37 ideas
| 18776 | Contextual definitions eliminate descriptions from contexts [Linsky,B] |
| Full Idea: A 'contextual' definition shows how to eliminate a description from a context. | |
| From: Bernard Linsky (Quantification and Descriptions [2014], 2) | |
| A reaction: I'm trying to think of an example, but what I come up with are better described as 'paraphrases' than as 'definitions'. |
| 21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
| Full Idea: The ban on 'impredicative' definitions says you can't define a class in terms of a totality to which that class must be seen as belonging. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: So that would be defining 'citizen' in terms of the community to which the citizen belongs? If you are asked to define 'community' and 'citizen' together, where do you start? But how else can it be done? Russell's Reducibility aimed to block this. |
| 21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
| Full Idea: The Axiom of Reducibility avoids impredicativity, by asserting that for any predicate of given arguments defined by quantifying over higher-order functions or classes, there is another co-extensive but predicative function of the same type of arguments. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Eventually the axiom seemed too arbitrary, and was dropped. Linsky's book explores it. |
| 18774 | Definite descriptions, unlike proper names, have a logical structure [Linsky,B] |
| Full Idea: Definite descriptions seem to have a logical structure in a way that proper names do not. | |
| From: Bernard Linsky (Quantification and Descriptions [2014], 1.1.1) | |
| A reaction: Thus descriptions have implications which plain names do not. |
| 21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
| Full Idea: The theory of definite descriptions may eliminate apparent commitment to such entities as the present King of France, but certainly not to the present Queen of England. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.3) |
| 21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
| Full Idea: With the principle of extensionality anything true of one propositional functions will be true of every coextensive one. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.3) |
| 21723 | The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B] |
| Full Idea: The problem for logicism was to find definitions of the primitive notions of Peano's theory, number, successor and 0, in terms of logical notions, so that the postulates could then be derived by logic alone. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7) | |
| A reaction: Both Frege and Russell defined numbers as equivalence classes. Successor is easily defined (in various ways) in set theory. An impossible set can exemplify zero. The trouble for logicism is this all relies on sets. |
| 21721 | Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B] |
| Full Idea: The higher types are needed for intensional phenomena, cases where the same class is picked out by distinct propositional functions. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.4) | |
| A reaction: I take it that in this way 'x is renate' can be distinguished from 'x is cordate', a task nowadays performed by possible worlds. |
| 21703 | Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B] |
| Full Idea: The types is 'ramified' because there are further differences between the type of a function defined in terms of a quantifier ranging over other functions and the type of those other functions, despite the functions applying to the same simple type. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Not sure I understand this, but it evidently created difficulties for dealing with actual mathematics, and Ramsey showed how you could manage without the ramifications. |
| 21714 | The ramified theory subdivides each type, according to the range of the variables [Linsky,B] |
| Full Idea: The original ramified theory of types ...furthern subdivides each of the types of the 'simple' theory according to the range of the bound variables used in the definition of each propositional function. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: For a non-intiate like me it certainly sounds disappointing that such a bold and neat theory because a tangle of complications. Ramsey and Russell in the 1920s seem to have dropped the ramifications. |
| 21713 | Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B] |
| Full Idea: It is often thought that Logicism was a failure, because after Frege's contradiction, Russell required obviously nonlogical principles, in order to develop mathematics. The axioms of Reducibility, Infinity and Choice are cited. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: Infinity and Choice remain as axioms of the standard ZFC system of set theory, which is why set theory is always assumed to be 'up to its neck' in ontological commitments. Linsky argues that Russell saw ontology in logic. |
| 21715 | For those who abandon logicism, standard set theory is a rival option [Linsky,B] |
| Full Idea: ZF set theory is seen as a rival to logicism as a foundational scheme. Set theory is for those who have given up the project of reducing mathematics to logic. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.1) | |
| A reaction: Presumably there are other rivals. Set theory has lots of ontological commitments. One could start at the other end, and investigate the basic ontological commitments of arithmetic. I have no idea what those might be. |
| 21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
| Full Idea: Rather than directly constructing properties as sets of objects and proving neat facts about properties by proxy, we can assert biconditionals, such as that an object has a property if and only if it is in a certain set. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.6) | |
| A reaction: Linsky is describing Russell's method of logical construction. I'm not clear what is gained by this move, but at least it is a variant of the usual irritating expression of properties as sets of objects. |
| 7357 | People who control others with fluent language often end up being hated [Kongzi (Confucius)] |
| Full Idea: Of what use is eloquence? He who engages in fluency of words to control men often finds himself hated by them. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], V.5) | |
| A reaction: I don't recall Socrates making this very good point to any of the sophists (such as Gorgias). The idea that if you battle or connive your way to dominance over others then you are successful is false. Life is a much longer game than that. |
| 7358 | All men prefer outward appearance to true excellence [Kongzi (Confucius)] |
| Full Idea: I have yet to meet a man as fond of excellence as he is of outward appearances. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], IX.18) | |
| A reaction: Interestingly, this cynical view of the love of virtue is put by Plato into the mouths of Glaucon and Adeimantus (in Bk II of 'Republic', e.g. Idea 12), and not into the mouth of Socrates, who goes on to defend the possibility of true virtue. |
| 7362 | Humans are similar, but social conventions drive us apart (sages and idiots being the exceptions) [Kongzi (Confucius)] |
| Full Idea: In our natures we approximate one another; habits put us further and further apart. The only ones who do not change are sages and idiots. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XVII.2) | |
| A reaction: I find most of Confucius rather uninteresting, but this is a splendid remark about the influence of social conventions on human nature. Sages can achieve universal morality if they rise above social convention, and seek the true virtues of human nature. |
| 7360 | Do not do to others what you would not desire yourself [Kongzi (Confucius)] |
| Full Idea: Do not do to others what you would not desire yourself. Then you will have no enemies, either in the state or in your home. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XII.2) | |
| A reaction: The Golden Rule, but note the second sentence. Logically, it leads to the absurdity of not giving someone an Elvis record for Christmas because you yourself don't like Elvis. Kant (Idea 3733) and Nietzsche (Idea 4560) offer good criticisms. |
| 7359 | Excess and deficiency are equally at fault [Kongzi (Confucius)] |
| Full Idea: Excess and deficiency are equally at fault. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XI.16) | |
| A reaction: This is the sort of wisdom we admire in Aristotle (and in any sensible person), but it may also be the deepest motto of conservatism, and it is a long way from romantic philosophy, and the clarion call of Nietzsche to greater excitement in life. |
| 7363 | The virtues of the best people are humility, maganimity, sincerity, diligence, and graciousness [Kongzi (Confucius)] |
| Full Idea: He who in this world can practise five things may indeed be considered Man-at-his-best: humility, maganimity, sincerity, diligence, and graciousness. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XVII.5) | |
| A reaction: A very nice list. Who could resist working with a colleague who had such virtues? Who could go wrong if they married a person who had them? I can't think of anything important that is missing. |
| 7361 | Men of the highest calibre avoid political life completely [Kongzi (Confucius)] |
| Full Idea: Men of the highest calibre avoid political life completely. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XIV.37) | |
| A reaction: Plato notes that such people tend to avoid political life (and a left sheltering, as if from a wild storm!), but he thinks they should be dragged into the political arena for the common good. Confucius seems to approve of the avoidance. Plato is right. |
| 23393 | Confucianism assumes that all good developments have happened, and there is only one Way [Norden on Kongzi (Confucius)] |
| Full Idea: The two major limitations of Confucianism are that it assumes that all worthwhile cultural, social and ethical innovation has already occurred, and that it does not recognise the plurality of worthwhile ways of life. | |
| From: comment on Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE]) by Bryan van Norden - Intro to Classical Chinese Philosophy 3.III | |
| A reaction: In modern liberal terms that is about as conservative as it is possible to get. We think of it as the state of mind of an old person who can only long for the way things were when they were young. But 'hold fast to that which is good'! |
| 7337 | In Mosaic legal theory, crimes are sins and sins are crimes [Johnson,P] |
| Full Idea: In Mosaic legal theory, all breaches of the law offend God. All crimes are sins, just as all sins are crimes. | |
| From: Paul Johnson (The History of the Jews [1987], Pt I) | |
| A reaction: This would seem to define Josephus called a 'theocracy'. Not just rule by a priesthood, but also an attempt to make civil law coincide with the teachings of sacred texts. But doing 80 m.p.h. on a motorway at 2 a.m. hardly seems like a sin. |
| 7339 | Because human life is what is sacred, Mosaic law has no death penalty for property violations [Johnson,P] |
| Full Idea: Where other codes provided the death penalty for offences against property, in Mosaic law no property offence is capital; human life is too sacred, where the rights of property alone are violated. | |
| From: Paul Johnson (The History of the Jews [1987], Pt I) | |
| A reaction: We still preserve this idea in our law, and also in our culture, where we are keen to insist that catastrophes like earthquakes or major fires are measured almost entirely by the loss of life, not the loss of property. I approve. |
| 7353 | The Pharisees undermined slavery, by giving slaves responsibility and status in law courts [Johnson,P] |
| Full Idea: It is no accident that slavery among Jews disappeared with the rise of the Pharisees, as they insisted that all were equal before God in a court. Masters were no longer responsible for actions of slaves, so a slave had status, and slavery could not work. | |
| From: Paul Johnson (The History of the Jews [1987], Pt II) | |
| A reaction: As in seventeenth century England, the rise of social freedom comes from religious sources, not social sources. A slave has status in the transcendent world of souls, despite being a nobody in the physical world. |
| 7340 | Mosaic law was the first to embody the rule of law, and equality before the law [Johnson,P] |
| Full Idea: Mosaic law meant that God ruled through his laws, and since all were equally subject to the law, the system was the first to embody the double merits of the rule of law and equality before the law. | |
| From: Paul Johnson (The History of the Jews [1987], Pt I) | |
| A reaction: If this is correct, it seems to be a hugely important step, combined with Idea 1659, that revenge should be the action of a the state, not of the individual. They are the few simple and essential keys to civilization. |
| 7338 | Man's life is sacred, because it is made in God's image [Johnson,P] |
| Full Idea: In Mosaic theology, man is made in God's image, and so his life is not just valuable, it is sacred. | |
| From: Paul Johnson (The History of the Jews [1987], Pt I) | |
| A reaction: The obvious question is what exactly is meant by "in God's image". Physically, spiritually, intellectually, morally? I am guessing that the original idea was intellectual, because we are the only rational animal. The others seem unlikely, or arrogant. |
| 7348 | The Jews sharply distinguish human and divine, but the Greeks pull them closer together [Johnson,P] |
| Full Idea: The Jews drew an absolute distinction between the human and the divine; the Greeks constantly elevated the human - they were Promethean - and lowered the divine. | |
| From: Paul Johnson (The History of the Jews [1987], Pt II) | |
| A reaction: An intriguing observation. The Greek idea runs right through European culture, surfacing (for example) in 'Faust', or 'Frankenstein', or the films of James Cameron. I'm with the Greeks; I want to see how far humanity can be elevated. |
| 7336 | A key moment is the idea of a single moral God, who imposes his morality on humanity [Johnson,P] |
| Full Idea: The discovery of monotheism, and not just of monotheism but of a sole, omnipotent God actuated by ethical principles and seeking methodically to impose them on human beings, is one of the greatest turning-points in history, perhaps the greatest of all. | |
| From: Paul Johnson (The History of the Jews [1987], Pt I) | |
| A reaction: 'Discovery' begs some questions, but when put like this you realise what a remarkable event it was. It is a good candidate for the most influential idea ever, even if large chunks of humanity, especially in the orient, never took to monotheism. |
| 7341 | Sampson illustrates the idea that religious heroes often begin as outlaws and semi-criminals [Johnson,P] |
| Full Idea: Sampson is the outstanding example of the point which the Book of Judges makes again and again, that the Lord and society are often served by semi-criminal types, outlaws and misfits, who become folk-heroes and then religious heroes. | |
| From: Paul Johnson (The History of the Jews [1987], Pt I) | |
| A reaction: This illustrates nicely Nietzsche's claim, that the jews were responsible for his 'inversion of values', in which aristocratic virtues are downgraded, and the virtues of a good slave are elevated (though Sampson may not show that point so well!). |
| 7342 | Isaiah moved Israelite religion away from the local, onto a more universal plane [Johnson,P] |
| Full Idea: The works of Isaiah (740-700 BCE) mark the point at which the Israelite religion began to spiritualize itself, to move from a specific location in space and time on to the universalist plane. | |
| From: Paul Johnson (The History of the Jews [1987], Pt I) | |
| A reaction: This is necessary if any religion is going to make converts outside the local culture. The crucial step would be to disembody God, so that He cannot be represented by a statue. The difficulty is for him to be universal, but retain a 'chosen people'. |
| 7355 | The Torah pre-existed creation, and was its blueprint [Johnson,P] |
| Full Idea: The Torah was not just a book about God. It pre-existed creation, in the same way as God did. In fact, it was the blueprint of creation. | |
| From: Paul Johnson (The History of the Jews [1987], Pt III) | |
| A reaction: You can only become a 'people of the book' (which Moslems resented in Judaism, and then emulated) if you give this stupendously high status to your book. Hence Christian fundamentalism makes sense, with its emphasis on the divinity of the Bible. |
| 7344 | Judaism involves circumcision, Sabbath, Passover, Pentecost, Tabernacles, New Year, and Atonement [Johnson,P] |
| Full Idea: The practices of Judaism developed during their Exile: circumcision, the Sabbath, the Passover (founding of the nation), Pentecost (giving of the laws), the Tabernacles, the New Year, and the Day of Atonement. | |
| From: Paul Johnson (The History of the Jews [1987], Pt II) | |
| A reaction: These were the elements of ritual created to replace the existence of a physically located state. An astonishing achievement, not even remotely achieved by any other state that was driven off its lands. A culture is an idea, not a country. |
| 7345 | In exile the Jews became a nomocracy [Johnson,P] |
| Full Idea: In exile the Jews, deprived of a state, became a nomocracy - voluntarily submitting to rule by a Law which could only be enforced by consent. Nothing like this had occurred before in history. | |
| From: Paul Johnson (The History of the Jews [1987], Pt II) | |
| A reaction: It is the most remarkable case in history of a people united and strengthened by adversity, and it became an important experiment in the building of human cultures. But what is the point of preserving a culture, with no land? Why not just integrate? |
| 7347 | Zoroastrians believed in one eternal beneficent being, Creator through the holy spirit [Johnson,P] |
| Full Idea: Cyrus the Great was a Zoroastrian, believing in one, eternal, beneficent being, 'Creator of all things through the holy spirit'. | |
| From: Paul Johnson (The History of the Jews [1987], Pt II) | |
| A reaction: Is this the actual origin of monotheism, or did they absorb this idea from the Jews? The interesting bit is the fact that the supreme being (called Marduk) is 'beneficent', which one doesn't associate with these remote and supposed pagans. |
| 7349 | Immortality based on judgement of merit was developed by the Egyptians (not the Jews) [Johnson,P] |
| Full Idea: The idea of judgement at death and immortality on the basis of merit were developed in Egypt before 1000 BCE. It is not Jewish because it was not in the Torah, and the Sadducees, who stuck to their texts, seemed to have denied the afterlife completely. | |
| From: Paul Johnson (The History of the Jews [1987], Pt II) | |
| A reaction: This is the idea considered crucial to religion by Immanuel Kant (Idea 1455), who should be declared an honorary Egyptian. To me the idea that only the good go to heaven sounds like sadly wishful thinking - a fictional consolation for an unhappy life. |
| 7354 | The main doctrine of the Pharisees was belief in resurrection and the afterlife [Johnson,P] |
| Full Idea: Belief in resurrection and the afterlife was the main distinguishing mark of Pharisaism, and thus fundamental of rabbinic Judaism. | |
| From: Paul Johnson (The History of the Jews [1987], Pt II) | |
| A reaction: Belief in an afterlife seems to go back to the Egyptians, but this development in Judaism was obviously very influential, even among early Christians, who initially seem to have only believed in resurrection of the body. |
| 7356 | Pious Jews saw heaven as a vast library [Johnson,P] |
| Full Idea: Pious Jews saw heaven as a vast library, with the Archangel Metatron as the librarian: the books in the shelves there pressed themselves together to make room for a newcomer. | |
| From: Paul Johnson (The History of the Jews [1987], Pt III) | |
| A reaction: I'm tempted to convert to Judaism. |