40 ideas
| 10163 | Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman] |
| Full Idea: At the age of 19 Saul Kripke published a completeness proof of propositional modal logic. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Feferman / Feferman - Alfred Tarski: life and logic Int V |
| 10760 | With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg] |
| Full Idea: Kripke gave a possible worlds semantics to a whole range of modal logics, and S4 and S5 turned out to be both sound and complete with this semantics. Hence more systems could be designed. S1-S3 failed in soundness, leading to 'impossible worlds'. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Marcus Rossberg - First-order Logic, 2nd-order, Completeness §4 |
| 16189 | The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen] |
| Full Idea: Kripke's variable domain approach to quantified modal logic famously invalidates the Barcan Formula. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Ori Simchen - The Barcan Formula and Metaphysics §3 | |
| A reaction: [p.9 and p.16] In a single combined domain all the possibilia must be present, but with variable domains objects in remote domains may not exist in your local domain. BF is committed to those possible objects. |
| 15132 | The Barcan formulas fail in models with varying domains [Kripke, by Williamson] |
| Full Idea: Kripke showed that the Barcan formula ∀x□A⊃□∀xA and its converse fail in models which require varying domains. | |
| From: report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Timothy Williamson - Truthmakers and Converse Barcan Formula §1 | |
| A reaction: I think this is why I reject the Barcan formulas for metaphysics - because the domain of metaphysics should be seen as varying, since some objects are possible in some contexts and not in others. Hmm… |
| 458 | Nothing could come out of nothing, and existence could never completely cease [Empedocles] |
| Full Idea: From what in no wise exists, it is impossible for anything to come into being; for Being to perish completely is incapable of fulfilment and unthinkable. | |
| From: Empedocles (fragments/reports [c.453 BCE], B012), quoted by Anon (Lyc) - On Melissus 975b1-4 |
| 5112 | Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle] |
| Full Idea: Empedocles claims that things are alternately changing and at rest - that they are changing whenever love is creating a unity out of plurality, or hatred is creating plurality out of unity, and they are at rest in the times in between. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Physics 250b26 | |
| A reaction: I suppose one must say that this an example of Ruskin's 'pathetic fallacy' - reading human emotions into the cosmos. Being constructive little creatures, we think goodness leads to construction. I'm afraid Empedocles is just wrong. |
| 13209 | There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle] |
| Full Idea: Empedocles says there is no coming-to-be of anything, but only a mingling and a divorce of what has been mingled. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314b08 | |
| A reaction: Aristotle comments that this prevents Empedocleans from distinguishing between superficial alteration and fundamental change of identity. Presumably, though, that wouldn't bother them. |
| 457 | Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles] |
| Full Idea: There is no creation of substance in any one of mortal existence, nor any end in execrable death, but only mixing and exchange of what has been mixed. | |
| From: Empedocles (fragments/reports [c.453 BCE], B008), quoted by Plutarch - 74: Reply to Colotes 1111f | |
| A reaction: also Aristotle 314b08 |
| 462 | One vision is produced by both eyes [Empedocles] |
| Full Idea: One vision is produced by both eyes | |
| From: Empedocles (fragments/reports [c.453 BCE], B088), quoted by Strabo - works 8.364.3 |
| 22765 | Wisdom and thought are shared by all things [Empedocles] |
| Full Idea: Wisdom and power of thought, know thou, are shared in by all things. | |
| From: Empedocles (fragments/reports [c.453 BCE]), quoted by Sextus Empiricus - Against the Logicians (two books) II.286 | |
| A reaction: Sextus quotes this, saying that it is 'still more paradoxical', and that it explicitly includes plants. This may mean that Empedocles was not including inanimate matter. |
| 1524 | For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus] |
| Full Idea: Empedocles assumes that thinking is either identical to or very similar to sense-perception. | |
| From: report of Empedocles (fragments/reports [c.453 BCE], A86) by Theophrastus - On the Senses 9 | |
| A reaction: Not to be sniffed at. We can, of course, control our thinking (though we can't control the controller) and we contemplate abstractions, but that might be seen as a sort of perception. Vision is not as visual as we think. |
| 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. |
| 552 | Empedocles said good and evil were the basic principles [Empedocles, by Aristotle] |
| Full Idea: Empedocles was the first to give evil and good as principles. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Metaphysics 985a | |
| A reaction: Once you start to think that good and evil will only matter if they have causal powers, it is an easy step to the idea of a benevolent god, and a satanic anti-god. Otherwise the 'principles' could be ignored. |
| 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). |
| 589 | 'Nature' is just a word invented by people [Empedocles] |
| Full Idea: Nature is but a word of human framing. | |
| From: Empedocles (fragments/reports [c.453 BCE], B008), quoted by Aristotle - Metaphysics 1015a |
| 21823 | The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus] |
