52 ideas
10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
Full Idea: It is often the case that the concern for rigor gets in the way of a true understanding of the phenomena to be explained. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
A reaction: This is a counter to Timothy Williamson's love affair with rigour in philosophy. It strikes me as the big current question for analytical philosophy - of whether the intense pursuit of 'rigour' will actually deliver the wisdom we all seek. |
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. |
10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
Full Idea: There is no stage at which we can take all the sets to have been generated, since the set of all those sets which have been generated at a given stage will itself give us something new. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
Full Idea: We might combine the standard axioms of set theory with the standard axioms of mereology. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
Full Idea: We are tempted to ask of second-order quantifiers 'what are you quantifying over?', or 'when you say "for some F" then what is the F?', but these questions already presuppose that the quantifiers are first-order. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005]) |
10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
Full Idea: In doing semantics we normally assign some appropriate entity to each predicate, but this is largely for technical convenience. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
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 |
10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
Full Idea: Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
A reaction: See Idea 10572. |
10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
Full Idea: By what right can Dedekind suppose that there is a number corresponding to any pair of irrationals that constitute an irrational cut? | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
Full Idea: What is the union of the singleton {0}, of zero, and the singleton {φ}, of the null set? Is it the one-element set {0}, or the two-element set {0, φ}? Unless the question of identity between 0 and φ is resolved, we cannot say. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
Full Idea: Set-theoretic imperialists think that it must be possible to represent every mathematical object as a set. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
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. |
10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
Full Idea: Logicists traditionally claim that the theorems of mathematics can be derived by logical means from the relevant definitions of the terms, and that these theorems are epistemically innocent (knowable without Kantian intuition or empirical confirmation). | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
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. |
10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
Full Idea: It is natural to have a generative conception of abstracts (like the iterative conception of sets). The abstracts are formed at stages, with the abstracts formed at any given stage being the abstracts of those concepts of objects formed at prior stages. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
A reaction: See 10567 for Fine's later modification. This may not guarantee 'levels', but it implies some sort of conceptual priority between abstract entities. |
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. |
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) |
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) |
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) |
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) |
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) |
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. |
10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
Full Idea: Abstraction-theoretic imperialists think that it must be possible to represent every mathematical object as a Fregean abstract. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
Full Idea: I propose a unified theory which is a version of ZF or ZFC with urelements, where the urelements are taken to be the abstracts. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
Full Idea: Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
A reaction: The point is that no particular object is now required to make the abstraction. |
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. |
7829 | God no more has human perfections than we have animal perfections [Spinoza] |
Full Idea: To ascribe to God those attributes which make a man perfect would be as wrong as to ascribe to a man the attributes that make perfect an elephant or an ass. | |
From: Baruch de Spinoza (Letters to Blijenburgh [1665], 1665), quoted by Matthew Stewart - The Courtier and the Heretic Ch.10 | |
A reaction: This would be a difficulty for Aquinas's Fourth Way (Idea 1432), and one which I think Aquinas might acknowledge, given his desire that we should be humble when trying to comprehend God (Idea 1410). It leaves us struggling to grasp the concept of God. |
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) |
7830 | A talking triangle would say God is triangular [Spinoza] |
Full Idea: If a triangle could speak it would say that God is eminently triangular. | |
From: Baruch de Spinoza (Letters to Blijenburgh [1665], 1665), quoted by Matthew Stewart - The Courtier and the Heretic Ch.10 | |
A reaction: Spinoza had a rather appealing waspish wit. This nicely dramatises an ancient idea (Idea 407). You can, of course, if you believe in God, infer some of His characteristics from His creation. But then see Hume: Ideas 1439, 6960, 6967, 1440. |