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. |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic. | |
From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5 | |
A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?). |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth. | |
From: George Boolos (On Second-Order Logic [1975], p.45) | |
A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification. |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts. | |
From: George Boolos (On Second-Order Logic [1975], p.44) | |
A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction? |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed. | |
From: George Boolos (On Second-Order Logic [1975], p.46) | |
A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain. |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
From: George Boolos (On Second-Order Logic [1975], p.52) | |
A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |
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 |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
Full Idea: The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity. | |
From: George Boolos (On Second-Order Logic [1975], p.48) |
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. |
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. |
21059 | General rules of action also need a judgement about when to apply them [Kant] |
Full Idea: A concept of the understanding, which contains the general rule, must be supplemented by an act of judgement whereby the practitioner distinguishes instances where the rule applies from those where it does not. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], Intro) | |
A reaction: This is Aristotle's phronesis, and Hart's 'rules of recognition' in law courts. So is the link between theory and practice an intellectual one, or a sort of inarticulate intuition? I like 'common sense' for this ability. |
21061 | Duty does not aim at an end, but gives rise to universal happiness as aim of the will [Kant] |
Full Idea: My conception of duty does not need to be based on any particular end, but rather itself occasions a new end for the human will, that of striving with all one's power towards the highest good possible on earth, the universal happiness of the whole world. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 1B) | |
A reaction: I see nothing in the categorical imperative that demands 'all one's power', and nothing that specifies happiness as what has to be universalised. Nietzsche, for one, thinks happiness is overrated. |
21060 | It can't be a duty to strive after the impossible [Kant] |
Full Idea: It would not be a duty to strive after a certain effect of our will if this effect were impossible in experience. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], Intro) | |
A reaction: 'Ought implies can' has become a familiar slogan. The quickest way to get shot of a tiresome duty is to persuade yourself that it is impossible. The seemingly impossible is occasionally achieved. |
21062 | The will's motive is the absolute law itself, and moral feeling is receptivity to law [Kant] |
Full Idea: The will must have motives. But these are not objects of physical feeling as predetermined ends in themselves. They are none other than the absolute law itself, and the will's receptivity to it as an absolute compulsion is known as moral feeling. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 1Bb) | |
A reaction: This sounds like our natural motivation to get the right answer when doing arithmetic, which is the innate motivation towards truth. I once heard it said that truth is the only value. So why does Donald Trump fail to value truth? |
21071 | There can be no restraints on freedom if reason does not reveal some basic rights [Kant] |
Full Idea: If there is nothing which commands immediate respect through reason, such as the basic rights of man, no influence can prevail upon man's arbitrary will and restrain his freedom. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-Concl) | |
A reaction: I think this is the nearest Kant gets to natural rights. It is hard to see how basic rights can be identified by pure reason, without some inbuilt human values. Kant's usual move is to say denial of them leads to a contradiction, but I'm going off that. |
21063 | Personal contracts are for some end, but a civil state contract involves a duty to share [Kant] |
Full Idea: In all social contracts, we find a union of many individuals for some common end which they all share. But a union as an end in itself which they all ought to share …is only found in a society insofar as it constitutes a civil state i.e. a commonwealth. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 2 Intro) | |
A reaction: This makes a nice link between the contractarian individual morality of Hobbes and his social contract view of society. Kant seems to reject the first but accept the second. Presumably because the first implies benefit and the second implies duty. |
21068 | There must be a unanimous contract that citizens accept majority decisions [Kant] |
Full Idea: The actual principle of being content with majority decisions must be accepted unanimously and embodied in a contract, and this itself must be the ultimate basis on which a civil constitution is established. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-3) | |
A reaction: This is the contract which combines a social contract with democracy. We unanimously agree not to be unanimous? Cf Idea 21065. What should the minority do when the majority elect criminal Nazi leaders? |
21069 | A contract is theoretical, but it can guide rulers to make laws which the whole people will accept [Kant] |
Full Idea: The original contract …is merely an idea of reason, which nonetheless has undoubted practical reality; for it can oblige every legislator to frame his laws in such a way that they could have been produced by the united will of a whole nation. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-Concl) | |
A reaction: The contractualist theory of morality of Thomas Scanlon approaches this. Note that Kant says it 'can' oblige the legislators. Nothing would compel them to follow such a principle. |
21070 | A law is unjust if the whole people could not possibly agree to it [Kant] |
Full Idea: If the law is such that a whole people could not possibly agree to it …it is unjust. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-Concl) | |
A reaction: Kant is explicitly trying to approximate Rousseau's general will. The categorical imperative was greatly influenced by Rousseau. The key point is not whether they accept it, but that unanimous acceptance is unthinkable. Unfair laws will fail. |
21067 | A citizen must control his own life, and possess property or an important skill [Kant] |
Full Idea: The only qualification required by a citizen (apart, of course, from being an adult male) is that he must be his own master, and must have some property (which can include any skill, trade, fine art or science) to support himself. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-3) | |
A reaction: Of course! Being one's own master evidently allows for being an employee, as long as this is a free contract, and not exploitation. Invites lots of interesting test cases. We need a Marxist commentary on this idea. |
21064 | A lawful civil state must embody freedom, equality and independence for its members [Kant] |
Full Idea: The civil state, regarded purely as a lawful state, is based on the following a priori principles. 1) the freedom of every member as a human being, 2) the equality of each as a subject, 3) the independence of each as a subject. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 2 Intro) | |
A reaction: Written in 1792, three years after the start of the French Revolution. He says that a state with an inbuilt hierarchy or aristocracy is unlawful. Which freedoms, equality in what respects, and independence from what? |
21066 | Citizens can rise to any rank that talent, effort and luck can achieve [Kant] |
Full Idea: Every member of the commonwealth must be entitled to reach any degree of rank which a subject can earn through his talent, his industry and his good fortune. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-2) | |
A reaction: This is equality of opportunity, which is a mantra for liberals, but has been subjected to good criticisms in modern times. The main question is whether there is formal and legal equality, or actual practical equality. |
21065 | You can't make a contract renouncing your right to make contracts! [Kant] |
Full Idea: No one can voluntarily renounce his rights by a contract ..to the effect that he has no rights but only duties, for such a contract would deprive him of the right to make a contract, and would thus invalidate the one he had already made. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 2-2) | |
A reaction: Kant tries to establish all of his principles by showing that their denial is contradictory. But this example is blatantly wrong. King Lear didn't nullify his previous legislation when he abdicated, and his two daughters legally kept their territories. |
21072 | The people (who have to fight) and not the head of state should declare a war [Kant] |
Full Idea: Each state must be organised so that the head of state, for whom the war costs nothing (for he wages it at the expense of the people) must no longer have the deciding vote on whether war is to be declared or not, for the people who pay for it must decide. | |
From: Immanuel Kant (True in Theory, but not in Practice [1792], 3) | |
A reaction: I would guess that he has Louis XIV particularly in mind. Imagine if Kant's proposal had been implemented in 1914. A referendum takes ages, and the people would need the facts (from the intelligence agencies). |
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) |