81 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. |
9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
Full Idea: Until the 1960s standard truth-table semantics were the only ones that there were. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.10.1) | |
A reaction: The 1960s presumably marked the advent of possible worlds. |
9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
Full Idea: 'dom R' indicates the 'domain' of a relation, that is, the set of all objects that are members of ordered pairs and that have that relation. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
Full Idea: 'fld R' indicates the 'field' of a relation, that is, the set of all objects that are members of ordered pairs on either side of the relation. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
Full Idea: 'ran R' indicates the 'range' of a relation, that is, the set of all objects that are members of ordered pairs and that are related to by the first objects. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
Full Idea: We write F : A → B to indicate that A maps into B, that is, the domain of relating things is set A, and the things related to are all in B. If we add that F = B, then A maps 'onto' B. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
Full Idea:
F(x) is a 'function', which indicates the unique value which y takes in |
|
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
Full Idea: The 'powerset' of a set is all the subsets of a given set. Thus: PA = {x : x ⊆ A}. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
Full Idea: Two sets are 'disjoint' iff their intersection is empty (i.e. they have no members in common). | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
Full Idea: The 'domain' of a relation is the set of all objects that are members of ordered pairs that are members of the relation. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9701 | A 'relation' is a set of ordered pairs [Enderton] |
Full Idea: A 'relation' is a set of ordered pairs. The ordering relation on the numbers 0-3 is captured by - in fact it is - the set of ordered pairs {<0,1>,<0,2>,<0,3>,<1,2>,<1,3>,<2,3>}. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) | |
A reaction: This can't quite be a definition of order among numbers, since it relies on the notion of a 'ordered' pair. |
9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
Full Idea: A 'function' is a relation which is single-valued. That is, for each object, there is only one object in the function set to which that object is related. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
Full Idea: A function 'maps A into B' if the domain of relating things is set A, and the things related to are all in B. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
Full Idea: A function 'maps A onto B' if the domain of relating things is set A, and the things related to are set B. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
Full Idea: A relation is 'reflexive' on a set if every member of the set bears the relation to itself. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
Full Idea: A relation is 'symmetric' on a set if every ordered pair in the set has the relation in both directions. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
Full Idea: A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
Full Idea: A relation is 'transitive' on a set if the relation can be carried over from two ordered pairs to a third. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
Full Idea: A relation satisfies 'trichotomy' on a set if every ordered pair is related (in either direction), or the objects are identical. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
Full Idea: An 'equivalence relation' is a binary relation which is reflexive, and symmetric, and transitive. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
Full Idea: Equivalence classes will 'partition' a set. That is, it will divide it into distinct subsets, according to each relation on the set. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
Full Idea: The process is dubbed 'conversational implicature' when the inference is not from the content of what has been said, but from the fact that it has been said. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.7.3) |
9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
Full Idea: The point of logic is to give an account of the notion of validity,..in two standard ways: the semantic way says that a valid inference preserves truth (symbol |=), and the proof-theoretic way is defined in terms of purely formal procedures (symbol |-). | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.3..) | |
A reaction: This division can be mirrored in mathematics, where it is either to do with counting or theorising about things in the physical world, or following sets of rules from axioms. Language can discuss reality, or play word-games. |
9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
Full Idea: A is a logical truth (tautology) (|= A) iff it is a semantic consequence of the empty set of premises (φ |= A), that is, every interpretation makes A true. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.3.4) | |
A reaction: So the final column of every line of the truth table will be T. |
9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
Full Idea: A truth assignment 'satisfies' a formula, or set of formulae, if it evaluates as True when all of its components have been assigned truth values. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.2) | |
A reaction: [very roughly what Enderton says!] The concept becomes most significant when a large set of wff's is pronounced 'satisfied' after a truth assignment leads to them all being true. |
9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
Full Idea: If every proof-theoretically valid inference is semantically valid (so that |- entails |=), the proof theory is said to be 'sound'. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.7) |
9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
Full Idea: If every semantically valid inference is proof-theoretically valid (so that |= entails |-), the proof-theory is said to be 'complete'. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.7) |
9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
Full Idea: If a wff is tautologically implied by a set of wff's, it is implied by a finite subset of them; and if every finite subset is satisfiable, then so is the whole set of wff's. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 2.5) | |
A reaction: [Enderton's account is more symbolic] He adds that this also applies to models. It is a 'theorem' because it can be proved. It is a major theorem in logic, because it brings the infinite under control, and who doesn't want that? |
9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
Full Idea: A set of expressions is 'decidable' iff there exists an effective procedure (qv) that, given some expression, will decide whether or not the expression is included in the set (i.e. doesn't contradict it). | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.7) | |
A reaction: This is obviously a highly desirable feature for a really reliable system of expressions to possess. All finite sets are decidable, but some infinite sets are not. |
9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
Full Idea: The Enumerability Theorem says that for a reasonable language, the set of valid wff's can be effectively enumerated. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 2.5) | |
A reaction: There are criteria for what makes a 'reasonable' language (probably specified to ensure enumerability!). Predicates and functions must be decidable, and the language must be finite. |
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 |
17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
Full Idea: If we count the concept 'coin in this box', we could regard coin as the 'unit', while taking 'in this box' to limit the scope. Counting coins in two boxes would be not a difference in unit (kind of object), but in scope. | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Counting') | |
A reaction: This is a very nice alternative to the Fregean view of counting, depending totally on the concept, and rests more on a natural concept of object. I prefer Ayers. Compare 'count coins till I tell you to stop'. |
17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
Full Idea: If we accepted that counting objects always presupposes some sortal, it is surely clear that the class of objects to be counted could be designated by two sortals rather than one. | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Realist' vii) | |
A reaction: His nice example is an object which is both 'a single piece of wool' and a 'sweater', which had better not be counted twice. Wiggins struggles to argue that there is always one 'substance sortal' which predominates. |
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) | |
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. |
17520 | Events do not have natural boundaries, and we have to set them [Ayers] |
Full Idea: In order to know which event has been ostensively identified by a speaker, the auditor must know the limits intended by the speaker. ...Events do not have natural boundaries. | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') | |
A reaction: He distinguishes events thus from natural objects, where the world, to a large extent, offers us the boundaries. Nice point. |
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) |
17519 | To express borderline cases of objects, you need the concept of an 'object' [Ayers] |
Full Idea: The only explanation of the power to produce borderline examples like 'Is this hazelnut one object or two?' is the possession of the concept of an object. | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Counting') |
17511 | Recognising continuity is separate from sortals, and must precede their use [Ayers] |
Full Idea: The recognition of the fact of continuity is logically independent of the possession of sortal concepts, whereas the formation of sortal concepts is at least psychologically dependent upon the recognition of continuity. | |
From: M.R. Ayers (Individuals without Sortals [1974], Intro) | |
A reaction: I take this to be entirely correct. I might add that unity must also be recognised. |
17510 | Speakers need the very general category of a thing, if they are to think about it [Ayers] |
Full Idea: If a speaker indicates something, then in order for others to catch his reference they must know, at some level of generality, what kind of thing is indicated. They must categorise it as event, object, or quality. Thinking about something needs that much. | |
From: M.R. Ayers (Individuals without Sortals [1974], Intro) | |
A reaction: Ayers defends the view that such general categories are required, but not the much narrower sortal terms defended by Geach and Wiggins. I'm with Ayers all the way. 'What the hell is that?' |
17522 | We use sortals to classify physical objects by the nature and origin of their unity [Ayers] |
Full Idea: Sortals are the terms by which we intend to classify physical objects according to the nature and origin of their unity. | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') | |
A reaction: This is as opposed to using sortals for the initial individuation. I take the perception of the unity to come first, so resemblance must be mentioned, though it can be an underlying (essentialist) resemblance. |
17515 | Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers] |
Full Idea: It is unnecessary to call moths 'caterpillars' or caterpillars 'moths' to see that they can be the same individual. It may be that our sortal concepts reflect our beliefs about continuity, but our beliefs about continuity need not reflect our sortals. | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Realist' vi) | |
A reaction: Something that metamorphosed through 15 different stages could hardly required 15 different sortals before we recognised the fact. Ayers is right. |
17517 | Could the same matter have more than one form or principle of unity? [Ayers] |
Full Idea: The abstract question arises of whether the same matter could be subject to more than one principle of unity simultaneously, or unified by more than one 'form'. | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Realist' vii) | |
A reaction: He suggests that the unity of the sweater is destroyed by unravelling, and the unity of the thread by cutting. |
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. |
17513 | If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers] |
Full Idea: The statue is marble and man-shaped, but so is the piece of marble. So not only are the two objects in the same place, but two marble and man-shaped objects in the same place, so 'that marble, man-shaped object' must be ambiguous or indefinite. | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Prob') | |
A reaction: It strikes me as basic that it can't be a piece of marble if you subtract its shape, and it can't be a statue if you subtract its matter. To treat a statue as an object, separately from its matter, is absurd. |
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. |
17523 | Sortals basically apply to individuals [Ayers] |
Full Idea: Sortals, in their primitive use, apply to the individual. | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') | |
A reaction: If the sortal applies to the individual, any essence must pertain to that individual, and not to the class it has been placed in. |
17521 | You can't have the concept of a 'stage' if you lack the concept of an object [Ayers] |
Full Idea: It would be impossible for anyone to have the concept of a stage who did not already possess the concept of a physical object. | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') |
17514 | Temporal 'parts' cannot be separated or rearranged [Ayers] |
Full Idea: Temporally extended 'parts' are still mysteriously inseparable and not subject to rearrangement: a thing cannot be cut temporally in half. | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Prob') | |
A reaction: A nice warning to anyone accepting a glib analogy between spatial parts and temporal parts. |
17509 | Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers] |
Full Idea: Some hold that the 'covering concept' completes the incomplete concept of identity, determining the kind of sameness involved. Others strongly deny the identity itself is incomplete, and locate the covering concept within the necessary act of reference. | |
From: M.R. Ayers (Individuals without Sortals [1974], Intro) | |
A reaction: [a bit compressed; Geach is the first view, and Quine the second; Wiggins is somewhere between the two] |
17512 | If diachronic identities need covering concepts, why not synchronic identities too? [Ayers] |
Full Idea: Why are covering concepts required for diachronic identities, when they must be supposed unnecessary for synchronic identities? | |
From: M.R. Ayers (Individuals without Sortals [1974], 'Prob') |
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. |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
Full Idea: Not all sentences using 'if' are conditionals. Consider 'if you want a banana, there is one in the kitchen'. The rough test is that a conditional can be rewritten as 'that A implies that B'. | |
From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.6.4) |
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) |