19 ideas
13134 | We negate predicates but do not negate names [Westerhoff] |
Full Idea: We negate predicates but do not negate names. | |
From: Jan Westerhoff (Ontological Categories [2005], §88) | |
A reaction: This is a point for anyone like Ramsey who wants to collapse the distinction between particulars and universals, or singular terms and their predicates. |
16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
Full Idea: Geometrical concepts appear to depend in some way on a spatial ability. Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of the propositions seems to me to be thereby lost. | |
From: Tyler Burge (Frege on Apriority (with ps) [2000], 4) | |
A reaction: I think this is a widely held view nowadays. Giaquinto has a book on it. A successful model of something can't replace it. Set theory can't replace arithmetic. |
16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
Full Idea: In the Peano axiomatisation, arithmetic seems primitively to involve the thought that 0 is a number. | |
From: Tyler Burge (Frege on Apriority (with ps) [2000], 5) | |
A reaction: Burge is pointing this out as a problem for Frege, for whom only the logic is primitive. |
13124 | Categories can be ordered by both containment and generality [Westerhoff] |
Full Idea: Categories are usually not assumed to be ordered by containment, but also be generality. | |
From: Jan Westerhoff (Ontological Categories [2005], §02) | |
A reaction: I much prefer generality, which is responsive to the full picture, whereas containment seems to appeal too much to the orderly and formalised mind. Containments overlap, so we can't dream of a perfectly neat system. |
13117 | How far down before we are too specialised to have a category? [Westerhoff] |
Full Idea: How far down are we allowed to go before the categories become too special to qualify as ontological categories? | |
From: Jan Westerhoff (Ontological Categories [2005], Intro) | |
A reaction: A very nice question, because we can't deny a category to a set with only one member, otherwise the last surviving dodo would not have been a dodo. |
13116 | Maybe objects in the same category have the same criteria of identity [Westerhoff] |
Full Idea: There is an idea that objects belonging to the same category have the same criteria of identity. This view was first explicitly endorsed by Frege (1884), and was later systematized by Dummett (1981). | |
From: Jan Westerhoff (Ontological Categories [2005], Intro) | |
A reaction: This approach is based on identity between equivalence classes. Westerhoff says it means, implausibly, that the resulting categories cannot share properties. |
13118 | Categories are base-sets which are used to construct states of affairs [Westerhoff] |
Full Idea: My fundamental idea is that 'form-sets' are intersubstitutable constituents of states of affairs with the same form, and 'base-sets' are special form-sets which can be used to construct other form-sets. Ontological categories are the base-sets. | |
From: Jan Westerhoff (Ontological Categories [2005], Intro) | |
A reaction: The spirit of this is, of course, to try to achieve the kind of rigour that is expected in contemporary professional philosophy, by aiming for some sort of axiom-system that is related to a well established precise discipline like set theory. Maybe. |
13125 | Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff] |
Full Idea: It is usually assumed of ontological categories that they can explain why certain substitutions make a statement false ('prime' for 'odd'), while others make it meaningless ('sweet' for 'odd', of numbers). | |
From: Jan Westerhoff (Ontological Categories [2005], §05) | |
A reaction: So there is a strong link between big ontological questions, and Ryle's famous identification of the 'category mistake'. The phenomenon of the category mistake is undeniable, and should make us sympathetic to the idea of categories. |
13126 | Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff] |
Full Idea: Systems of ontological categories are systematizations of our intuitions about generality, intersubstitutability, and identity. | |
From: Jan Westerhoff (Ontological Categories [2005], §23) | |
A reaction: I think we might be able to concede this without conceding the relativism about categories which Westerhoff espouses. I would claim that our 'intuitions' are pretty accurate about the joints of nature, and hence accurate about these criteria. |
13130 | Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff] |
Full Idea: Categories in terms of generality, dependence and containment are unsatisfactory because of the 'cut-off point problem': they don't give an account of how far down the order we can go and be sure we are still dealing with categories. | |
From: Jan Westerhoff (Ontological Categories [2005], §27) | |
A reaction: I don't see why this should be a devastating objection to any theory. I have a very clear notion of a human being, but a very hazy notion of how far back towards its conception a human being extends. |
13131 | The aim is that everything should belong in some ontological category or other [Westerhoff] |
Full Idea: It seems to be one of the central points of constructing systems of ontological categories that everything can be placed in some category or other. | |
From: Jan Westerhoff (Ontological Categories [2005], §49) | |
A reaction: After initial resistance to this, I suppose I have to give in. The phoenix (a unique mythological bird) is called a 'phoenix', though it might just be called 'John' (cf. God). If there were another phoenix, we would know how to categorise it. |
13123 | All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff] |
Full Idea: Surveyed ontological systems show overlaps: properties and relations turn up in every system; individuals form part of five systems; abstracta, collections/sets and events are in four; facts are in two. | |
From: Jan Westerhoff (Ontological Categories [2005], §02) | |
A reaction: Westerhoff is a hero for doing such a useful survey. Of course, Quine challenges properties, and relations are commonly given a reductive analysis. Individuals can be challenged, and abstracta reduced. Sets are fictions. Events or facts? Etc. |
13115 | Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff] |
Full Idea: I deny the absolutism of a unique system of ontological categories and the essentialist view of membership in ontological categories as necessary features. ...I regard ontological categories as similar to axioms of formalized theories. | |
From: Jan Westerhoff (Ontological Categories [2005], Intro) | |
A reaction: The point is that modern axioms are not fundamental self-evident truths, but an economic set of basic statements from which some system can be derived. There may be no unique set of axioms for a formal system. |
13119 | Categories merely systematise, and are not intrinsic to objects [Westerhoff] |
Full Idea: My conclusion is that categories are relativistic, used for systematization, and that it is not an intrinsic feature of an object to belong to a category, and that there is no fundamental distinction between individuals and properties. | |
From: Jan Westerhoff (Ontological Categories [2005], Intro) | |
A reaction: [compressed] He calls his second conclusion 'anti-essentialist', but I think we can still get an account of (explanatory) essence while agreeing with his relativised view of categories. Wiggins might be his main opponent. |
13135 | A thing's ontological category depends on what else exists, so it is contingent [Westerhoff] |
Full Idea: What ontological category a thing belongs to is not dependent on its inner nature, but dependent on what other things there are in the world, and this is a contingent matter. | |
From: Jan Westerhoff (Ontological Categories [2005], §89) | |
A reaction: This is aimed at those, like Wiggins, who claim that category is essential to a thing, and there is no possible world in which that things could belong to another category. Sounds good, till you try to come up with examples. |
13129 | Essential kinds may be too specific to provide ontological categories [Westerhoff] |
Full Idea: Essential kinds can be very specific, and arguably too specific for the purposes of ontological categories. | |
From: Jan Westerhoff (Ontological Categories [2005], §27) | |
A reaction: Interesting. There doesn't seem to be any precise guideline as to how specific an essential kind might be. In scientific essentialism, each of the isotopes of tin has a distinct essence, but why should they not be categories |
16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
Full Idea: Whereas Leibniz and Frege predicate apriority primarily of truths (or more fundamentally, proofs of truths), Kant predicates apriority primarily of cognition and the employment of representations. | |
From: Tyler Burge (Frege on Apriority (with ps) [2000], 1) |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
Full Idea: Philosophers are the forefathers of heretics. | |
From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
6610 | I believe because it is absurd [Tertullian] |
Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |