57 ideas
| 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. |
| 3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
| Full Idea: Von Neumann defines each number as the set of all smaller numbers. | |
| From: report of John von Neumann (works [1935]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280 |
| 3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
| Full Idea: Von Neumann suggested that functions be pressed into service to replace sets. | |
| From: report of John von Neumann (works [1935]) by José A. Benardete - Metaphysics: the logical approach Ch.23 |
| 15592 | The usual Tarskian interpretation of variables is to specify their range of values [Fine,K] |
| Full Idea: The usual Tarskian way of indicating how a variable is to be interpreted is to simply specify its range of values. | |
| From: Kit Fine (Semantic Relationism [2007], 1.B) |
| 15593 | Variables can be viewed as special terms - functions taking assignments into individuals [Fine,K] |
| Full Idea: The alternative Tarskian way of indicating how a variable is to be interpreted is that a variable x will be a special case of the semantic value of the term; it will be a function which takes each assignment into the individual which it assigns to x. | |
| From: Kit Fine (Semantic Relationism [2007], 1.B) |
| 15590 | It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that [Fine,K] |
| Full Idea: Once Frege had provided a clear syntactic account of variables and once Tarski had supplemented this with a rigorous semantic account, it would appear that there was nothing more of significance to be said. | |
| From: Kit Fine (Semantic Relationism [2007], 1) | |
| A reaction: He later remarks that there are now three semantic accounts: the Tarskian, the instantial, and the algebraic [see xref ideas]. He offers a fourth account in his Semantic Relationism. This grows from his puzzles about variables. |
| 15591 | In separate expressions variables seem identical in role, but in the same expression they aren't [Fine,K] |
| Full Idea: When we consider the semantic role of 'x' and 'y' in two distinct expressions x>0 and y>0, their semantic roles seems the same. But in the same expression, such as x>y, their roles seem to be different. | |
| From: Kit Fine (Semantic Relationism [2007], 1.A) | |
| A reaction: [compressed] This new puzzle about variables leads Fine to say that the semantics of variables, and other expressions, is not intrinsic to them, but depends on their external relations. Variables denote any term - unless another variable got there first. |
| 15595 | The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K] |
| Full Idea: In the 'algebraic' approach to variables, we move from a quantified sentence to the term specifying a property (the λ-term), and then reducing to the algebraic operations for atomic formulas. | |
| From: Kit Fine (Semantic Relationism [2007], 1.C) | |
| A reaction: [Bealer is a source for this view] Fine describes it as an 'algebra of operations'. I presume this is a thoroughly formalist approach to the matter, which doesn't seem to get to the heart of the semantic question. |
| 15594 | 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K] |
| Full Idea: According to the 'instantial' approach to variables, a closed quantified sentence is to be understood on the basis of one of its instances; from an understanding of an instance we understand satisfaction by an arbitrary individual. | |
| From: Kit Fine (Semantic Relationism [2007], 1.D) | |
| A reaction: Fine comments that this is intuitively plausible, but not very precise, because it depends on 'abstraction' of the individual from the expression. |
| 15599 | Cicero/Cicero and Cicero/Tully may differ in relationship, despite being semantically the same [Fine,K] |
| Full Idea: There may be a semantic relationship between 'Cicero' and 'Cicero' that does not hold between 'Cicero' and 'Tully', despite the lack of an intrinsic semantic difference between the names themselves. | |
| From: Kit Fine (Semantic Relationism [2007], 2.E) | |
| A reaction: This is the key idea of Fine's book, and a most original and promising approach to a rather intractable problem in reference. He goes on to distinguish names which are 'strictly' coreferential (the first pair) from those that are 'accidentally' so. |
| 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 |
| 22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
| Full Idea: At age twenty, Von Neumann devised the formal definition of ordinal numbers that is used today: an ordinal number is the set of all smaller ordinal numbers. | |
| From: report of John von Neumann (works [1935]) by William Poundstone - Prisoner's Dilemma 02 'Sturm' | |
| A reaction: I take this to be an example of an impredicative definition (not predicating something new), because it uses 'ordinal number' in the definition of ordinal number. I'm guessing the null set gets us started. |
| 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. |
| 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) |
| 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. |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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. |
| 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) |
| 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) |
| 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) |
| 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. |
| 15603 | I can only represent individuals as the same if I do not already represent them as the same [Fine,K] |
| Full Idea: I can only represent two individuals as being the same if I do not already represent them as the same. | |
| From: Kit Fine (Semantic Relationism [2007], 3.A) | |
| A reaction: A very nice simple point. If I say 'Hesperus is Hesperus' I am unable to comment on the object, but 'Hesperus is Phosphorus' has a different expressive power. Start from contexts where it is necessary to say that two things are actually one. |
| 15604 | If Cicero=Tully refers to the man twice, then surely Cicero=Cicero does as well? [Fine,K] |
| Full Idea: 'Cicero=Cicero' and 'Cicero=Tully' are both dyadic predications. It is unnatural to suppose that the use of the same name converts a dyadic predicate into a reflexive predicate, or that there is one reference to Cicero in the first and two in the second. | |
