49 ideas
| 6814 | Instead of prayer and charity, sinners pursue vain disputes and want their own personal scripture [Mohammed] |
| Full Idea: The sinners will say 'we never prayed or fed the hungry. We engaged in vain disputes and denied the Day of Reckoning'. Indeed, each one of them demands a scripture of his own to be unrolled before him. | |
| From: Mohammed (The Koran [c.622], Ch.74) | |
| A reaction: The implication seems to be that most disputes are 'vain'. The charge that everyone wants a 'scripture of his own' is a nice challenge to the world of liberal education, where we are all enjoined to pursue our personalised routes to our own truth. |
| 22270 | Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege] |
| Full Idea: Frege's 1879 logic transformed philosophy because it greatly expanded logic's reach - what thought can achieve unaided - and hence compelled a re-examination of everything previously said about the grounds of thought when logic gives out. | |
| From: comment on Gottlob Frege (Begriffsschrift [1879]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 Intro | |
| A reaction: I loved the gloss on logic as 'what thought can achieve unaided'. I largely see logic in terms of what is mechanically computable. |
| 8939 | We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher] |
| Full Idea: Frege disagree that logic should merely describe the laws of thought - how people actually did reason. Logic is essentially normative, not descriptive. We want the one logic which successfully tracks the truth. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Jennifer Fisher - On the Philosophy of Logic 1.III | |
| A reaction: This explains Frege's sustained attack on psychologism, and it also explains we he ended up as a platonist about logic - because he wanted its laws to be valid independently of human thinking. A step too far, perhaps. Brains are truth machines. |
| 4971 | I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege] |
| Full Idea: A distinction of subject and predicate finds no place in my way of representing a judgement. | |
| From: Gottlob Frege (Begriffsschrift [1879], §03) | |
| A reaction: Perhaps this sentence could be taken as the beginning of modern analytical philosophy. The old view doesn't seem to me entirely redundant - merely replaced by a much more detailed analysis of what makes a 'subject' and what makes a 'predicate'. |
| 17745 | For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki] |
| Full Idea: 'All A's are B's' meant for Frege that the concept A implies the concept B, or that to be A implies also to be B. Moreover this applies to arbitrary x which happens to be A. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Michal Walicki - Introduction to Mathematical Logic History D.2 | |
| A reaction: This seems to hit the renate/cordate problem. If all creatures with hearts also have kidneys, does that mean that being enhearted logically implies being kidneyfied? If all chimps are hairy, is that a logical requirement? Is inclusion implication? |
| 9406 | A class is natural when everybody can spot further members of it [Quinton] |
| Full Idea: To say that a class is natural is to say that when some of its members are shown to people they pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: He concedes a number of problems with his view, but I admire his attempt to at least begin to distinguish the natural (real!) classes from the ersatz ones. A mention of causal powers would greatly improve his story. |
| 7728 | Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner] |
| Full Idea: Frege distinguished between asserting a proposition and expressing it, and he introduced the judgement stroke (a small vertical line, assertion) and the content stroke (a long horizontal line, expression) to represent them. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege Ch.3 | |
| A reaction: There are also strokes for conditional and denial. |
| 16881 | The laws of logic are boundless, so we want the few whose power contains the others [Frege] |
| Full Idea: Since in view of the boundless multitude of laws that can be enunciated we cannot list them all, we cannot achieve completeness except by searching out those that, by their power, contain all of them. | |
| From: Gottlob Frege (Begriffsschrift [1879], §13) | |
| A reaction: He refers to these laws in the previous sentence as the 'core'. His talk of 'power' is music to my ears, since it implies a direction of explanation. Burge says the power is that of defining other concepts. |
| 7622 | In 1879 Frege developed second order logic [Frege, by Putnam] |
| Full Idea: By 1879 Frege had discovered an algorithm, a mechanical proof procedure, that embraces what is today standard 'second order logic'. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Hilary Putnam - Reason, Truth and History Ch.5 | |
| A reaction: Note that Frege did more than introduce quantifiers, and the logic of predicates. |
| 7729 | Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner] |
| Full Idea: Frege's regimentation is based on the view of the simplest sort of statement as having, not subject/predicate form (as in Aristotle), but function/argument form. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege | |
| A reaction: This looks like being a crucial move into the modern world, where one piece of information is taken in and dealt with, as in computer procedures. Have educated people reorganised their minds along Fregean lines? |
| 9950 | A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman] |
| Full Idea: The contribution of the quantifier to the truth conditions of sentences of which it is a part cannot be adequately explained if it is treated as other than a second-level predicate (for instance, if it is viewed as name). | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: They suggest that this makes it something like a 'property of properties'. With this account it becomes plausible to think of numbers as quantifiers (since they do, after all, specify quantities). |
| 9991 | For Frege the variable ranges over all objects [Frege, by Tait] |
| Full Idea: For Frege the variable ranges over all objects. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by William W. Tait - Frege versus Cantor and Dedekind XII | |
| A reaction: The point is that Frege had not yet seen the necessity to define the domain of quantification, and this leads him into various difficulties. |
| 10536 | Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege] |
| Full Idea: For Frege there is no need to specify the domain of the individual variables, which is taken as the totality of all objects. This contrasts with the standard notion of an interpretation, which demands that we first fix the domain. | |
| From: comment on Gottlob Frege (Begriffsschrift [1879]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
| A reaction: What intrigues me is how domains of quantification shift according to context in ordinary usage, even in mid-sentence. I ought to go through every idea in this database, specifying its domain of quantification. Any volunteers? |
| 7730 | Frege introduced quantifiers for generality [Frege, by Weiner] |
| Full Idea: In order to express generality, Frege introduced quantifier notation. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege | |
| A reaction: This is the birth of predicate logic, beloved of analytical philosophers (but of no apparent interest to phenomenalists, deconstructionists, existentialists?). Generality is what you get from induction (which is, of course, problematic). |
| 7742 | Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh] |
| Full Idea: Frege treated 'everything' as basic, and suggested ways of recasting propositions containing other quantifiers so that this was the only one remaining. He recast 'something' as 'at least one thing', and defined this in terms of 'everything' and 'not'. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Gregory McCullogh - The Game of the Name 1.6 | |
| A reaction: Extreme parsimony seems highly desirable in logic as well as ontology, but it can lead to frustrations, especially over the crucial question of the existence of things quantified over. See Idea 6068. |
| 13824 | Proof theory began with Frege's definition of derivability [Frege, by Prawitz] |
| Full Idea: Frege's formal definition of derivability is perhaps the first investigation in general proof theory. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Dag Prawitz - Gentzen's Analysis of First-Order Proofs 2 n2 | |
| A reaction: In 'On General Proof Theory §1' Prawitz says "proof theory originated with Hilbert" in 1900. Presumably Frege offered a theory, and then Hilbert saw it as a general project. |
| 13609 | Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan] |
| Full Idea: Frege's work supplied a set of axioms for logic itself, at least partly because it was a well-known way of presenting the foundations in other disciplines, especially mathematics, but it does not nowadays strike us as natural for logic. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by David Kaplan - Dthat 5.1 | |
| A reaction: What Bostock has in mind is the so-called 'natural' deduction systems, which base logic on rules of entailment, rather than on a set of truths. The axiomatic approach uses a set of truths, plus the idea of possible contradictions. |
| 17855 | It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C] |
| Full Idea: Frege's account of the ancestral has made it possible, in effect, to define the natural numbers as entities for which induction holds. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Crispin Wright - Frege's Concept of Numbers as Objects 4.xix | |
| A reaction: This is the opposite of the approach in the Peano Axioms, where induction is used to define the natural numbers. |
| 10607 | Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P] |
