52 ideas
8349 | The best way to do ontology is to make sense of our normal talk [Davidson] |
Full Idea: I do not know any better way of showing what there is than looking at the assumptions needed to make sense of our normal talk. | |
From: Donald Davidson (Causal Relations [1967], §4) | |
A reaction: Davidson was a pupil of Quine. This I take to be the last flowering of twentieth century linguistic philosophy. The ontology we deduce from talk in a children's playground might be very bizarre, but we are unlikely to endorse it. 'Honest, it's true!' |
224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
Full Idea: Doubtful questions should not be discussed in terms of visible objects or in relation to them, but only with reference to ideas conceived by the intellect. | |
From: Plato (Parmenides [c.364 BCE], 135e) |
232 | Opposites are as unlike as possible [Plato] |
Full Idea: Opposites are as unlike as possible. | |
From: Plato (Parmenides [c.364 BCE], 159a) |
8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
Full Idea: Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic. | |
From: comment on Plato (Parmenides [c.364 BCE]) by Georg W.F.Hegel - Phenomenology of Spirit Pref 71 | |
A reaction: It is a long way from the analytic tradition of philosophy to be singling out a classic text for its 'artistic' achievement. Eventually we may even look back on, say, Kripke's 'Naming and Necessity' and see it in that light. |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
Full Idea: Impredicative Definitions are definitions of an object by reference to the totality to which the object itself (and perhaps also things definable only in terms of that object) belong. | |
From: Kurt Gödel (Russell's Mathematical Logic [1944], n 13) |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
Full Idea: In the superior realist and simple theory of types, the place of the axiom of reducibility is not taken by the axiom of classes, Zermelo's Aussonderungsaxiom. | |
From: report of Kurt Gödel (Russell's Mathematical Logic [1944], p.140-1) by Bernard Linsky - Russell's Metaphysical Logic 6.1 n3 | |
A reaction: This is Zermelo's Axiom of Separation, but that too is not an axiom of standard ZFC. |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
Full Idea: 'Mathematical Logic' is a precise and complete formulation of formal logic, and is both a section of mathematics covering classes, relations, symbols etc, and also a science prior to all others, with ideas and principles underlying all sciences. | |
From: Kurt Gödel (Russell's Mathematical Logic [1944], p.447) | |
A reaction: He cites Leibniz as the ancestor. In this database it is referred to as 'theory of logic', as 'mathematical' seems to be simply misleading. The principles of the subject are standardly applied to mathematical themes. |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
Full Idea: One may, on good grounds, deny that reference to a totality necessarily implies reference to all single elements of it or, in other words, that 'all' means the same as an infinite logical conjunction. | |
From: Kurt Gödel (Russell's Mathematical Logic [1944], p.455) |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
Full Idea: In order to be sure that new expression can be translated into expressions not containing them, it is necessary to have a survey of all possible expressions, and this can be furnished only by syntactical considerations. | |
From: Kurt Gödel (Russell's Mathematical Logic [1944], p.448) | |
A reaction: [compressed] |
13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
Full Idea: Plato (in 'Parmenides') shows that the theory that 'Eide' are substances, and Kant that space and time are substances, and Bradley that relations are substances, all lead to aninomies. | |
From: report of Plato (Parmenides [c.364 BCE]) by Gilbert Ryle - Are there propositions? 'Objections' |
14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
Full Idea: Plato's 'Parmenides' is perhaps the best collection of antinomies ever made. | |
From: comment on Plato (Parmenides [c.364 BCE]) by Bertrand Russell - The Principles of Mathematics §337 |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
Full Idea: The generalized Continuum Hypothesis says that there exists no cardinal number between the power of any arbitrary set and the power of the set of its subsets. | |
From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
Full Idea: It has turned out that the solution of certain arithmetical problems requires the use of assumptions essentially transcending arithmetic. | |
From: Kurt Gödel (Russell's Mathematical Logic [1944], p.449) | |
A reaction: A nice statement of the famous result, from the great man himself, in the plainest possible English. |
16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
From: Plato (Parmenides [c.364 BCE], 144a) | |