| From: Kit Fine (Semantic Relationism [2007], 3.A) | |
| A reaction: I am deeply suspicious of the supposed 'property' of being self-identical, but that may not deny that it could be a genuine truth (shorthand for 'the C you saw is the same as the C I saw'). Having an identity makes equality with self possible. |
| 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. |
| 15602 | Mental files are devices for keeping track of basic coordination of objects [Fine,K] |
| Full Idea: Mental files should be seen as a device for keeping track of when objects are coordinated (represented as-the-same) and, rather than understand coordination in terms of mental files, we should understand mental files in terms of coordination. | |
| From: Kit Fine (Semantic Relationism [2007], 3.A) | |
| A reaction: Personally I think that the metaphor of a 'label' is much closer to the situation than that of a 'file'. Thus my concept of Cicero is labelled 'Tully', 'Roman', 'orator', 'philosophical example'... My problem is to distinguish the concept from its labels. |
| 15588 | You cannot determine the full content from a thought's intrinsic character, as relations are involved [Fine,K] |
| Full Idea: There is no determining the full content of what someone thinks or believes from the individual things that he thinks or believes; we must also look at the threads that tie the contents of these thoughts or beliefs together. | |
| From: Kit Fine (Semantic Relationism [2007], Intro) | |
| A reaction: I'm not sure what 'full' content could possibly mean. Does that include all our background beliefs which we hardly ever articulate. Content comes in degrees, or needs an arbitrary boundary? |
| 15596 | The standard aim of semantics is to assign a semantic value to each expression [Fine,K] |
| Full Idea: The aim of semantics, as standardly conceived, is to assign a semantic value to each (meaningful) expression of the language under consideration. | |
| From: Kit Fine (Semantic Relationism [2007], 1.G) | |
| A reaction: Fine is raising the difficulty that these values can get entangled with one another. He proposes 'semantic connections' as a better aim. |
| 15587 | That two utterances say the same thing may not be intrinsic to them, but involve their relationships [Fine,K] |
| Full Idea: In my 'Semantic Relationism' the fact that two utterances say the same thing is not entirely a matter of their intrinsic semantic features; it may also turn on semantic relationships among the utterances of their parts not reducible to those features. | |
| From: Kit Fine (Semantic Relationism [2007], Intro) | |
| A reaction: You'll need to read the book slowly several times to get the hang of this, but at least it allows that two different utterances might say the same thing (express the same proposition, I would say). |
| 15589 | The two main theories are Holism (which is inferential), and Representational (which is atomistic) [Fine,K] |
| Full Idea: For holists a proper theory will be broadly inferential, while for their opponents it will be representational in character, describing relations between expressions and reality. Representational semantics is atomist, holist semantics inferential. | |
| From: Kit Fine (Semantic Relationism [2007], Intro) | |
| A reaction: Fine presents these as the two main schools in semantics. His own theory then proposes a more holistic version of the Representational view. He seeks the advantages of Frege's position, but without 'sense'. |
| 15598 | We should pursue semantic facts as stated by truths in theories (and not put the theories first!) [Fine,K] |
| Full Idea: A 'semantics' is a body of semantic facts, and a 'semantic theory' is a body of semantic truths. The natural order is a theory being understood as truths, which state facts. Davidson, alas, reversed this order, with facts understood through theories. | |
| From: Kit Fine (Semantic Relationism [2007], 2.C) | |
| A reaction: [compressed; he cites Davidson 1967, and calls it 'one of the most unfortunate tendencies in modern philosophy of language, ..as if chemistry were understood in terms of formulae rather than chemical facts']. |
| 15600 | Referentialist semantics has objects for names, properties for predicates, and propositions for connectives [Fine,K] |
| Full Idea: The standard referentialist semantics for a language with names is that the semantic value of the name is the object, the content of a predicate is a property, and the content of a logical connective is an operation on propositions. | |
| From: Kit Fine (Semantic Relationism [2007], 2.F) | |
| A reaction: My particular bęte noire is the idea that every predicate names a property. It is the tyranny of having to have a comprehensive semantic theory that drives this implausible picture. And I don't see how an object can be a semantic value… |
| 15601 | Fregeans approach the world through sense, Referentialists through reference [Fine,K] |
| Full Idea: Fregeans emphasise an orientation towards the speaker: possession of sense makes language meaningful, and language relates to the world through sense. For the Referentialist its representational relationships make it meaningful, and relate it to the world | |
| From: Kit Fine (Semantic Relationism [2007], 2.G) | |
| A reaction: The Referentialist approach is for Kripkean fans of direct reference, rather than the Fregean reference through descriptions. I am inclined to favour the old-fashioned, deeply discredited, much mocked Fregean approach. |
| 15605 | I take indexicals such as 'this' and 'that' to be linked to some associated demonstration [Fine,K] |
| Full Idea: Demonstrative uses of an indexical such as 'this' or 'that' should be taken to be anaphoric on an associated demonstration. It is a semantic requirement on the use of the indexical that it be coreferential with the demonstration. | |
| From: Kit Fine (Semantic Relationism [2007], Post 'Indexicals') | |
| A reaction: Similarly 'now' must connect to looking at a clock, and 'I' to pointing at some person. The demonstration could be of a verbal event, as much as a physical one. |
| 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. |
| 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) |