| Full Idea: Frege's general logical system involves a type hierarchy, distinguishing objects from properties from properties-of-properties etc., with every item belonging to a determinate level. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Peter Smith - Intro to Gödel's Theorems 14.1 | |
| A reaction: The Theory of Types went on to apply this hierarchy to classes, where Frege's disastrous Basic Law V flattens the hierarchy of classes, putting them on the same level (Smith p.119) |
| 11008 | Existence is not a first-order property, but the instantiation of a property [Frege, by Read] |
| Full Idea: When Kant said that existence was not a property, what he meant was, according to Frege, that existence is not a first-order property - it is not a property of individuals but a property of properties, that the property has an instance. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Stephen Read - Thinking About Logic Ch.5 |
| 15730 | Extreme nominalists say all classification is arbitrary convention [Quinton] |
| Full Idea: Pure, extreme nominalism sees all classification as the product of arbitrary convention. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I'm not sure what the word 'arbitrary' is doing there. Nominalists are not daft, and if they can classify any way they like, they are not likely to choose an 'arbitrary' system. Pragmatism tells the right story here. |
| 15728 | The naturalness of a class depends as much on the observers as on the objects [Quinton] |
| Full Idea: The naturalness of a class depends as essentially on the nature of the observers who classify as it does on the nature of the objects that they classify. ...It depends on our perceptual apparatus, and on our relatively mutable needs and interests. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: This seems to translate 'natural' as 'natural for us', which is not much use to scientists, who spend quite a lot of effort combating folk wisdom. Do desirable sports cars constitute a natural class? |
| 9407 | Properties imply natural classes which can be picked out by everybody [Quinton] |
| Full Idea: To say there are properties is to say there are natural classes, classes introduction to some of whose members enables people to pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: Aristotle would like this approach, but it doesn't find many friends among modern logician/philosophers. We should go on to ask why people agree on these things. Causal powers will then come into it. |
| 15729 | Uninstantiated properties must be defined using the instantiated ones [Quinton] |
| Full Idea: Properties that have no concrete instances must be defined in terms of those that have. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I wonder what the dodo used to smell like? |
| 8520 | An individual is a union of a group of qualities and a position [Quinton, by Campbell,K] |
| Full Idea: Quinton proposes that an individual is a union of a group of qualities and a position. | |
| From: report of Anthony Quinton (The Nature of Things [1973], Pt I) by Keith Campbell - The Metaphysic of Abstract Particulars §5 | |
| A reaction: This seems the obvious defence of a bundle account of objects against the charge that indiscernibles would have to be identical. It introduces, however, 'positions' into the ontology, but maybe that price must be paid. Materialism needs space. |
| 22280 | Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter] |
| Full Idea: Frege's account was top-down, not bottom-up: he aimed to decompose and discern function-argument structure in already existing sentences, not to explain how those sentences acquired their meanings in the first place. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'Func' | |
| A reaction: This goes with the holistic account of meaning, which leads to Quine's gavagai and Kuhn's obfuscation of science. I recommend compositionality for everthing. |
| 6823 | Repay evil with good and your enemies will become friends (though this is hard) [Mohammed] |
| Full Idea: Requite evil with good, and he who is your enemy will become your dearest friend; but none will attain this save those who endure with fortitude and are greatly favoured by Allah. | |
| From: Mohammed (The Koran [c.622], Ch.41) | |
| A reaction: This seems opposed to some of the more vengeful remarks in the Koran. It strikes me as good common sense, since vengeance only seems to breed counter-vengeance. It doesn't carry the full altruistic commitment, though, of unrewarded love. |
| 6828 | You may break off a treaty if you fear treachery from your ally [Mohammed] |
| Full Idea: If you fear treachery from any of your allies, you may retaliate by breaking off your treaty with them; Allah does not love the treacherous. | |
| From: Mohammed (The Koran [c.622], Ch.8) | |
| A reaction: I do not think this is good advice. Everybody fears treachery, but if we all acted on that fear human relationships and society would immediately collapse. If anyone thought this was good advice, I would not want to make a treaty with them. |
