28 ideas
| 10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
| Full Idea: Truth in a model is interesting because it provides a transparent and mathematically tractable model - in the 'ordinary' rather than formal sense of the term 'model' - of the less tractable notion of truth. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This is an important warning to those who wish to build their entire account of truth on Tarski's rigorously formal account of the term. Personally I think we should start by deciding whether 'true' can refer to the mental state of a dog. I say it can. |
| 10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
| Full Idea: There is an enormous difference between the truth of sentences in the interpreted language of set theory and truth in some model for the disinterpreted skeleton of that language. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.132) | |
| A reaction: This is a warning to me, because I thought truth and semantics only entered theories at the stage of 'interpretation'. I must go back and get the hang of 'skeletal' truth, which sounds rather charming. [He refers to set theory, not to logic.] |
| 10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
| Full Idea: Brand higher-order logic as unintelligible if you will, but don't conflate it with set theory. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: [he gives Boolos 1975 as a further reference] This is simply a corrective, because the conflation of second-order logic with set theory is an idea floating around in the literature. |
| 10011 | Identity is a level one relation with a second-order definition [Hodes] |
| Full Idea: Identity should he considered a logical notion only because it is the tip of a second-order iceberg - a level 1 relation with a pure second-order definition. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) |
| 10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
| Full Idea: A model is created when a language is 'interpreted', by assigning non-logical terms to objects in a set, according to a 'true-in' relation, but we must bear in mind that this 'interpretation' does not associate anything like Fregean senses with terms. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This seems like a key point (also made by Hofweber) that formal accounts of numbers, as required by logic, will not give an adequate account of the semantics of number-terms in natural languages. |
| 10027 | Mathematics is higher-order modal logic [Hodes] |
| Full Idea: I take the view that (agreeing with Aristotle) mathematics only requires the notion of a potential infinity, ...and that mathematics is higher-order modal logic. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: Modern 'modal' accounts of mathematics I take to be heirs of 'if-thenism', which seems to have been Russell's development of Frege's original logicism. I'm beginning to think it is right. But what is the subject-matter of arithmetic? |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
| Full Idea: Arithmetic should be able to face boldly the dreadful chance that in the actual world there are only finitely many objects. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.148) | |
| A reaction: This seems to be a basic requirement for any account of arithmetic, but it was famously a difficulty for early logicism, evaded by making the existence of an infinity of objects into an axiom of the system. |
| 10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
| Full Idea: The mathematical object-theorist says a number is an object that represents a cardinality quantifier, with the representation relation as the entire essence of the nature of such objects as cardinal numbers like 4. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: [compressed] This a classic case of a theory beginning to look dubious once you spell it our precisely. The obvious thought is to make do with the numerical quantifiers, and dispense with the objects. Do other quantifiers need objects to support them? |
| 10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
| Full Idea: The dogmatic Frege is more right than wrong in denying that numerical terms can stand for numerical quantifiers, for there cannot be a language in which object-quantifiers and objects are simultaneously viewed as level zero. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.142) | |
| A reaction: Subtle. We see why Frege goes on to say that numbers are level zero (i.e. they are objects). We are free, it seems, to rewrite sentences containing number terms to suit whatever logical form appeals. Numbers are just quantifiers? |
| 10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
| Full Idea: Talk about mirror images is a sort of fictional discourse. Statements 'about' such fictions are not made true or false by our whims; rather they 'encode' facts about the things reflected in mirrors. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.146) | |
| A reaction: Hodes's proposal for how we should view abstract objects (c.f. Frege and Dummett on 'the equator'). The facts involved are concrete, but Hodes is offering 'encoding fictionalism' as a linguistic account of such abstractions. He applies it to numbers. |
| 541 | Virtue comes more from habit than character [Critias] |
| Full Idea: More men are good through habit than through character. | |
| From: Critias (fragments/reports [c.440 BCE], B09), quoted by John Stobaeus - Anthology 3.29.41 |
| 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. |
| 542 | Fear of the gods was invented to discourage secret sin [Critias] |
| Full Idea: When the laws forbade men to commit open crimes of violence, and they began to do them in secret, a wise and clever man invented fear of the gods for mortals, to frighten the wicked, even if they sin in secret. | |
| From: Critias (fragments/reports [c.440 BCE], B25), quoted by Sextus Empiricus - Against the Professors (six books) 9.54 |
| 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. |