45 ideas
| 12667 | Metaphysics aims at the simplest explanation, without regard to testability [Ellis] |
| Full Idea: The methodology of metaphysics... is that of arguing to the simplest explanation, without regard to testability. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 1) | |
| A reaction: I love that! I'd be a bit cautious about 'simplest', since 'everything is the output of an ineffable God' is beautifully simple, and brings the whole discussion to a halt. I certainly think metaphysics goes deeper than testing. String Theory? |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 12666 | We can base logic on acceptability, and abandon the Fregean account by truth-preservation [Ellis] |
| Full Idea: In logic, acceptability conditions can replace truth conditions, ..and the only price one has to pay for this is that one has to abandon the implausible Fregean idea that logic is the theory of truth preservation. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 1) | |
| A reaction: This has always struck me as correct, given that if you assign T and F in a semantics, they don't have to mean 'true' and 'false', and that you can do very good logic with propositions which you think are entirely false. |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 12688 | Mathematics is the formal study of the categorical dimensions of things [Ellis] |
| Full Idea: I wish to explore the idea that mathematics is the formal study of the categorical dimensions of things. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 6) | |
| A reaction: Categorical dimensions are spatiotemporal relations and other non-causal properties. Ellis defends categorical properties as an aspect of science. The obvious connection seems to be with structuralism in mathematics. Shapiro is sympathetic. |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 12683 | Objects and substances are a subcategory of the natural kinds of processes [Ellis] |
| Full Idea: The category of natural kinds of objects or substances should be regarded simply as a subcategory of the category of the natural kinds of processes. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 3) | |
| A reaction: This is a new, and interesting, proposal from Ellis (which will be ignored by the philosophical community, as all new theories coming from elderly philosophers are ignored! Cf Idea 12652). A good knowledge of physics is behind Ellis's claim. |
| 12670 | A physical event is any change of distribution of energy [Ellis] |
| Full Idea: We may define a physical event as any change of distribution of energy in any of its forms. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 2) | |
| A reaction: This seems to result in an awful lot of events. My own (new this morning) definition is: 'An event is a process which can be individuated in time'. Now you just have to work out what a 'process' is, but that's easier than understanding an 'event'. |
| 12673 | Physical properties are those relevant to how a physical system might act [Ellis] |
| Full Idea: We may define a physical property as one whose value is relevant, in some circumstances, to how a physical system is likely to act. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 2) | |
| A reaction: Fair enough, but can we use the same 'word' property when we are discussing abstractions? Does 'The Enlightenment' have properties? Do very simple things have properties? Can 'red' act, if it isn't part of any physical system? |
| 12665 | I support categorical properties, although most people only want causal powers [Ellis] |
| Full Idea: I want to insist on the existence of a class of categorical properties distinct from causal powers. This is contentious, for there is a growing body of opinion that all properties are causal powers. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], Intro) | |
| A reaction: Alexander Bird makes a case against categorical properties. If what is meant is that 'being an electron' is the key property of an electron, then I disagree (quite strongly) with Ellis. Ellis says they are needed to explain causal powers. |
| 12682 | Essentialism needs categorical properties (spatiotemporal and numerical relations) and dispositions [Ellis] |
| Full Idea: Essentialist metaphysics seem to require that there be at least two kinds of properties in nature: dispositional properties (causal powers, capacities and propensities), and categorical ones (spatiotemporal and numerical relations). | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 3) | |
| A reaction: At last someone tells us what a 'categorical' property is! Couldn't find it in Stanford! Bird and Molnar reject the categorical ones as true properties. If there are six cats, which cat has the property of being six? Which cat is 'three metres apart'? |
| 12684 | Spatial, temporal and numerical relations have causal roles, without being causal [Ellis] |
| Full Idea: Spatial, temporal and numerical relations can have various causal roles without themselves being instances of causal powers. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 3) | |
| A reaction: He cites gaps, aggregates, orientations, approaching and receding, as examples of categorical properties which make a causal difference. I would have thought these could be incorporated in accounts of more basic causal powers. |
| 12672 | Properties and relations are discovered, so they can't be mere sets of individuals [Ellis] |
| Full Idea: To regard properties as sets of individuals, and relations as sets of ordered individuals, is to make a nonsense of the whole idea of discovering a new property or relationship. Sets are defined or constructed, not discovered. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 2) | |
| A reaction: This bizarre view of properties (as sets) drives me crazy, until it dawns on you that they are just using the word 'property' in a different way, probably coextensively with 'predicate', in order to make the logic work. |
| 12676 | Causal powers can't rest on things which lack causal power [Ellis] |
| Full Idea: A causal power can never be dependent on anything that does not have any causal powers. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 3) | |
| A reaction: Sounds right, though you worry when philosophers make such bold assertions about such extreme generalities. But see Idea 12667. This is, of course, the key argument for saying that causal powers are the bedrock of reality, and of explanation. |
| 23781 | Categoricals exist to influence powers. Such as structures, orientations and magnitudes [Ellis, by Williams,NE] |
| Full Idea: Ellis allows categoricals alongside powers, …to influence the sort of manifestations produced by powers. He lists structures, arrangements, distances, orientations, and magnitudes. | |
| From: report of Brian Ellis (The Metaphysics of Scientific Realism [2009]) by Neil E. Williams - The Powers Metaphysics 05.2 | |
| A reaction: I would have thought that all of these could be understood as manifestations of powers. The odd one out is distances, but then space and time are commonly overlooked in every attempt to produce a complete ontology. [also Molnar 2003:164]. |
| 12686 | Causal powers are a proper subset of the dispositional properties [Ellis] |
| Full Idea: The causal powers are just a proper subset of the dispositional properties. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 5) | |