| 6826 | Allah rewards those who are devout, sincere, patient, humble, charitable, chaste, and who fast [Mohammed] |
| Full Idea: Allah will bestow forgiveness and a rich reward on those, both men and women, who are devout, sincere, patient, humble, charitable and chaste; who fast and are ever mindful of Allah. | |
| From: Mohammed (The Koran [c.622], Ch.33) | |
| A reaction: Most people would still agree that all of these are virtues, though other lists will show interesting virtues that are not mentioned here, and many on this list seem overrated in the modern pantheon of virtues. |
| 6822 | Those who avenge themselves when wronged incur no guilt [Mohammed] |
| Full Idea: Those who avenge themselves when wronged incur no guilt. | |
| From: Mohammed (The Koran [c.622], Ch.42) | |
| A reaction: Compare Ideas 1659 (Protagoras), 346 (Socrates), 6288 (Jesus), and 4286 (Scruton!). In the light of those ideas, this comment in the Koran strikes me as coming from an older and less civilized world. |
| 6833 | Punish theft in men or women by cutting off their hands [Mohammed] |
| Full Idea: As for the man or woman who is guilty of theft, cut off their hands to punish them for their crimes. | |
| From: Mohammed (The Koran [c.622], Ch.5) | |
| A reaction: I find this shocking because it is irrevocable and offers no hope of redemption. It is particularly shocking that the text does not enjoin any caution about inflicting the punishment on the young, most of whom reform from thieving in later life. |
| 6825 | Do not kill except for a just cause [Mohammed] |
| Full Idea: Do not kill except for a just cause. | |
| From: Mohammed (The Koran [c.622], Ch.25) | |
| A reaction: Slippery slope! I can see that pleasure would not be a just cause, and ensuring the entry of all humanity to paradise might be one, but I find the area in between a little unclear. The Koran seems to allow you to decide for yourself. |
| 6832 | Killing a human, except as just punishment, is like killing all mankind [Mohammed] |
| Full Idea: We laid it down for the Israelites that whoever killed a human being, except as a punishment for murder or other wicked crimes, should be looked upon as though he had killed all mankind. | |
| From: Mohammed (The Koran [c.622], Ch.5) | |
| A reaction: It seems inconceivable that the Koran could be used to justify indiscriminate terrorism, in the light of remarks such as this. |
| 6811 | Allah is lord of creation, compassionate, merciful, king of judgement-day [Mohammed] |
| Full Idea: Praise be to Allah, Lord of Creation, The Compassionate, the Merciful, King of Judgement-day! | |
| From: Mohammed (The Koran [c.622], Exord) | |
| A reaction: The Muslim concept of God confronts directly a clear theological difficulty, a difficulty faced by any judge: the conflict between mercy and justice. Christianity seems to emphasise mercy, and Islam emphasises justice. |
| 7741 | The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner] |
| Full Idea: On Frege's logical analysis, the predicate 'exists' is actually a natural language expression for a quantifier. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege Ch.8 | |
| A reaction: However see Idea 6067, for McGinn's alternative view of quantifiers. In the normal conventions of predicate logic it may be that existence is treated as a quantifier, but that is not the same as saying that existence just IS a quantifier. |
| 6819 | True believers see that Allah made the night for rest and the day to give light [Mohammed] |
| Full Idea: Do they not see how We have made the night for them to rest in and the day to give them light? Surely there are signs in this for true believers. | |
| From: Mohammed (The Koran [c.622], Ch.27) | |
| A reaction: The main traditional argument for God implied in the Koran is the design argument. It is clear from this that Islam will not be comfortable with Darwinian evolution, which implies we are 'designed' for the Earth, not the Earth for us. |
| 6818 | Allah cannot have begotten a son, as He is self-sufficient [Mohammed] |
| Full Idea: They say: 'Allah has begotten a son.' Allah forbid! Self-sufficient is He. | |
| From: Mohammed (The Koran [c.622], Ch.10) | |
| A reaction: This is quite persuasive, except that the point of Jesus is that he suffers a cruel death, and we are required to identify with God's parental feelings here, His involvement, which would not occur with the death of one of His prophets. |
| 6829 | There shall be no compulsion in religion [Mohammed] |
| Full Idea: There shall be no compulsion in religion. | |
| From: Mohammed (The Koran [c.622], Ch.2) | |
| A reaction: This seems to contradict some of the more aggressive remarks in the Koran, such as Idea 6827. As I read it, the three non-compelling ideas that lead to true religion in the Koran are desire for paradise, fear of punishment, and worship of divine design. |
