91 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. |
| 4194 | Metaphysics is concerned with the fundamental structure of reality as a whole [Lowe] |
| Full Idea: Metaphysics is concerned with the fundamental structure of reality as a whole. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.2) | |
| A reaction: I think it is vital to hang on to this big definition, focusing on ontology, and not retreat (like Kant) to the epistemological question of how humans happen to see reality, even if we are stuck with being humans. |
| 4214 | Maybe such concepts as causation, identity and existence are primitive and irreducible [Lowe] |
| Full Idea: It may well be that after all our attempts at analysis, we have to accept the notions of causality, identity and existence as being primitive and irreducible. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.191) | |
| A reaction: They may be irreducible, but it seems possible that the relationships between them might be revealed (as between Platonic Forms). To exist is to have identity and causal powers? |
| 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? |
| 4222 | If all that exists is what is being measured, what about the people and instruments doing the measuring? [Lowe] |
| Full Idea: If we think, in a positivistic spirit, that only measurements and observations exist, this is strikingly naïve. The scientists and their instruments can't be composed merely of measurements. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.234) | |
| A reaction: A strong rebuff to crude positivism and 'operationalism'. Such mistakes are the usual confusion of epistemology and ontology. |
| 4217 | It is more extravagant, in general, to revise one's logic than to augment one's ontology [Lowe] |
| Full Idea: It is more extravagant, in general, to revise one's logic than to augment one's ontology. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.219) | |
| A reaction: Meaning there are stronger principles of thought which can trump Ockham's Razor. A few more entities won't hurt. Sound right. |
| 8188 | Davidson takes truth to attach to individual sentences [Davidson, by Dummett] |
| Full Idea: Davidson, by contrast to Frege, has taken truth as attaching to linguistic items, that is, to actual or hypothetical token sentences. | |
| From: report of Donald Davidson (True to the Facts [1969]) by Michael Dummett - Truth and the Past 1 | |
| A reaction: My personal notion of truth is potentially applicable to animals, so this doesn't appeal to me. I am happy to think of animals as believing simple propositions that never get as far as language, and being right or wrong about them. |
| 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) |
| 4229 | An infinite series of tasks can't be completed because it has no last member [Lowe] |
| Full Idea: It appears to be impossible to complete an infinite series of tasks, since such a series has, by definition, no last member. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.290) | |
| A reaction: This pinpoints the problem. So are there infinite tasks in a paradox of subdivision like the Achilles? |
| 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'. |
| 4240 | It might be argued that mathematics does not, or should not, aim at truth [Lowe] |
| Full Idea: It might be argued that mathematics does not, or should not, aim at truth. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.375) | |
| A reaction: Intriguing. Sounds wrong to me. At least maths seems to need the idea of the 'correct' answer. If, however, maths is a huge pattern, there is no correctness, just the pattern. We can be wrong, but maths can't be wrong. Ah, I see…! |
| 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) |
| 4241 | If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe] |
| Full Idea: The Peano postulates imply an infinity of numbers, but there are probably not infinitely many concrete objects in existence, so natural numbers must be abstract objects. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.375) | |
| A reaction: Presumably they are abstract objects even if they aren't universals. 'Abstract' is an essential term in our ontological vocabulary to cover such cases. Perhaps possible concrete objects are infinite. |
| 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) |
| 4239 | Nominalists deny abstract objects, because we can have no reason to believe in their existence [Lowe] |
| Full Idea: Nominalists tend to deny the existence of abstract objects since, given their purported nature (non-causal), we can have no reason to believe in their existence. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.372) | |
| A reaction: A good point. Aristotle worried about the causal inadequacy of the Forms. My mind can conceive of a 'thing' with no causal powers, just sitting there. |
| 4202 | Change can be of composition (the component parts), or quality (properties), or substance [Lowe] |
