62 ideas
| 13395 | If an analysis shows the features of a concept, it doesn't seem to 'reduce' the concept [Jubien] |
| Full Idea: An analysis of a concept tells us what the concept is by telling us what its constituents are and how they are combined. ..The features of the concept are present in the analysis, making it surprising the 'reductive' analyses are sought. | |
| From: Michael Jubien (Possibility [2009], 4.5) | |
| A reaction: He says that there are nevertheless reductive analyses, such as David Lewis's analysis of modality. We must disentangle conceptual analysis from causal analysis (e.g. in his example of the physicalist reduction of mind). |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| Full Idea: Definition provides us with the means for converting our intuitions into mathematically usable concepts. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| Full Idea: When you have proved something you know not only that it is true, but why it must be true. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-2) | |
| A reaction: Note the word 'must'. Presumably both the grounding and the necessitation of the truth are revealed. |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
| Full Idea: Set theory cannot be an axiomatic theory, because the very notion of an axiomatic theory makes no sense without it. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.413-2) | |
| A reaction: This will come as a surprise to Penelope Maddy, who battles with ways to accept the set theory axioms as the foundation of mathematics. Mayberry says that the basic set theory required is much more simple and intuitive. |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| Full Idea: We can give a semi-categorical axiomatisation of set-theory (all that remains undetermined is the size of the set of urelements and the length of the sequence of ordinals). The system is second-order in formalisation. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.413-2) | |
| A reaction: I gather this means the models may not be isomorphic to one another (because they differ in size), but can be shown to isomorphic to some third ingredient. I think. Mayberry says this shows there is no such thing as non-Cantorian set theory. |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| Full Idea: The (misnamed!) Axiom of Infinity expresses Cantor's fundamental assumption that the species of natural numbers is finite in size. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
| Full Idea: The idea of 'generating' sets is only a metaphor - the existence of the hierarchy is established without appealing to such dubious notions. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) | |
| A reaction: Presumably there can be a 'dependence' or 'determination' relation which does not involve actual generation. |
| 17803 | Limitation of size is part of the very conception of a set [Mayberry] |
| Full Idea: Our very notion of a set is that of an extensional plurality limited in size. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-2) |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| Full Idea: In the mainstream tradition of modern logic, beginning with Boole, Peirce and Schröder, descending through Löwenheim and Skolem to reach maturity with Tarski and his school ...saw logic as a branch of mathematics. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.410-1) | |
| A reaction: [The lesser tradition, of Frege and Russell, says mathematics is a branch of logic]. Mayberry says the Fregean tradition 'has almost died out'. |
| 13378 | It is a mistake to think that the logic developed for mathematics can clarify language and philosophy [Jubien] |
| Full Idea: It has often been uncritically assumed that logic that was initially a tool for clarifying mathematics could be seamlessly and uniformly applied in the effort to clarify ordinary language and philosophy, but this has been a real mistake. | |
| From: Michael Jubien (Possibility [2009], Intro) | |
| A reaction: I'm not saying he's right (since you need stupendous expertise to make that call) but my intuitions are that he has a good point, and he is at least addressing a crucial question which most analytical philosophers avert their eyes from. |
| 17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
| Full Idea: First-order logic is very weak, but therein lies its strength. Its principle tools (Compactness, Completeness, Löwenheim-Skolem Theorems) can be established only because it is too weak to axiomatize either arithmetic or analysis. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.411-2) | |
| A reaction: He adds the proviso that this is 'unless we are dealing with structures on whose size we have placed an explicit, finite bound' (p.412-1). |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| Full Idea: Second-order logic is a powerful tool of definition: by means of it alone we can capture mathematical structure up to isomorphism using simple axiom systems. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 13402 | We only grasp a name if we know whether to apply it when the bearer changes [Jubien] |