| Full Idea: In Empedocles we have a dividing principle, 'Strife', set against 'Friendship' - which is the One and is to him bodiless, while the elements represent matter. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Plotinus - The Enneads 5.1.09 | |
| A reaction: The first time I've seen the principle of Love in Empedocles identified with the One of Parmenides. Plotinus is a trustworthy reporter, I think, because he was well read, and had access to lost texts. |
| 2680 | Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle] |
| Full Idea: Empedocles holds that the corporeal elements are four, but that all the elements, including those which create motion, are six in number. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314a16 |
| 6002 | Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood] |
| Full Idea: Empedocles used numerical ratios to explain different kinds of matter; for example, bone is two parts water, four parts fire, two parts earth; and blood is an equal blend of all four elements. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Brad Inwood - Empedocles | |
| A reaction: Why isn't the ration 1:2:1? This presumably shows the influence of Pythagoras (who had also been based in Italy, like Empedocles), as well as that of the earlier naturalistic philosophers. It was a very good theory, though wrong. |
| 13207 | Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle] |
| Full Idea: Empedocles says that Fire, Water, Air and Earth are four elements, and are thus 'simple' rather than flesh, bone and bodies which, like these, are 'homoeomeries'. | |
| From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314a26 | |
| A reaction: The translation is not quite clear. I take it that flesh and bone may look simple, because they are homoeomerous, but they are not really - but what is his evidence for that? Compare Idea 13208. |
| 459 | All change is unity through love or division through hate [Empedocles] |
| Full Idea: These elements never cease their continuous exchange, sometimes uniting under the influence of Love, so that all become One, at other times again moving apart through the hostile force of Hate. | |
| From: Empedocles (fragments/reports [c.453 BCE], B017), quoted by Simplicius - On Aristotle's 'Physics' 158.1- |
| 13218 | The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles] |
| Full Idea: Empedocles says it is evident that all the other bodies down to the 'elements' have their coming-to-be and their passing-away: but it is not clear how the 'elements' themselves, severally in their aggregated masses, come-to-be and pass-away. | |
| From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 325b20 | |
| A reaction: Presumably the elements are like axioms - and are just given. How do electrons and quarks come-to-be? |
| 13225 | Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles] |
| Full Idea: It is not an adequate explanation to say that 'Love and Strife set things moving', unless the very nature of Love is a movement of this kind and the very nature of Strife a movement of that kind. | |
| From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 333b23 | |
| A reaction: I take this to be of interest for showing Aristotle's quest for explanations, and his unwillingness to be fobbed off with anything superficial. I take a task of philosophy to be to push explanations further than others wish to go. |
| 460 | If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles] |
| Full Idea: Besides these elements, nothing else comes into being, nor does anything cease. For if they had been perishing continuously, they would Be no more; and what could increase the Whole? And whence could it have come? | |
| From: Empedocles (fragments/reports [c.453 BCE], B017), quoted by Simplicius - On Aristotle's 'Physics' 158.1- |
| 5090 | Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle] |
| Full Idea: Is it just an accident that teeth and other parts of the body seem to have some purpose, and creatures survive because they happen to be put together in a useful way? Everything else has been destroyed, as Empedocles says of his 'cow with human head'. | |
| From: report of Empedocles (fragments/reports [c.453 BCE], 61) by Aristotle - Physics 198b29 | |
| A reaction: Good grief! Has no one ever noticed that Empedocles proposed the theory of evolution? It isn't quite natural selection, because we aren't told what does the 'destroying', but it is a little flash of genius that was quietly forgotten. |
| 466 | God is pure mind permeating the universe [Empedocles] |
| Full Idea: God is mind, holy and ineffable, and only mind, which darts through the whole cosmos with its swift thought. | |
| From: Empedocles (fragments/reports [c.453 BCE], B134), quoted by Ammonius - On 'De Interpretatione' 4.5.249.6 |
| 461 | God is a pure, solitary, and eternal sphere [Empedocles] |
| Full Idea: God is equal in all directions to himself and altogether eternal, a rounded Sphere enjoying a circular solitude. | |
| From: Empedocles (fragments/reports [c.453 BCE], B028), quoted by John Stobaeus - Anthology 1.15.2 |
| 1719 | In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles] |
| Full Idea: It is a consequence of Empedocles' view that God is the most unintelligent thing, for he alone is ignorant of one of the elements, namely strife, whereas mortal creatures are familiar with them all. | |
| From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - De Anima 410b08 |
| 1522 | It is wretched not to want to think clearly about the gods [Empedocles] |
| Full Idea: Wretched is he who cares not for clear thinking about the gods. | |
| From: Empedocles (fragments/reports [c.453 BCE], B132), quoted by Clement - Miscellanies 5.140.5.1 |