| Full Idea: There seem to be three kinds of change: compositional change (of component parts), qualitative change (of properties), or substantial change (when underlying essence begins or ceases). | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.59) | |
| A reaction: Notice this gives 'components' a more prominent ontological status than usual. Is this computer a component of my study? |
| 4201 | Four theories of qualitative change are 'a is F now', or 'a is F-at-t', or 'a-at-t is F', or 'a is-at-t F' [Lowe, by PG] |
| Full Idea: Qualitative change is seen as either (i) 'Presentism' - 'a is F now', or (ii) 'relational properties' - 'a is F-at-t', or (iii) 'temporal parts' - 'a-at-t is F', or (iv) 'adverbial' - 'a is-a-t F'. | |
| From: report of E.J. Lowe (A Survey of Metaphysics [2002], p.44) by PG - Db (ideas) | |
| A reaction: The traditional view would let a stay the same over time, and change its property (ii). Lewis favours (iii). My suspicion is that thinking collapses if you abandon the tradtional view. |
| 4219 | Numerically distinct events of the same kind (like two battles) can coincide in space and time [Lowe] |
| Full Idea: Numerically distinct events of the same kind (like two battles) can plausible coincide in space and time. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.225) | |
| A reaction: This is certainly discouraging for anyone who wanted to make events ontologically basic. Physicalist need to be able to individuate events in a reductive way. |
| 4221 | Maybe modern physics requires an event-ontology, rather than a thing-ontology [Lowe] |
| Full Idea: It is sometimes said that modern physics requires us to espouse an event-ontology, rather than a thing-ontology. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.233) | |
| A reaction: It has to be a mistake to build our philosophical ontology on current physics, because even the physicists say they don't understand the latter very well. |
| 4220 | Maybe an event is the exemplification of a property at a time [Lowe] |
| Full Idea: Maybe an event is the exemplification of a property at a time. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.229) | |
| A reaction: What exactly would 'exemplify' mean here? This probably turns out to be circular when you attempt to explain what a property is. |
| 4225 | Events are changes in the properties of or relations between things [Lowe] |
| Full Idea: My own preference is for a conception of events which reduces them to changes in the properties of or relations between things. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.245) | |
| A reaction: Changes of property and changes of relations are two very different things. Is a 'near miss' an event? If so, is any movement an event? If movement is relative, then so are events. |
| 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. |
| 4196 | The main categories of existence are either universal and particular, or abstract and concrete [Lowe] |
| Full Idea: Some metaphysicians think the fundamental categories of existence are universals and particulars, while other prefer the division between abstract and concrete. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.15) | |
| A reaction: Interestingly, in trying to choose between these, it is tempting to think about the capacities of the brain. Which is the cart and which is the horse? |
| 4234 | Trope theory says blueness is a real feature of objects, but not the same as an identical blue found elsewhere [Lowe] |
| Full Idea: The trope theorist holds that the blueness of a blue chair really exists as much as the chair, but is not identified with the blueness of anything else, even if it resembles it exactly. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.361) | |
| A reaction: You are left with explaining how 'resemblance' works if you cannot spot some 'thing' in common. It is an inviting idea, though, because it avoids the ontological baggage of universals. |
| 4235 | Maybe a cushion is just a bundle of tropes, such as roundness, blueness and softness [Lowe] |
| Full Idea: The trope theorist says that a cushion is just a 'bundle' of tropes, such as roundness, blueness and softness. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.362) | |
| A reaction: Certainly if you dispense with the idea of substance (which is clearly bad science even if it is good metaphysics), something like this is what remains of a cushion, though it sounds more epistemological than ontological. Only philosophers care about this |
| 4236 | Tropes seem to be abstract entities, because they can't exist alone, but must come in bundles [Lowe] |
| Full Idea: Tropes seem to be abstract entities because, unlike concrete entities, they are ontologically dependent; ..there are no 'free' tropes, and they must always be bundled with other appropriate tropes to exist. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.367) | |