| A reaction: Sounds wrong. Causal powers have a physical reality, while a disposition sounds as if it can wholly described by a counterfactual claim. It seems better to say that things have dispositions because they have powers. |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 14961 | Clearly a pipe can survive being taken apart [Cartwright,R] |
| Full Idea: There is at the moment a pipe on my desk. Its stem has been removed but it remains a pipe for all that; otherwise no pipe could survive a thorough cleaning. | |
| From: Richard Cartwright (Scattered Objects [1974], p.175) | |
| A reaction: To say that the pipe survives dismantling is not to say that it is fully a pipe during its dismantled phase. He gives a further example of a book in two volumes. |
| 14962 | Bodies don't becomes scattered by losing small or minor parts [Cartwright,R] |
| Full Idea: If a branch falls from a tree, the tree does not thereby become scattered, and a human body does not become scattered upon loss of a bit of fingernail. | |
| From: Richard Cartwright (Scattered Objects [1974], p.184) | |
| A reaction: This sort of observation draws me towards essentialism. A body is scattered if you divide it in a major way, but not if you separate off a minor part. It isn't just a matter of size, or even function. We have broader idea of what is essential. |
| 12685 | Categorical properties depend only on the structures they represent [Ellis] |
| Full Idea: I would define categorical properties as those whose identities depend only on the kinds of structures they represent. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 3 n8) | |
| A reaction: Aha. So categorical properties would be much more perspicaciously labelled as 'structural' properties. Why does philosophical terminology make it all more difficult than it needs to be? |
| 12679 | A real essence is a kind's distinctive properties [Ellis] |
| Full Idea: A distinctive set of intrinsic properties for a given kind is called a 'real essence'. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 3) | |
| A reaction: Note that he thinks essence is a set of properties (rather than what gives rise to the properties), and that it is kinds (and not individuals) which have real essences, and that one role of the properties is to be 'distinctive' of the kind. Cf. Oderberg. |
| 12668 | Metaphysical necessity holds between things in the world and things they make true [Ellis] |
| Full Idea: Metaphysical necessitation is the relation that holds between things in the world and the things they make true. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 1) | |
| A reaction: Not sure about that. It implies that it is sentences that have necessity, and he confirms it by calling it 'a semantic relation'. So there are no necessities if there are no sentences? Not the Brian Ellis we know and love. |
| 12687 | Metaphysical necessities are those depending on the essential nature of things [Ellis] |
| Full Idea: A metaphysically necessary proposition is one that is true in virtue of the essential nature of things. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 6) | |
| A reaction: It take this to be what Kit Fine argues for, though it tracks back to Aristotle. I also take it to be correct, though one might ask whether there are any other metaphysical necessities, ones not depending on essences. |
| 12669 | Science aims to explain things, not just describe them [Ellis] |
| Full Idea: The primary aim of science is to explain what happens, not just to describe it. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 2) | |
| A reaction: This I take to be a good motto for scientific essentialism. Any scientist who is happy with anything less than explanation is a mere journeyman, a servant in the kitchens of the great house of science. |
| 12681 | There are natural kinds of processes [Ellis] |
| Full Idea: There are natural kinds of processes. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 3) | |
| A reaction: Interesting. I am tempted by the view that processes are the most basic feature of reality, since I think of the mind as a process, and quantum reality seems more like processes than like objects. |
| 12680 | Natural kind structures go right down to the bottom level [Ellis] |
| Full Idea: Natural kind structures go all the way down to the most basic levels of existence. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 3) | |
| A reaction: Even the bottom level? Is there anything to explain why the bottom level is a kind, given that all the higher kinds presumably have an explanation? |
| 12675 | Laws of nature are just descriptions of how things are disposed to behave [Ellis] |
| Full Idea: The laws of nature must be supposed to be just descriptions of the ways in which things are intrinsically disposed to behave: of how they would behave if they existed as closed and isolated systems. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 3) | |
| A reaction: I agree with this, and therefore take 'laws of nature' to be eliminable from any plausible ontology (which just contains the things and their behaviour). Ellis tends to defend laws, when he doesn't need to. |
| 12671 | I deny forces as entities that intervene in causation, but are not themselves causal [Ellis] |
| Full Idea: The classical conception of force is an entity that intervenes between a physical cause and its effect, but is not itself a physical cause. I see no reason to believe in forces of this kind. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 2) | |
| A reaction: The difference of view between Leibniz and Newton is very illuminating on this one (coming this way soon!). Can you either have forces and drop causation, or have causation and drop forces? |
| 12674 | Energy is the key multi-valued property, vital to scientific realism [Ellis] |
| Full Idea: Perhaps the most important of all multi-valued properties is energy itself. I think a scientific realist must believe that energy exists. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 2) | |
| A reaction: It's odd that the existence of the most basic thing in physics needs a credo from a certain sort of believer. I have been bothered by notion of 'energy' for fifty years, and am still none the wiser. I'm sure I could be scientific realist without it. |
| 12689 | Simultaneity can be temporal equidistance from the Big Bang [Ellis] |
| Full Idea: Cosmologists have a concept of objective simultaneity, which they take to mean something like 'temporally equidistant from the Big Bang'. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 6) | |
| A reaction: I find this very appealing, when faced with all the relativity theory that tells me there is no such thing as global simultaneity, a claim which I find deeply counterintuitive, but seems to have the science on its side. Bravo. |
| 12690 | The present is the collapse of the light wavefront from the Big Bang [Ellis] |
| Full Idea: The global wavefront that collapses when a light signal from the Big Bang is observed is what most plausibly defines the frontier between past and future. | |
| From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 6) | |
| A reaction: I'm not sure I understand this, but it is clearly worth passing on. Of all the deep mysteries, the 'present' time may be the deepest. |