. Nature is not strictly uniform, even if some things tend to be the case. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.6) | |
| A reaction: Something wrong here. The examples are high-level and complex. When someone survives smoking, or bread fails to nourish, we don't infer a disruption of uniform nature, we infer some other uniformity that has intervened. Are there natural kinds? |
| 14569 | It is tempting to think that only entailment provides a full explanation [Mumford/Anjum] |
| Full Idea: It is tempting to think that entailment is the only adequate kind of explanation because of the idea that if A does not entail B, it must have fallen short of (fully) explaining it. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.5) | |
| A reaction: Yes. One might dream of saying 'this, and only this, necessitates what happened', but it is doubtful whether causes necessitate effects. It is a quirky view to think that every car accident is necessitated. Nuclear explosions block most events. |
| 14568 | A structure won't give a causal explanation unless we know the powers of the structure [Mumford/Anjum] |
| Full Idea: Knowing the structure that something has does not in itself causally explain that thing's behaviour unless we also know what sorts of behaviour a thing of that structure can cause. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.2) | |
| A reaction: I agree with this. If you focus on the lowest possible levels of causal explanation, I can see only powers. Whatever you come up with, it had better be something active. Geometry never started any bonfires. |
| 14556 | Strong emergence seems to imply top-down causation, originating in consciousness [Mumford/Anjum] |
| Full Idea: A problem for strong emergence is that it opens the way for top-down causation if, for instance, our consciousness is causally productive of physical events. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 4.3d) | |
| A reaction: This is what most fans of 'emergent' consciousness would love, presumably because it makes humans really important (nay, godlike!) in the scheme of things. It take it to be based on a hopelessly simplistic view of what is going on around here. |
| 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. |
| 14784 | Ethics is the science of aims [Peirce] |
| Full Idea: Ethics is the science of aims. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], II) | |
| A reaction: Intriguing slogan. He is discussing the aims of logic. I think what he means is that ethics is the science of value. 'Science' may be optimistic, but I would sort of agree with his basic idea. |
| 14566 | Causation by absence is not real causation, but part of our explanatory practices [Mumford/Anjum] |
| Full Idea: Causation by absence should be understood in terms of our explanatory practices rather than as a case of genuine causation. There are indeed no powers at work. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.1) | |
| A reaction: This seems right, even if from a human point of view some evil person has deliberately desisted from some life-saving action. It is just allowing other causation to happen. A tricky forensic issue, but not an ontological one. |
| 14577 | Causation may not be transitive. Does a fire cause itself to be extinguished by the sprinklers? [Mumford/Anjum] |
| Full Idea: Causation is not always transitive. ...The fire started the sprinkler system and the sprinkler system put the fire out; would we want to say that, by transitivity, the fire caused the fire to be extinguished? | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 7.6) | |
| A reaction: There wouldn't have been an extinguishing of the fire if there had been no fire. But this is a very nice example, against the Millian view that causation consists of every event prior to the effect. The fire is, though, a precondition. |
| 14563 | Causation is the passing around of powers [Mumford/Anjum] |
| Full Idea: Causation is the passing around of powers. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 5.5 3) | |
| A reaction: Hm. This doesn't feel right. Compare 'causation is the passing around of tennis balls'. Can you explain what a power is without mentioning causation? |
| 14587 | We take causation to be primitive, as it is hard to see how it could be further reduced [Mumford/Anjum] |
| Full Idea: We accept primitivism about causation, for how could there be something even more basic in the world than causation, which might allow us to bring forth a reductive analysis? | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], Concl) | |
| A reaction: I think I agree with this view, and for the same reason. I can't imagine how one could cite any 'categorical' or 'structural' properties, or anything else, without invoking causal phenomena in their characterisation. |
| 14533 | Causation doesn't have two distinct relata; it is a single unfolding process [Mumford/Anjum] |
| Full Idea: Rather than depicting causation as between two wholly distinct relata, we argue that it should be seen as a single unfolding process that occurs when a number of mutual manifestation partners meet. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], Pref) | |
| A reaction: I am in sympathy with this view, and like the notion of 'process' in metaphysics, but I worry about what a 'process' consists of. Does it have ingredients? It can last a long time, so presumably it can have parts. Mere time slices? |
| 14558 | A collision is a process, which involves simultaneous happenings, but not instantaneous ones [Mumford/Anjum] |
| Full Idea: When billiard balls collide they deform, and we have a process rather than a momentary collision. Causation is a matter of simultaneity, and simultaneous does not entail instantaneous. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 5.3) | |
| A reaction: This is why they reject the idea that causal relata are abutting events meeting at timeless joints. I think they have got this bit right. It's amazing what a muddle philosophers have got into in just describing what happens in front of their eyes. |
| 14559 | Does causation need a third tying ingredient, or just two that meet, or might there be a single process? [Mumford/Anjum] |
| Full Idea: If causation connects two events, do we need some invisible third element to tie them together? Might there be just two elements so close together that they come as a package deal? Or a single event or process in which one thing turns into another? | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 5.3) | |
| A reaction: [compressed] Hence you find yourself drawn to 'process' philosophy, but preferably without the mystical crust laid over it by A.N. Whitehead. If we could individuate processes, we could dump all sorts of other stuff from our ontology. |
| 14565 | Sugar dissolving is a process taking time, not one event and then another [Mumford/Anjum] |
| Full Idea: It would be counterintuitive to say that we have the cause only when the sugar cube first comes into contact with the water, and the effect only once the whole sugar cube has dissolved. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 5.6) | |