A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
Full Idea: Classes and concepts may be conceived of as real objects, ..and are as necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions, with neither case being about 'data'. | |
From: Kurt Gödel (Russell's Mathematical Logic [1944], p.456) | |
A reaction: Note that while he thinks real objects are essential for mathematics, be may not be claiming the same thing for our knowledge of logic. If logic contains no objects, then how could mathematics be reduced to it, as in logicism? |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
Full Idea: Impredicative definitions are admitted into ordinary mathematics. | |
From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) | |
A reaction: The issue is at what point in building an account of the foundations of mathematics (if there be such, see Putnam) these impure definitions should be ruled out. |
229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
Full Idea: The one was and is and will be and was becoming and is becoming and will become. | |
From: Plato (Parmenides [c.364 BCE], 155d) | |
A reaction: This seems to be rhetorical, rather a precise theory, given that the One is said to be eternal and unchanging. The One is not just what we call 'reality'. |
21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
Full Idea: The Platonic Parmenides is more exact [than Parmenides himself]; the distinction is made between the Primal One, a strictly pure Unity, and a secondary One which is a One-Many, and a third which is a One-and-Many. | |
From: report of Plato (Parmenides [c.364 BCE]) by Plotinus - The Enneads 5.1.08 | |
A reaction: Plotinus approves of this three-part theory. Parmenides has the problem that the highest Being contains no movement. By placing the One outside Being you can give it powers which an existent thing cannot have. Cf the concept of God. |
8348 | If we don't assume that events exist, we cannot make sense of our common talk [Davidson] |
Full Idea: The assumption, ontological and metaphysical, that there are events, is one without which we cannot make sense of much of our most common talk. | |
From: Donald Davidson (Causal Relations [1967], §4) | |
A reaction: He considers events to be unanalysable basics. Explanation of normal talk also needs ghosts, premonitions, telepathy and Father Christmas. It is extremely hard to individuate events, unless they are subatomic, and rather numerous. |
221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
Full Idea: The absolute good and the beautiful and all which we conceive to be absolute ideas are unknown to us. | |
From: Plato (Parmenides [c.364 BCE], 134c) | |
A reaction: These seems to thoroughly pre-empt Plato's Theory of Forms a century before he created it. Which shows (as Simone Weil says) that Plato was just part of a long tradition. |
227 | You must always mean the same thing when you utter the same name [Plato] |
Full Idea: You must always mean the same thing when you utter the same name. | |
From: Plato (Parmenides [c.364 BCE], 147d) |
223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
Full Idea: If a person denies that the idea of each thing is always the same, he will utterly destroy the power of carrying on discussion. | |
From: Plato (Parmenides [c.364 BCE], 135c) |
210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
Full Idea: Are there abstract ideas for such things as hair, mud and dirt, which are particularly vile and worthless? That would be quite absurd. | |
From: Plato (Parmenides [c.364 BCE], 130d) |
219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
Full Idea: None of the absolute ideas exists in us, because then it would no longer be absolute. | |
From: Plato (Parmenides [c.364 BCE], 133c) |
228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
Full Idea: These two ideas, greatness and smallness, exist, do they not? For if they did not exist, they could not be opposites of one another, and could not come into being in things. | |
From: Plato (Parmenides [c.364 BCE], 149e) |
211 | If admirable things have Forms, maybe everything else does as well [Plato] |
Full Idea: It is troubling that if admirable things have abstract ideas, then perhaps everything else must have ideas as well. | |
From: Plato (Parmenides [c.364 BCE], 130d) |
220 | The concept of a master includes the concept of a slave [Plato] |
Full Idea: Mastership in the abstract is mastership of slavery in the abstract. | |
From: Plato (Parmenides [c.364 BCE], 133e) |
16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
Full Idea: It seems to me that Plato in the later dialogues, beginning with the second half of 'Parmenides', wants to substitute a theory of genera and theory of principles that constitute these genera for the earlier theory of forms. | |