| A reaction: Only a Platonist would think that a universal property could 'exist alone'. I presume Aristotle thought universals were real, though bound up with substances. |
| 4197 | The category of universals can be sub-divided into properties and relations [Lowe] |
| Full Idea: One might want to divide the category of 'universals' into two sub-categories of properties and relations. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.15) | |
| A reaction: This means a Platonic form like 'horse' ends up as a cluster of properties and relations. Is a substance not also a universal? |
| 4232 | Nominalists believe that only particulars exist [Lowe] |
| Full Idea: Nominalists believe that only particulars exist. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.352) | |
| A reaction: A neat definition. Hence they deny universals. I suspect that nominalism is incoherent. Rational thought seems easy to create with universals, impossible with just particulars. Robotics is nominalist, which is why it will fail. |
| 4205 | 'Is non-self-exemplifying' is a predicate which cannot denote a property (as it would be a contradiction) [Lowe] |
| Full Idea: Not every meaningful predicate expresses an existing property; thus 'is non-self-exemplifying' cannot refer to a property, because the property would contradict the predicate. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.100) | |
| A reaction: Needs thought. The example is based on Russell's so-called Barber's Paradox. If it can't be a property, can it be a predicate? |
| 4233 | If 'blueness' is a set of particulars, there is danger of circularity, or using universals, in identifying the set [Lowe] |
| Full Idea: If sets are particulars, a nominalist may say that 'blueness' is a set of particulars, but which set? If the particulars 'are blue' this threatens circularity - though resemblance is usually appealed to to avoid this. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.355) | |
| A reaction: This supports my suspicion that nominalism is superficially attractive and 'scientific', but when you dig deep into it the theory won't get off the ground without universals. |
| 4206 | Conventionalists see the world as an amorphous lump without identities, but are we part of the lump? [Lowe] |
| Full Idea: For the conventionalist the world is doomed to merge into an amorphous lump with no real individuality or differentiation, ..but we can hardly make our own identity in the world in the way we are supposed to conventionally create identity for objects. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.113) | |
| A reaction: Very nice argument! We need to 'cut nature at the joints' (Plato), and one joint is screamingly obvious - that between observer and world. You could try denying this, but it would be a bizarre view. |
| 4204 | Statues can't survive much change to their shape, unlike lumps of bronze, which must retain material [Lowe] |
| Full Idea: A statue is a kind of object which cannot survive much change to its shape, unlike a lump of bronze, which cannot survive any change to its material composition. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.70) | |
| A reaction: Also the statue could survive being hollowed out, changing its material composition. Hence a statue is not just a lump of bronze, but we knew that. |
| 4200 | If old parts are stored and then appropriated, they are no longer part of the original (which is the renovated ship). [Lowe] |
| Full Idea: The parts of a ship in a warehouse belong to no ship at all, ..and once they are appropriated by another ship they cease to be parts of the original, ..so it seems that the renovated ship (not the reconstruction) is identified with the original. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.31) | |
| A reaction: The parts in the warehouse could belong to the original (they might even labelled), but assigning them to a new ship does indeed look like a crucial break in the continuity. |
| 4198 | If 5% replacement preserves a ship, we can replace 4% and 4% again, and still retain the ship [Lowe] |
| Full Idea: If we say that up to 5% of a ship's parts can be replaced without the ship ceasing to exist, we could replace 4% and then 4% again, and it would retain its identity, if identity is transitive. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.26) | |
| A reaction: One suspected that all attempts at precision with the ship of Theseus were doomed, but this nicely demonstrates it. |
| 4199 | A renovation or a reconstruction of an original ship would be accepted, as long as the other one didn't exist [Lowe] |
| Full Idea: If a ship is renovated without reconstruction of original parts, we happily identify the renovation with the original; if there was a reconstruction without the renovated version, we would identify the reconstruction with the original. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.27) | |
| A reaction: This really shakes our belief in identity as a natural rather than mental phenomenon. The existence of clones undermines our normal idea of personal identity. |