| Full Idea: We cannot be said to have a full grasp of a name unless we have a definite disposition to apply it or to withhold it under whatever conceivable changes the bearer of the name might come to undergo. | |
| From: Michael Jubien (Possibility [2009], 5.3) | |
| A reaction: This is right, and an excellent counterproposal to the logicians' notion that names have to rigidly designate. As a bare minimum, you are not supposed to deny the identity of your parents because they have grown a bit older, or a damaged painting. |
| 13405 | The baptiser picks the bearer of a name, but social use decides the category [Jubien] |
| Full Idea: The person who introduces a proper name gets to pick its bearer, but its category - and consequently the meaning of the name - is determined by social use. | |
| From: Michael Jubien (Possibility [2009], 7) | |
| A reaction: New 'division of labour'. The idea that a name has some sort of meaning seems right and important. If babies were switched after baptism, social use might fix the name to the new baby. The namer could stipulate the category at the baptism. Too neat. |
| 13399 | Examples show that ordinary proper names are not rigid designators [Jubien] |
| Full Idea: There are plenty of examples to show that ordinary proper names simply are not rigid designators. | |
| From: Michael Jubien (Possibility [2009], 5.1) | |
| A reaction: His examples are the planet Venus and the dust of which it is formed, and a statue made of clay. In other words, for some objects, perhaps under certain descriptions (e.g. functional ones), the baptised matter can change. Rigidity is an extra topping. |
| 13398 | We could make a contingent description into a rigid and necessary one by adding 'actual' to it [Jubien] |
| Full Idea: 'The winner of the Derby' satisfies some horse, but only accidentally. But we could 'rigidify' the description by inserting 'actual' into it, giving 'the actual winner of the Derby'. Winning is a contingent property, but actually winning is necessary. | |
| From: Michael Jubien (Possibility [2009], 5.1) | |
| A reaction: I like this unusual proposal because instead of switching into formal logic in order to capture the ideas we are after, he is drawing on the resources of ordinary language, offering philosophers a way of speaking plain English more precisely. |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| Full Idea: The 'logica magna' [of the Fregean tradition] has quantifiers ranging over a fixed domain, namely everything there is. In the Boolean tradition the domains differ from interpretation to interpretation. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.410-2) | |
| A reaction: Modal logic displays both approaches, with different systems for global and local domains. |
| 13392 | Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien] |
| Full Idea: There is a readiness of philosophers to 'translate' English, with its seeming multitude of kind-driven quantifiers, into first-order logic, with its single wide-open quantifier. | |
| From: Michael Jubien (Possibility [2009], 4.1) | |
| A reaction: As in example he says that reference to a statue involves a 'statue-quantifier'. Thus we say things about the statue that we would not say about the clay, which would involve a 'clay-quantifier'. |
| 17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
| Full Idea: No logic which can axiomatize real analysis can have the Löwenheim-Skolem property. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
| Full Idea: The purpose of a 'classificatory' axiomatic theory is to single out an otherwise disparate species of structures by fixing certain features of morphology. ...The aim is to single out common features. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.406-2) |
| 17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
| Full Idea: The central dogma of the axiomatic method is this: isomorphic structures are mathematically indistinguishable in their essential properties. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.406-2) | |
| A reaction: Hence it is not that we have to settle for the success of a system 'up to isomorphism', since that was the original aim. The structures must differ in their non-essential properties, or they would be the same system. |
| 17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
| Full Idea: The purpose of what I am calling 'eliminatory' axiomatic theories is precisely to eliminate from mathematics those peculiar ideal and abstract objects that, on the traditional view, constitute its subject matter. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-1) | |
| A reaction: A very interesting idea. I have a natural antipathy to 'abstract objects', because they really mess up what could otherwise be a very tidy ontology. What he describes might be better called 'ignoring' axioms. The objects may 'exist', but who cares? |
| 17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
| Full Idea: No logic which can axiomatise arithmetic can be compact or complete. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) | |
| A reaction: I take this to be because there are new truths in the transfinite level (as well as the problem of incompleteness). |