| A reaction: The way we end up thinking about causation is largely dictated by the language we use to describe it. The whole point of philosophy is to scrape away the language and see what is really going on. |
| 14567 | Privileging one cause is just an epistemic or pragmatic matter, not an ontological one [Mumford/Anjum] |
| Full Idea: To speak of 'the' causal explanation privileges some causal powers, but it is implausible that this has a special metaphysical status. Instead, that status should be understood in epistemic or pragmatic terms. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.2) | |
| A reaction: I suppose so, but I see a distinction between actions of powers which only explain that one event (striking the match), and actions of powers which explain a whole family of surrounding events (presence of oxygen). |
| 14537 | Coincidence is conjunction without causation; smoking causing cancer is the reverse [Mumford/Anjum] |
| Full Idea: There can be constant conjunction without causation (coincidences) and causation without constant conjunction (smoking causes cancer). | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 1.2) | |
| A reaction: This seems to be presented as a knock-down argument, but I think Humeans can reply to both of them. If you look at the wider pattern of coincidence, or the deeper pattern of coincidence, both of these counterexamples seem to fail. |
| 14573 | Occasionally a cause makes no difference (pre-emption, perhaps) so the counterfactual is false [Mumford/Anjum] |
| Full Idea: Causes can - perhaps they usually do - make a difference but not always. In cases where they don't (such as overdetermination, or late pre-emption), the corresponding counterfactual will be false. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.8) | |
| A reaction: The whole idea that we might be able to give a full account of causation in terms of some sort of logical relationship between possible worlds etc. appals me. We need to label something as 'Scientific Logicism', so that we can attack it. |
| 14572 | Is a cause because of counterfactual dependence, or is the dependence because there is a cause? [Mumford/Anjum] |
| Full Idea: There is an obvious Euthyphro question to be asked: is it true that c caused e because e counterfactually depended on c; or did e counterfactually depend on c precisely because c caused e? | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.8) | |
| A reaction: The idea that causes could depend on a logical relationship of counterfactual dependence strikes me as so bizarre that only a philosopher could think of it. |
| 14574 | Cases of preventing a prevention may give counterfactual dependence without causation [Mumford/Anjum] |
| Full Idea: We could argue that there can be counterfactual dependence between events without causation, namely, cases of double prevention (an event preventing what would have prevented the second). | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.8) | |
| A reaction: Since the whole idea of causation as counterfactual dependence strikes me as utterly counterintuitive, I don't really need these arguments, but it is nice to know that they can be found. Lewis devoted reams of discussion to such problems. |
| 14539 | Nature can be interfered with, so a cause never necessitates its effects [Mumford/Anjum] |
| Full Idea: A natural process can be interfered with, and thus a cause never necessitates its effects. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 1.3) | |
| A reaction: There is the simple point that the world could cease to exist at the instant between cause and effect. But Mumford and Anjum say these two coexist. Finks and antidotes are not conclusive here. Depends what you mean by 'cause' and 'effect'. |
| 14550 | We assert causes without asserting that they necessitate their effects [Mumford/Anjum] |
| Full Idea: We can assert the general claim that smoking causes cancer without endorsing the claim that smoking necessitates cancer. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 3.11) | |
| A reaction: This is the simplest demolition of the idea that effects necessarily follow causes. Necessitarians might wriggle out of it by focusing on the word 'causes' more closely here. Maybe this example isn't a 'strict' usage. |
| 14546 | Necessary causation should survive antecedent strengthening, but no cause can always survive that [Mumford/Anjum] |
| Full Idea: If causation involves any kind of necessity, it should survive the test of antecedent strengthening. ...It is plausible that for any type of causal process, that some new cause can be added which typically results in the effect no longer being caused. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 3.5) | |
| A reaction: [Idea expanded p.57] This is their key argument against the idea that causation involves necessity. In simple terms, show me a cause which necessarily leads to some result, and I will show you how you could prevent that result. Sounds good. |
| 14575 | A 'ceteris paribus' clause implies that a conditional only has dispositional force [Mumford/Anjum] |
| Full Idea: The most persuasive view of a 'ceteris paribus' clause is that the best non-trivially true account that we can give of their meaning is that they indicate that the conditional has dispositional force only. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.8) | |
| A reaction: [They cite Lipton 1999] As a general fan of dispositions (as are Mumford and Lill Anjum), this sounds right. If you then add that virtually every event in nature needs a ceteris paribus clause (see N. Cartwright), the whole thing becomes dispositional. |
| 14548 | There may be necessitation in the world, but causation does not supply it [Mumford/Anjum] |
| Full Idea: Causation is consistent with there being necessitation in the world, but we claim that causation does not itself provide that necessitation. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 3.8) | |
| A reaction: Interesting. One might distinguish between causation being necessary, and causation supplying the necessity. The obvious alternative is that essences supply the necessity. |
| 14554 | Laws are nothing more than descriptions of the behaviour of powers [Mumford/Anjum] |
| Full Idea: What we take to be laws are just descriptions of how the powers behave and affect each other. | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 4.3c) | |
| A reaction: This is precisely my view, which I first gleaned in its boldest from from Mumford 2004. I idea that ontology does not contain any 'laws of nature' I find wonderfully liberating. Weak emergence is just epistemic. |
| 14564 | If laws are equations, cause and effect must be simultaneous (or the law would be falsified)! [Mumford/Anjum] |
| Full Idea: Physical laws are typically understood as equations, ...but then factors must vary simultaneously, since if one factor varied before the others, there would be a time when the two sides of the equation didn't equate (so Newton's 2nd Law would be false). | |
| From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 5.5) | |
| A reaction: Nice. Presumably this thought seems to require action-at-a-distance, which no one could understand. Science oversimplifes the world. See Nancy Cartwright. |