41 ideas
| 3358 | Metaphysics focuses on Platonism, essentialism, materialism and anti-realism [Benardete,JA] |
| Full Idea: In contemporary metaphysics the major areas of discussion are Platonism, essentialism, materialism and anti-realism. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], After) |
| 3312 | There are the 'is' of predication (a function), the 'is' of identity (equals), and the 'is' of existence (quantifier) [Benardete,JA] |
| Full Idea: At least since Russell, one has routinely distinguished between the 'is' of predication ('Socrates is wise', Fx), the 'is' of identity ('Morning Star is Evening Star', =), and the 'is' of existence ('the cat is under the bed', Ex). | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch. 7) | |
| A reaction: This seems horribly nitpicking to many people, but I love it - because it is just true, and it is a truth right at the basis of the confusions in our talk. Analytic philosophy forever! [P.S. 'Tiddles is a cat' - the 'is' membership] |
| 3352 | Analytical philosophy analyses separate concepts successfully, but lacks a synoptic vision of the results [Benardete,JA] |
| Full Idea: Analytical philosophy excels in the piecemeal analysis of causation, perception, knowledge and so on, but there is a striking poverty of any synoptic vision of these independent studies. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.22) |
| 3329 | Presumably the statements of science are true, but should they be taken literally or not? [Benardete,JA] |
| Full Idea: As our bible, the Book of Science is presumed to contain only true sentences, but it is less clear how they are to be construed, which literally and which non-literally. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.13) |
| 9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
| Full Idea: Any set with a concrete member is 'impure'. 'Pure' sets are those that are not impure, and are paradigm cases of abstract entities, such as the sort of sets apparently dealt with in Zermelo-Fraenkel (ZF) set theory. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.116) | |
| A reaction: [I am unclear whether Jubien is introducing this distinction] This seems crucial in accounts of mathematics. On the one had arithmetic can be built from Millian pebbles, giving impure sets, while logicists build it from pure sets. |
| 3326 | Set theory attempts to reduce the 'is' of predication to mathematics [Benardete,JA] |
| Full Idea: Set theory offers the promise of a complete mathematization of the 'is' of predication. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.13) |
| 3327 | The set of Greeks is included in the set of men, but isn't a member of it [Benardete,JA] |
| Full Idea: Set inclusion is sharply distinguished from set membership (as the set of Greeks is found to be included in, but not a member of, the set of men). | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.13) |
| 3335 | The standard Z-F Intuition version of set theory has about ten agreed axioms [Benardete,JA, by PG] |
| Full Idea: Zermelo proposed seven axioms for set theory, with Fraenkel adding others, to produce the standard Z-F Intuition. | |
| From: report of José A. Benardete (Metaphysics: the logical approach [1989], Ch.17) by PG - Db (ideas) |
| 9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
| Full Idea: A first-order model can be viewed as a kind of ordered set, and if the domain of the model contains only concrete entities then it is a 'fundamental' model. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.117) | |
| A reaction: An important idea. Fundamental models are where the world of logic connects with the physical world. Any account of relationship between fundamental models and more abstract ones tells us how thought links to world. |
| 3332 | Greeks saw the science of proportion as the link between geometry and arithmetic [Benardete,JA] |
| Full Idea: The Greeks saw the independent science of proportion as the link between geometry and arithmetic. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.15) |
| 3330 | Negatives, rationals, irrationals and imaginaries are all postulated to solve baffling equations [Benardete,JA] |
| Full Idea: The Negative numbers are postulated (magic word) to solve x=5-8, Rationals postulated to solve 2x=3, Irrationals for x-squared=2, and Imaginaries for x-squared=-1. (…and Zero for x=5-5) …and x/0 remains eternally open. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.14) |
| 3337 | Natural numbers are seen in terms of either their ordinality (Peano), or cardinality (set theory) [Benardete,JA] |
| Full Idea: One approaches the natural numbers in terms of either their ordinality (Peano), or cardinality (set theory). | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.17) |
| 9965 | There couldn't just be one number, such as 17 [Jubien] |
| Full Idea: It makes no sense to suppose there might be just one natural number, say seventeen. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.113) | |
| A reaction: Hm. Not convinced. If numbers are essentially patterns, we might only have the number 'twelve', because we had built our religion around anything which exhibited that form (in any of its various arrangements). Nice point, though. |
| 9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
| Full Idea: The subject-matter of (pure) mathematics is abstract structure per se. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.115) | |
| A reaction: This is the Structuralist idea beginning to take shape after Benacerraf's launching of it. Note that Jubien gets there by his rejection of platonism, whereas some structuralist have given a platonist interpretation of structure. |