| 17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
| Full Idea: We eliminate the real numbers by giving an axiomatic definition of the species of complete ordered fields. These axioms are categorical (mutually isomorphic), and thus are mathematically indistinguishable. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2) | |
| A reaction: Hence my clever mathematical friend says that it is a terrible misunderstanding to think that mathematics is about numbers. Mayberry says the reals are one ordered field, but mathematics now studies all ordered fields together. |
| 17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
| Full Idea: Quantities for Greeks were concrete things - lines, surfaces, solids, times, weights. At the centre of their science of quantity was the beautiful theory of ratio and proportion (...in which the notion of number does not appear!). | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-2) | |
| A reaction: [He credits Eudoxus, and cites Book V of Euclid] |
| 17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
| Full Idea: The abstract objects of modern mathematics, the real numbers, were invented by the mathematicians of the seventeenth century in order to simplify and to generalize the Greek science of quantity. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-2) |
| 17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
| Full Idea: In Cantor's new vision, the infinite, the genuine infinite, does not disappear, but presents itself in the guise of the absolute, as manifested in the species of all sets or the species of all ordinal numbers. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
| Full Idea: We may describe Cantor's achievement by saying, not that he tamed the infinite, but that he extended the finite. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
| Full Idea: If we grant, as surely we must, the central importance of proof and definition, then we must also grant that mathematics not only needs, but in fact has, foundations. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) |
| 17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
| Full Idea: The ultimate principles upon which mathematics rests are those to which mathematicians appeal without proof; and the primitive concepts of mathematics ...themselves are grasped directly, if grasped at all, without the mediation of definition. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) | |
| A reaction: This begs the question of whether the 'grasping' is purely a priori, or whether it derives from experience. I defend the latter, and Jenkins puts the case well. |
| 17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
| Full Idea: An account of the foundations of mathematics must specify four things: the primitive concepts for use in definitions, the rules governing definitions, the ultimate premises of proofs, and rules allowing advance from premises to conclusions. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-2) |
| 17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
| Full Idea: No axiomatic theory, formal or informal, of first or of higher order can logically play a foundational role in mathematics. ...It is obvious that you cannot use the axiomatic method to explain what the axiomatic method is. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-2) |
| 17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
| Full Idea: The sole theoretical interest of first-order Peano arithmetic derives from the fact that it is a first-order reduct of a categorical second-order theory. Its axioms can be proved incomplete only because the second-order theory is categorical. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
| Full Idea: If we did not know that the second-order axioms characterise the natural numbers up to isomorphism, we should have no reason to suppose, a priori, that first-order Peano Arithmetic should be complete. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
| Full Idea: The idea that set theory must simply be identified with first-order Zermelo-Fraenkel is surprisingly widespread. ...The first-order axiomatic theory of sets is clearly inadequate as a foundation of mathematics. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-2) | |
| A reaction: [He is agreeing with a quotation from Skolem]. |
| 17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
| Full Idea: One does not have to translate 'ordinary' mathematics into the Zermelo-Fraenkel system: ordinary mathematics comes embodied in that system. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-1) | |
| A reaction: Mayberry seems to be a particular fan of set theory as spelling out the underlying facts of mathematics, though it has to be second-order. |
| 17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
| Full Idea: The fons et origo of all confusion is the view that set theory is just another axiomatic theory and the universe of sets just another mathematical structure. ...The universe of sets ...is the world that all mathematical structures inhabit. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.416-1) |
| 13404 | To exist necessarily is to have an essence whose own essence must be instantiated [Jubien] |