| 4203 | Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties) [Lowe] |
| Full Idea: The Identity of Indiscernibles (no two objects can possess exactly the same properties) is not the same as Leibniz's Law (what is true of a thing is true of what is identical with that thing). | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.62) | |
| A reaction: Two things can't be the same because we can't discern the difference, which may be our inadequacy. But if they actually have identical properties, it is hard to see how they could be different. A universe with just two perfect spheres is couterexample. |
| 4195 | It is impossible to reach a valid false conclusion from true premises, so reason itself depends on possibility [Lowe] |
| Full Idea: Reasoning itself depends upon a grasp of possibilities, because a valid argument is one in which it is not possible for the conclusion to be false if the premises are true. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.11) | |
| A reaction: A very valuable corrective to my pessimistic view of philosophers' attempts to understand metaphysical necessity. But if we can only grasp natural necessity, then all reason is naturalistic. |
| 4207 | We might eliminate 'possible' and 'necessary' in favour of quantification over possible worlds [Lowe] |
| Full Idea: It may be possible to eliminate the modal operators (in English, 'is possible' and 'is necessary') in favour of quantifier expressions with variables ranging over possible worlds. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.121) | |
| A reaction: Hence 'necessary' becomes 'exists/is true in all possible worlds'. Deep problems, but at least we must show that referring to 'possible' worlds isn't a circular explanation of 'is possible'. |
| 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. |
| 4223 | Unfalsifiability may be a failure in an empirical theory, but it is a virtue in metaphysics [Lowe] |
| Full Idea: Although unfalsifiability is probably a defect in scientific hypothesis, because it is deprived of empirical content, it seems rather to be a virtue in a metaphysical hypothesis. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.241) | |
| A reaction: Presumably nothing could ever be found to count against a necessary truth. A nice point. 'Find me an instance where 2+2 is not 4'. |
| 4193 | The behaviour of persons and social groups seems to need rational rather than causal explanation [Lowe] |
| Full Idea: There are some entities which exist in time and space (such as persons or social groups) of which the behaviour seems to be subject to rational rather than merely causal explanation. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.2) | |
| A reaction: This begs of the question of whether 'rational' can be reduced to causal. We can't manage causal explanations of the very complex, so we use broad-brush second-best explanations? |
| 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. |
| 4238 | The centre of mass of the solar system is a non-causal abstract object, despite having a location [Lowe] |
| Full Idea: The centre of mass of the solar system seems to lack causal powers, and so is an abstract object, even though it has a location and movement. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.368) | |
| A reaction: Nice example, with rich ramifications. Abstraction is deeply tied into our understanding of the physical world, and our concept of identity. |
| 4237 | Concrete and abstract objects are distinct because the former have causal powers and relations [Lowe] |
| Full Idea: Concrete objects possess causal powers and relations, but abstract objects are incapable of having causal powers or relations. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.368) | |
| A reaction: Is this an observation or a definition? One might claim that an abstraction (such as a political ideal) can acquire causal power through a conscious mnd. |
| 4210 | If the concept of a cause says it precedes its effect, that rules out backward causation by definition [Lowe] |
| Full Idea: You can't include in your concept of causation a clause stipulating that the cause occurred earlier than the effect, because that would rule out backward causation by definition. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.176) | |
| A reaction: It may, though, be the case that backward causes can't occur, and time is essential to causes. The problem is our inability to know this for sure. |
| 4215 | It seems proper to say that only substances (rather than events) have causal powers [Lowe] |
| Full Idea: It seems proper to say that events of themselves possess no causal powers; only persisting objects (individual substances) possess causal powers. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.211) | |
| A reaction: This requires events to be reduced to substances, which invites Aristotle's question of where the movement comes from. In physcis, 'energy' is the key concept. |