| 9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
| Full Idea: If the intuition of mathematical objects were general, there would be no real debate over platonism. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.111) | |
| A reaction: It is particularly perplexing when Gödel says that his perception of them is just like sight or smell, since I have no such perception. How do you individuate very large numbers, or irrational numbers, apart from writing down numerals? |
| 9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
| Full Idea: I am unable to see how the mere existence of pure abstract entities enables us to concoct appropriate models to serve as interpretations. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.111) | |
| A reaction: Nice question. It is always assumed that once we have platonic realm, that everything else follows. Even if we are able to grasp the objects, despite their causal inertness, we still have to discern innumerable relations between them. |
| 9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
| Full Idea: The essential properties of mathematical entities seem to be relational, ...so we make no progress unless we can pick out some mathematical entities wihout presupposing other entities already picked out. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.112) | |
| A reaction: [compressed] Jubien is a good critic of platonism. He has identified the problem with Frege's metaphor of a 'borehole', where we discover delightful new properties of numbers simply by reaching them. |
| 3310 | If slowness is a property of walking rather than the walker, we must allow that events exist [Benardete,JA] |
| Full Idea: Once we conceded that Tom can walk slowly or quickly, and that the slowness and quickness is a property of the walking and not of Tom, we can hardly refrain from quantifying over events (such as 'a walking') in our ontology. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch. 6) |
| 15561 | The events that suit semantics may not be the events that suit causation [Lewis] |
| Full Idea: There is no guarantee that events made for semantics are the same as events that are causes and effects. | |
| From: David Lewis (Events [1986], I) | |
| A reaction: This little cri de couer could be a motto for a huge amount of analytic philosophy, which (for some odd reason) thought that mathematics, logic, set theory and formal semantics were good tools for explaining nature. |
| 15565 | Events have inbuilt essences, as necessary conditions for their occurrence [Lewis] |
| Full Idea: Events have their essences built in, in the form of necessary conditions for their occurrence. | |
| From: David Lewis (Events [1986], III) | |
| A reaction: Revealing. He thinks the essence of an event is something which precedes the event. I take it as obvious that if an event has an essence, it will be some features of the event that occur in it and during it. They need to be intrinsic. |
| 15566 | Events are classes, and so there is a mereology of their parts [Lewis] |
| Full Idea: If events are classes, as I propose, then they have a mereology in the way that all classes do: the parts of a class are its subclasses. | |
| From: David Lewis (Events [1986], V) | |
| A reaction: Lewis says events are properties, which he regards as classes. It is not clear that events are strictly mereological. Could one happening be two events? Is WWII a simple sum of its parts? [see p.260] |
| 15567 | Some events involve no change; they must, because causal histories involve unchanges [Lewis] |
| Full Idea: Not all events involve change. We cannot afford to count the unchanges as nonevents, for the unchanges may be needed to complete causal histories. | |
| From: David Lewis (Events [1986], VI) | |
| A reaction: You end up calling non-changes 'events' if you commit to a simplistic theory that all causal histories consist of events. Why not allow conditions as well as events? Lewis concedes that he may be abusing language. |
| 15564 | An event is a property of a unique space-time region [Lewis] |
| Full Idea: I propose to identify an event with a property, or in other words with a class, a unique spatio-temporal region corresponding to where that event occurs. | |
| From: David Lewis (Events [1986], II) | |
| A reaction: [I've run together two separate bits, on p.244 and 245] Lewis cites Montague's similar view, that events are properties of times. |
| 12793 | Early pre-Socratics had a mass-noun ontology, which was replaced by count-nouns [Benardete,JA] |
| Full Idea: With their 'mass-noun' ontologies, the early pre-Socratics were blind to plurality ...but the count-noun ontologists came to dominate the field forever after. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch. 6) | |
| A reaction: The mass-nouns are such things as earth, air, fire and water. This is a very interesting historical observation (cited by Laycock). Our obsession with identity seems tied to formal logic. There is a whole other worldview waiting out there. |
| 15563 | Properties are very abundant (unlike universals), and are used for semantics and higher-order variables [Lewis] |
| Full Idea: Properties are abundant, numbering at least beth-3 for properties of individuals alone; they are suited to serve as semantic values of arbitrarily complex predicates and gerunds, and higher-order variables. (If there are universals, they are sparse). | |
| From: David Lewis (Events [1986], II n2) | |
| A reaction: To me this is an outrageous hijacking of the notion of property which is needed for explaining the natural world. He seems to be talking about predicates. He wants to leave me with his silly universals - well I don't want them, thank you. |