| Full Idea: For a thing to exist necessarily is for it to have an entity-essence whose own entity-essence entails being instantiated. | |
| From: Michael Jubien (Possibility [2009], 6.4) | |
| A reaction: This is the culmination of a lengthy discussion, and is not immediately persuasive. For Jubien the analysis rests on a platonist view of properties, which doesn't help. |
| 13386 | If objects are just conventional, there is no ontological distinction between stuff and things [Jubien] |
| Full Idea: Under the Quinean (conventional) view of objects, there is no ontological distinction between stuff and things. | |
| From: Michael Jubien (Possibility [2009], 1.5) | |
| A reaction: This is the bold nihilistic account of physical objects, which seems to push all of our ontology into language (English?). We could devise divisions into things that were just crazy, and likely to lead to the rapid extinction of creatures who did it. |
| 13403 | The category of Venus is not 'object', or even 'planet', but a particular class of good-sized object [Jubien] |
| Full Idea: The category of Venus is not 'physical object' or 'mereological sum', but narrower. Surprisingly, it is not 'planet', since it might cease to be a planet and still merit the name 'Venus'. It is something like 'well-integrated, good-sized physical object'. | |
| From: Michael Jubien (Possibility [2009], 5.3) | |
| A reaction: Jubien is illustrating Idea 13402. This is a nice demonstration of how one might go about the task of constructing categories - by showing the modal profiles of things to which names have been assigned. Categories are file names. |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| Full Idea: The abstractness of the old fashioned real numbers has been replaced by generality in the modern theory of complete ordered fields. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2) | |
| A reaction: In philosophy, I'm increasingly thinking that we should talk much more of 'generality', and a great deal less about 'universals'. (By which I don't mean that redness is just the set of red things). |
| 13375 | The idea that every entity must have identity conditions is an unfortunate misunderstanding [Jubien] |
| Full Idea: The pervasiveness, throughout philosophy, of the assumption that entities of various kinds need identity conditions is one unfortunate aspect of Quine's important philosophical legacy. | |
| From: Michael Jubien (Possibility [2009], Intro) | |
| A reaction: Lowe seems to be an example of a philosopher who habitually demands individuation conditions for everything that is referred to. Presumably the alternative is to take lots of things as primitive, but this seems to be second best. |
| 13393 | Any entity has the unique property of being that specific entity [Jubien] |
| Full Idea: For any entity of any sort, abstract or concrete, I assume there is a property of being that specific entity. For want of a better term, I will call such properties entity-essences. They are 'singulary' - not instantiable by more than one thing at a time. | |
| From: Michael Jubien (Possibility [2009], 4.2) | |
| A reaction: Baffling. Why would someone who has mocked all sorts of bogus philosophical claims based on logic then go on to assert the existence of such weird things as these? I can't make sense of this property being added to a thing's other properties. |
| 13388 | It is incoherent to think that a given entity depends on its kind for its existence [Jubien] |
| Full Idea: It is simply far-fetched - even incoherent - to think that, given an entity, of whatever kind, its being a single entity somehow consists in its satisfying some condition involving the kind to which it belongs (or concepts related to that kind). | |
| From: Michael Jubien (Possibility [2009], 2.3) | |
| A reaction: Well said. I can't see how philosophers have allowed themselves to drift into such a daft view. Kinds blatantly depend on the individuals that constitute them, so how could the identity of the individuals depend on their kind? |
| 13384 | Objects need conventions for their matter, their temporal possibility, and their spatial possibility [Jubien] |
| Full Idea: We need a first convention to determine what matter constitutes objects, then a second to determine whether there are different temporal possibilities for a given object, then a third for different spatial possibilities. | |
| From: Michael Jubien (Possibility [2009], 1.5) | |
| A reaction: This is building up a Quinean account of objects, as mere matter in regions of spacetime, which are then precisely determined by a set of social conventions. |
| 13385 | Basically, the world doesn't have ready-made 'objects'; we carve objects any way we like [Jubien] |
| Full Idea: There is a certain - very mild - sense in which I don't think the physical world comes with ready-made objects. I think instead that we (conventionally) carve it up into objects, and this can be done any way we like. | |
| From: Michael Jubien (Possibility [2009], 1.5) | |
| A reaction: I have no idea how one could begin to refute such a view. Obviously there are divisions (even if only of physical density) in the world, but nothing obliges us to make divisions at those points. We happily accept objects with gaps in them. |