| 4209 | The theories of fact causation and event causation are both worth serious consideration [Lowe] |
| Full Idea: The theories of fact causation and event causation are both worth serious consideration. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.173) | |
| A reaction: This is slippery ground because both 'facts' and 'events' have uncertain ontological status, and seem partly conventional rather than natural. Events might be natural surges or transformations of energy? |
| 4211 | Causal overdetermination is either actual overdetermination, or pre-emption, or the fail-safe case [Lowe] |
| Full Idea: In causation there is 'overdetermination' (c and d occurred, and were both sufficient for e), 'pre-emption' (c and d occurred, and d would have stepped in if c hadn't), or 'fail-safe' (if c hadn't occurred, d would have occurred and done it). | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.179) | |
| A reaction: Two safety nets together, two safety nets spaced apart, or a second net which pops in if the first breaks. Nice distinctions. |
| 4213 | Causation may be instances of laws (seen either as constant conjunctions, or as necessities) [Lowe] |
| Full Idea: Causation relations between events may an instance of a causal law, with laws either interpreted as constant conjunctions (Hume), or as necessitation among universals (Armstrong). | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.190) | |
| A reaction: Hume's version is a thin idea of a law, but we can dream about the metaphysical status of laws, even if we don't know much about them. Lowe says a cause without a law is perfectly intelligible. |
| 4212 | Hume showed that causation could at most be natural necessity, never metaphysical necessity [Lowe] |
| Full Idea: One thing Hume has taught us is that the necessity which causation involves is at most 'natural' or 'physical' necessity, not metaphysical necessity. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.182) | |
| A reaction: Given Hume's epistemological scepticism, I don't think he would claim to have shown such a thing. See G.Strawson's book. Metaphysical necessity of causation is possible, but unknowable. |
| 14581 | The normative view says laws show the natural behaviour of natural kind members [Lowe, by Mumford/Anjum] |
| Full Idea: For Lowe law statements are in a sense about what 'ought' to be the case. The 'ought' is not an explicitly moral or anthropomorphic one but instead tells us what is the natural behaviour of kind members. | |
| From: report of E.J. Lowe (A Survey of Metaphysics [2002]) by S.Mumford/R.Lill Anjum - Getting Causes from Powers 8.6 | |
| A reaction: This is the 'normative' view of laws (as opposed to the intentional, dispositional, or regularity accounts). They cite Lowe 1989 Ch.8. The obvious immediate problem is things which evolved for one purpose and end up being used for another. |
| 4208 | 'If he wasn't born he wouldn't have died' doesn't mean birth causes death, so causation isn't counterfactual [Lowe] |
| Full Idea: Counterfactual analyses of event causation don't seem to work, because 'if Napoleon hadn't been born he wouldn't have died' is true, but doesn't mean his birth caused his death. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.161) | |
| A reaction: Nice counterexample, which looks pretty conclusive. Birth makes death possible; it creates the necessary conditions within which it can be caused. |
| 4224 | If motion is change of distance between objects, it involves no intrinsic change in the objects [Lowe] |
| Full Idea: If motion just is change of distance between two objects, it does not involve any kind of intrinsic change in the objects in question. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.242) | |
| A reaction: It sound respectably relativistic, but I doubt the definition. x is moving relative to y, then y attains x's velocity, so x ceases to move? Maybe. |
| 4227 | Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract [Lowe] |
| Full Idea: Surfaces, lines and points are not, strictly speaking, parts of space at all, but just 'limits' of certain kinds, and as such 'abstract' entities. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.254) | |
| A reaction: This is fairly crucial when dealing with Zeno's paradoxes. How many points in a line? How long to get through a point? |
| 4228 | If space is entirely relational, what makes a boundary, or a place unoccupied by physical objects? [Lowe] |
| Full Idea: If space does not exist at all, but is only relations between objects, what could one possibly mean by saying that there is a place which is unoccupied by any material object? And what determines whether space is bounded? | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.264) | |
| A reaction: Correct. People who assert that space is only relational have been misled by what we can know about space, not what it is. |