| 3353 | If there is no causal interaction with transcendent Platonic objects, how can you learn about them? [Benardete,JA] |
| Full Idea: How can you learn of the existence of transcendent Platonic objects if there is no causal interaction with them? | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.22) |
| 9969 | The empty set is the purest abstract object [Jubien] |
| Full Idea: The empty set is the pure abstract object par excellence. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.118 n8) | |
| A reaction: So a really good PhD on the empty set could crack the whole nature of reality. Get to work, whoever you are! |
| 3304 | Why should packed-together particles be a thing (Mt Everest), but not scattered ones? [Benardete,JA] |
| Full Idea: Why suppose these particles packed together constitute a macro-entity (namely, Mt Everest), whereas those, of equal number, scattered around, fail to add up to anything beyond themselves? | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch. 2) |
| 3350 | Could a horse lose the essential property of being a horse, and yet continue to exist? [Benardete,JA] |
| Full Idea: Is being a horse an essential property of a horse? Can we so much as conceive the abstract possibility of a horse's ceasing to be a horse even while continuing to exist? | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.20) |
| 3309 | If a soldier continues to exist after serving as a soldier, does the wind cease to exist after it ceases to blow? [Benardete,JA] |
| Full Idea: If a soldier need not cease to exist merely because he ceases to be a soldier, there is room to doubt that the wind ceases to exist when it ceases to be a wind. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch. 6) |
| 3351 | One can step into the same river twice, but not into the same water [Benardete,JA] |
| Full Idea: One can step into the same river twice, but one must not expect to step into the same water. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.21) |
| 3314 | Absolutists might accept that to exist is relative, but relative to what? How about relative to itself? [Benardete,JA] |
| Full Idea: With the thesis that to be as such is to be relative, the absolutist may be found to concur, but the issue turns on what it might be that a thing is supposed to be relative to. Why not itself? | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch. 8) |
| 3323 | Maybe self-identity isn't existence, if Pegasus can be self-identical but non-existent [Benardete,JA] |
| Full Idea: 'Existence' can't be glossed as self-identical (critics say) because Pegasus, even while being self-identical, fails to exist. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.11) |
| 3306 | The clearest a priori knowledge is proving non-existence through contradiction [Benardete,JA] |
| Full Idea: One proves non-existence (e.g. of round squares) by using logic to derive a contradiction from the concept; it is precisely here, in such proofs, that we find the clearest example of a priori knowledge. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch. 4) |
| 3349 | If we know truths about prime numbers, we seem to have synthetic a priori knowledge of Platonic objects [Benardete,JA] |
| Full Idea: Assume that we know to be true propositions of the form 'There are exactly x prime numbers between y and z', and synthetic a priori truths about Platonic objects are delivered to us on a silver platter. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.18) |
| 3341 | Logical positivism amounts to no more than 'there is no synthetic a priori' [Benardete,JA] |
| Full Idea: Logical positivism has been concisely summarised as 'there is no synthetic a priori'. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.18) |
| 3344 | Assertions about existence beyond experience can only be a priori synthetic [Benardete,JA] |
| Full Idea: No one thinks that the proposition that something exists that transcends all possible experience harbours a logical inconsistency. Its denial cannot therefore be an analytic proposition, so it must be synthetic, though only knowable on a priori grounds. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.18) |
| 3345 | Appeals to intuition seem to imply synthetic a priori knowledge [Benardete,JA] |
| Full Idea: Appeals to intuition - no matter how informal - can hardly fail to smack of the synthetic a priori. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.18) |
| 15562 | Causation is a general relation derived from instances of causal dependence [Lewis] |
| Full Idea: Causation is the ancestral of causal dependence: event c causes event e iff either e depends on c, or e depends on an intermediate event which in turn depends on c, or.... | |
| From: David Lewis (Events [1986], I) | |
| A reaction: This is Lewis making sure that we don't postulate some huge bogus thing called 'Causation' which is supposed to be in charge of Nature. Good point. |
| 3334 | Rationalists see points as fundamental, but empiricists prefer regions [Benardete,JA] |
| Full Idea: Rationalists have been happier with an ontology of points, and empiricists with an ontology of regions. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.16) |
| 3308 | In the ontological argument a full understanding of the concept of God implies a contradiction in 'There is no God' [Benardete,JA] |
| Full Idea: In the ontological argument a deep enough understanding of the very concept of God allows one to derive by logic a contradiction from the statement 'There is no God'. | |
| From: José A. Benardete (Metaphysics: the logical approach [1989], Ch. 4) |