| 13383 | If the statue is loved and the clay hated, that is about the object first qua statue, then qua clay [Jubien] |
| Full Idea: If a sculptor says 'I love the statue but I really hate that piece of clay - it is way too hard to work with' ...the statement is partly is partly about that object qua statue and partly about that object qua piece of clay. | |
| From: Michael Jubien (Possibility [2009], 1.4) | |
| A reaction: His point is that identity is partly determined by the concept or category under which the thing falls. Plausible. Lots of identity muddles seem to come from our conceptual scheme not being quite up to the job when things change. |
| 13400 | If one entity is an object, a statue, and some clay, these come apart in at least three ways [Jubien] |
| Full Idea: A single entity is a physical object, a piece of clay and a statue. We seem to have that the object could be scattered, but not the other two; the object and the clay could be spherical, but not the statue; and only the object could have different matter. | |
| From: Michael Jubien (Possibility [2009], 5.2) | |
| A reaction: His proposal, roughly, is to reduce object-talk to property-talk, and then see the three views of this object as referring to different sets of properties, rather than to a single thing. Promising, except that he goes platonist about properties. |
| 13401 | The idea of coincident objects is a last resort, as it is opposed to commonsense naturalism [Jubien] |
| Full Idea: I find it surprising that some philosophers accept 'coincident objects'. This notion clearly offends against commonsense 'naturalism' about the world, so it should be viewed as a last resort. | |
| From: Michael Jubien (Possibility [2009], 5.2 n9) | |
| A reaction: I'm not quite clear why he invokes 'naturalism', but I pass on his intuition because it seems right to me. |
| 13380 | Parts seem to matter when it is just an object, but not matter when it is a kind of object [Jubien] |
| Full Idea: When thought of just as an object, the parts of a thing seem definitive and their arrangement seems inconsequential. But when thought of as an object of a familiar kind it is reversed: the arrangement is important and the parts are inessential. | |
| From: Michael Jubien (Possibility [2009], 1.4) | |
| A reaction: This is analogous to the Ship of Theseus, where we say that the tour operator and the museum keeper give different accounts of whether it is the same ship. The 'kind' Jubien refers to is most likely to be a functional kind. |
| 13376 | We should not regard essentialism as just nontrivial de re necessity [Jubien] |
| Full Idea: I argue against the widely accepted characterization of the doctrine of 'essentialism' as the acceptance of nontrivial de re necessity | |
| From: Michael Jubien (Possibility [2009], Intro) | |
| A reaction: I agree entirely. The notion of an essence is powerful if clearly distinguished. The test is: can everything being said about essences be just as easily said by referring to necessities? If so, you are talking about the wrong thing. |
| 13381 | Thinking of them as 'ships' the repaired ship is the original, but as 'objects' the reassembly is the original [Jubien] |
| Full Idea: Thinking about the original ship as a ship, we think we continue to have the 'same ship' as each part is replaced; ...but when we think of them as physical objects, we think the original ship and the outcome of the reassembly are one and the same. | |
| From: Michael Jubien (Possibility [2009], 1.4) | |
| A reaction: It seems to me that you cannot eliminate how we are thinking of the ship as influencing how we should read it. My suggestion is to think of Theseus himself valuing either the repaired or the reassembled version. That's bad for Jubien's account. |
| 13382 | Rearranging the planks as a ship is confusing; we'd say it was the same 'object' with a different arrangement [Jubien] |
| Full Idea: That the planks are rearranged as a ship elevates the sense of mystery, because arrangements matter for ships, but if they had been arranged differently we would have the same intuition - that it still counts as the same object. | |
| From: Michael Jubien (Possibility [2009], 1.4) | |
| A reaction: Implausible. Classic case: can I have my pen back? - smashes it to pieces and hands it over with 'there you are' - that's not my pen! - Jubien says it's the same object! - it isn't my pen, and it isn't the same object either! Where is Shelley's skylark? |
| 13379 | If two objects are indiscernible across spacetime, how could we decide whether or not they are the same? [Jubien] |
| Full Idea: If a bit of matter has a qualitatively indistinguishable object located at a later time, with a path of spacetime connecting them, how could we determine they are identical? Neither identity nor diversity follows from qualitative indiscernibility. | |
| From: Michael Jubien (Possibility [2009], 1.3) | |
| A reaction: All these principles expounded by Leibniz were assumed to be timeless, but for identity over time the whole notion of things retaining identity despite changing has to be rethought. Essentialism to the rescue. |
| 13394 | Entailment does not result from mutual necessity; mutual necessity ensures entailment [Jubien] |
| Full Idea: Typically philosophers say that for P to entail Q is for the proposition that all P's are Q's to be necessary. I think this analysis is backwards, and that necessity rests on entailment, not vice versa. | |
| From: Michael Jubien (Possibility [2009], 4.4) | |
| A reaction: His example is that being a horse and being an animal are such that one entails the other. In other words, necessities arise out of property relations (which for Jubien are necessary because the properties are platonically timeless). Wrong. |
| 13391 | Modality concerns relations among platonic properties [Jubien] |
| Full Idea: I think modality has to do with relations involving the abstract part of the world, specifically with relations among (Platonic) properties. | |
| From: Michael Jubien (Possibility [2009], 3.2) | |
| A reaction: [Sider calls Jubien's the 'governance' view, since abstract relations govern the concrete] I take Jubien here (having done a beautiful demolition job on the possible worlds account of modality) to go spectacularly wrong. Modality starts in the concrete. |
| 13374 | To analyse modality, we must give accounts of objects, properties and relations [Jubien] |
| Full Idea: The ultimate analysis of possibility and necessity depends on two important ontological decisions: the choice of an analysis of the intuitive concept of a physical object, and the other is the positing of properties and relations. | |
| From: Michael Jubien (Possibility [2009], Intro) | |
| A reaction: In the same passage he adopts Quine's view of objects, leading to mereological essentialism, and a Platonic view of properties, based on Lewis's argument for taking some things at face value. One might start with processes and events instead. |
| 13389 | The love of possible worlds is part of the dream that technical logic solves philosophical problems [Jubien] |
| Full Idea: I believe the contemporary infatuation with possible worlds in philosophy stems in part from a tendency to think that technical logic offers silver-bullet solutions to philosophical problems. | |
| From: Michael Jubien (Possibility [2009], 3.2) | |
| A reaction: I would say that the main reason for the infatuation is just novelty. As a technical device it was only invented in the 1960s, so we are in a honeymoon period, as we would be with any new gadget. I can't imagine possible worlds figuring much in 100 years. |
| 13390 | Possible worlds don't explain necessity, because they are a bunch of parallel contingencies [Jubien] |
| Full Idea: The fundamental problem is that in world theory, what passes for necessity is in effect just a bunch of parallel 'contingencies'. | |
| From: Michael Jubien (Possibility [2009], 3.2) | |
| A reaction: Jubien's general complaint is that there is no connection between the possible worlds and the actual world, so they are irrelevant, but this is a nicely different point - that lots of contingent worlds can't add up to necessity. Nice. |
| 13396 | Analysing mental concepts points to 'inclusionism' - that mental phenomena are part of the physical [Jubien] |
| Full Idea: We have (physicalist) 'inclusionism' when the mental is included in the physical, and mental phenomena are to be found among physical phenomena. Only inclusionism is compatible with a genuine physicalist analysis of mental concepts. | |
| From: Michael Jubien (Possibility [2009], 4.5) | |
| A reaction: This isn't the thesis of conceptual dualism (which I like), but an interesting accompaniment for it. Jubien is offering this as an alternative to 'reductive' analysis, translating all the mental concepts into physical language. He extends 'physical'. |
| 19087 | The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce] |
| Full Idea: The entire intellectual purport of any symbol consists in the total of all modes of rational conduct which, conditionally upon all the possible different circumstances and desires, would ensue upon the acceptance of the symbol. | |
| From: Charles Sanders Peirce (Issues of Pragmaticism [1905], EP ii.246), quoted by Danielle Macbeth - Pragmatism and Objective Truth p.169 n1 | |
| A reaction: Macbeth says pragmatism is founded on this theory of meaning, rather than on a theory of truth. I don't see why the causes of a symbol shouldn't be as much a part of its meaning as the consequences are. |
| 13377 | First-order logic tilts in favour of the direct reference theory, in its use of constants for objects [Jubien] |
| Full Idea: First-order logic tilts in favor of the direct reference account of proper names by using individual constants to play the intuitive role of names, and by 'interpreting' the constants simply as the individuals that are assigned to them for truth-values. | |
| From: Michael Jubien (Possibility [2009], Intro) | |
| A reaction: This is the kind of challenge to orthodoxy that is much needed at the moment. We have an orthodoxy which is almost a new 'scholasticism', that logic will clarify our metaphysics. Trying to enhance the logic for the job may be a dead end. |