From: report of Plato (Parmenides [c.364 BCE]) by Michael Frede - Title, Unity, Authenticity of the 'Categories' V | |
A reaction: My theory is that the later Plato came under the influence of the brilliant young Aristotle, and this idea is a symptom of it. The theory of 'principles' sounds like hylomorphism to me. |
215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
Full Idea: If all things partake of ideas, must either everything be made of thoughts and everything thinks, or everything is thought, and so can't think? | |
From: Plato (Parmenides [c.364 BCE], 132c) |
212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
Full Idea: The whole idea of each form (of beauty, justice etc) must be found in each thing which participates in it. | |
From: Plato (Parmenides [c.364 BCE], 131a) |
213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
Full Idea: Just as day is in many places at once, but not separated from itself, so each idea might be in all its participants at once. | |
From: Plato (Parmenides [c.364 BCE], 131b) |
216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
Full Idea: That by participation in which like things are made like, will be the absolute idea, will it not? | |
From: Plato (Parmenides [c.364 BCE], 132e) |
218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
Full Idea: Participation is not by means of likeness, so we must seek some other method of participation. | |
From: Plato (Parmenides [c.364 BCE], 133a) |
217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
Full Idea: It is impossible for anything to be like an absolute idea, because a third idea will appear to make them alike, and if that is like anything, it will lead to another idea, and so on. | |
From: Plato (Parmenides [c.364 BCE], 133a) |
214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
Full Idea: If you regard the absolute great and the many great things in the same way, will not another appear beyond, by which all these must appear to be great? | |
From: Plato (Parmenides [c.364 BCE], 132a) |
15851 | Parts must belong to a created thing with a distinct form [Plato] |
Full Idea: The part would not be the part of many things or all, but of some one character ['ideas'] and of some one thing, which we call a 'whole', since it has come to be one complete [perfected] thing composed [created] of all. | |
From: Plato (Parmenides [c.364 BCE], 157d) | |
A reaction: A serious shot by Plato at what identity is. Harte quotes it (125) and shows that 'character' is Gk 'idea', and 'composed' will translate as 'created'. 'Form' links this Platonic passage to Aristotle's hylomorphism. |
15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
Full Idea: At the heart of the 'Parmenides' puzzles about composition is the thesis that composition is identity. Considered thus, a whole adds nothing to an ontology that already includes its parts | |
From: report of Plato (Parmenides [c.364 BCE]) by Verity Harte - Plato on Parts and Wholes 2.5 | |
A reaction: There has to be more to a unified identity that mere proximity of the parts. When do parts come together, and when do they actually 'compose' something? |
15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
Full Idea: In 'Parmenides' it is argued that a part cannot be part of a many, but must be part of something one. | |
From: report of Plato (Parmenides [c.364 BCE], 157c) by Verity Harte - Plato on Parts and Wholes 3.2 | |
A reaction: This looks like the right way to go with the term 'part'. We presuppose a unity before we even talk of its parts, so we can't get into contradictions and paradoxes about their relationships. |
15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
Full Idea: The whole of which the parts are parts must be one thing composed of many; for each of the parts must be part, not of a many, but of a whole. | |
From: Plato (Parmenides [c.364 BCE], 157c) | |
A reaction: This is a key move of metaphysics, and we should hang on to it. The other way madness lies. |
13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
Full Idea: The One must be composed of parts, both being a whole and having parts. So on both grounds the One would thus be many and not one. But it must be not many, but one. So if the One will be one, it will neither be a whole, nor have parts. | |
From: Plato (Parmenides [c.364 BCE], 137c09), quoted by Kathrin Koslicki - The Structure of Objects 5.2 | |
A reaction: This is the starting point for Plato's metaphysical discussion of objects. It seems to begin a line of thought which is completed by Aristotle, surmising that only an essential structure can bestow identity on a bunch of parts. |
15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
Full Idea: Everything is surely related to everything as follows: either it is the same or different; or, if it is not the same or different, it would be related as part to whole or as whole to part. | |
From: Plato (Parmenides [c.364 BCE], 146b) | |
A reaction: This strikes me as a really helpful first step in trying to analyse the nature of identity. Two things are either two or (actually) one, or related mereologically. |
8347 | Explanations typically relate statements, not events [Davidson] |
Full Idea: Explanations typically relate statements, not events. | |
From: Donald Davidson (Causal Relations [1967], §4) | |
A reaction: An oddly linguistic way of putting our attempts to understand the world. Presumably the statements are supposed to be about the events (or whatever), and they are supposed to be true, so we are trying to relate features of the world. |
222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
Full Idea: Only a man of very great natural gifts will be able to understand that everything has a class and absolute essence, and an even more wonderful man can teach this. | |
From: Plato (Parmenides [c.364 BCE], 135a) |
225 | The unlimited has no shape and is endless [Plato] |
Full Idea: The unlimited partakes neither of the round nor of the straight, because it has no ends nor edges. | |
From: Plato (Parmenides [c.364 BCE], 137e) |
233 | Some things do not partake of the One [Plato] |
Full Idea: The others cannot partake of the one in any way; they can neither partake of it nor of the whole. | |
From: Plato (Parmenides [c.364 BCE], 159d) | |
A reaction: Compare Idea 231 |
2062 | The only movement possible for the One is in space or in alteration [Plato] |
Full Idea: If the One moves it either moves spatially or it is altered, since these are the only motions. | |
From: Plato (Parmenides [c.364 BCE], 138b) |
231 | Everything partakes of the One in some way [Plato] |
Full Idea: The others are not altogether deprived of the one, for they partake of it in some way. | |
From: Plato (Parmenides [c.364 BCE], 157c) | |
A reaction: Compare Idea 233. |
10371 | Distinguish causation, which is in the world, from explanations, which depend on descriptions [Davidson, by Schaffer,J] |
Full Idea: Davidson distinguishes between causation, an extensional relation that holds between coarse events, and explanation, which is an intensional relation that holds between the coarse events under a description. | |
From: report of Donald Davidson (Causal Relations [1967]) by Jonathan Schaffer - The Metaphysics of Causation 1.2 | |
A reaction: I'm unclear why everything has to be so coarse, when reality and causal events seem to fine-grained, but the distinction strikes me as good. Explanations relate to human understanding and human interests. Cf. Anscombe's view. |
8403 | Either facts, or highly unspecific events, serve better as causes than concrete events [Field,H on Davidson] |
Full Idea: It is best to avoid Davidson's view that only quite concrete events can serve as causes; we should either say that facts as well as events can serve as causes; or that the events can be highly unspecific, including 'omissions'. | |
From: comment on Donald Davidson (Causal Relations [1967]) by Hartry Field - Causation in a Physical World 1 | |
A reaction: Something NOT happening might be the main cause of an effect (drought), or an effect may mainly result from a situation rather than an event (famine). |
8346 | Full descriptions can demonstrate sufficiency of cause, but not necessity [Davidson] |
Full Idea: The fuller we make the description of a cause, the better our chances of demonstrating that it was sufficient (as described) to produce the effect, and the worse our chances of demonstrating that it was necessary. (For the effect, it is the opposite). | |
From: Donald Davidson (Causal Relations [1967], §3) | |
A reaction: If the fullness of description is relevant, this suggests that Davidson is focusing on human explanations, rather than on the ontology of causation. If the cause IS necessary, why wouldn't a better description make that clearer? |
4778 | A singular causal statement is true if it is held to fall under a law [Davidson, by Psillos] |
Full Idea: For Davidson, what makes singular causal statements true is the existence of some regularities or laws. All causal is nomological: c causes e iff there is a law that connects events like c with events like e. | |
From: report of Donald Davidson (Causal Relations [1967]) by Stathis Psillos - Causation and Explanation §2.6 | |
A reaction: I wonder if the cart is before the horse here. Scriven says this is just a claim that there are "phantom laws". It is the Humean view of causation, but surely the laws come after the causation, so can't be used to explain it? |
234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |
Full Idea: There must be knowledge of the one, or else not even the meaning of the words 'if the one does not exist' would be known. | |
From: Plato (Parmenides [c.364 BCE], 160d) |