| 6834 | Unbelievers try to interpret the ambiguous parts of the Koran, simply to create dissension [Mohammed] |
| Full Idea: Some of the verses of the Koran are precise in meaning - they are the foundations of the Book - and others are ambiguous. Disbelievers follow the ambiguous part, to create dissension by seeking to explain it. No one knows its meaning except Allah. | |
| From: Mohammed (The Koran [c.622], Ch.3) | |
| A reaction: It is tempting to ask why some of the verses are ambiguous. The implication here is that they are a deliberate test for believers, like the apple in the garden of Eden. |
| 6817 | The Koran is certainly composed by Allah; no one could compose a chapter like it [Mohammed] |
| Full Idea: This Koran could not have been composed by any but Allah. It is beyond doubt from the Lord of the Creation. If they say: 'It is your own invention', say: 'Compose one chapter like it. Call on your false gods to help you!' | |
| From: Mohammed (The Koran [c.622], Ch.10) | |
| A reaction: I find this unpersuasive, firstly because I couldn't imitate the sonnets of Shakespeare either, and secondly because the authority of a text must be asserted outside the text, not within it. Scribble "this is a ten pound note" on a scrap of paper. |
| 6824 | Do not split into sects, exulting in separate beliefs [Mohammed] |
| Full Idea: Do not split up your religion into sects, each exulting in its own beliefs. | |
| From: Mohammed (The Koran [c.622], Ch.30) | |
| A reaction: This seems like good advice to a religion, but it is very difficult to retrace steps and reunite once it has happened. Which sect should make the greatest concessions? Must they both admit to being somewhat wrong? |
| 6821 | I created mankind that it might worship Me [Mohammed] |
| Full Idea: I created mankind and the jinn in order that they might worship Me. | |
| From: Mohammed (The Koran [c.622], Ch.51) | |
| A reaction: This seems to be a view common to all the monotheistic religions, with monasticism as its clearest (and most logical) outcome. Nietzsche is the most obvious opponent of this idea that the abasement of mankind is its highest ideal. |
| 6815 | Be patient with unbelievers, and leave them to the judgement of Allah [Mohammed] |
| Full Idea: Bear patiently with what the unbelievers say, and leave their company without recrimination; leave to Me those that deny the truth. | |
| From: Mohammed (The Koran [c.622], Ch.73) | |
| A reaction: This explicitly says Muslims should not attack infidels simply for their unbelief in Allah. |
| 6827 | Make war on the unbelievers until Allah's religion reigns supreme [Mohammed] |
| Full Idea: Make war on the unbelievers until idolatry is no more and Allah's religion reigns supreme. | |
| From: Mohammed (The Koran [c.622], Ch.8) | |
| A reaction: This should presumably be seen in context, as a war speech written during a conflict, like Churchill 'fighting them on the beaches', which does not apply to modern German tourists. However, one worries about how fundamentalists might read it. |
| 6831 | He that kills a believer by design shall burn in Hell for ever [Mohammed] |
| Full Idea: He that kills a believer by design shall burn in Hell for ever. | |
| From: Mohammed (The Koran [c.622], Ch.4) | |
| A reaction: This would appear to make modern indiscriminate urban terrorism a damning sin for a Muslim. |
| 6820 | The righteous shall dwell on couches in gardens, wedded to dark-eyed houris [Mohammed] |
| Full Idea: In fair gardens the righteous shall dwell in bliss, rejoicing in what their Lord will give them. They shall recline on couches ranged in rows. To dark-eyed houris We shall wed them. | |
| From: Mohammed (The Koran [c.622], Ch.52) | |
| A reaction: What I find distressing about this is that we have gradually worked out how young men can recline on couches in gardens with dark-eyed houris before death, and the Koran seems to depict it as the highest form of living. |
| 6812 | Heaven will be reclining on couches, eating fruit, attended by virgins [Mohammed] |
| Full Idea: All who dwell in heaven shall recline on couches lined with thick brocade, and within their reach will hang the fruits of gardens; they shall dwell with bashful virgins whom neither men nor jinnee will have touched before. | |
| From: Mohammed (The Koran [c.622], Ch.55) | |
| A reaction: In the seventh century this was more impressive than it seems now. I still find it sad (though understandable) that paradise must always be depicted in terms of physical pleasure. Aristotle wouldn't have yearned for such an immortality. |
| 6830 | Unbelievers will have their skin repeatedly burned off in hell [Mohammed] |
| Full Idea: Those that deny Our revelations We will burn in Hell-fire. No sooner will their skins be consumed that We shall give them other skins, so that they may truly taste Our scourge. Allah is mighty and wise. | |
| From: Mohammed (The Koran [c.622], Ch.4) | |
| A reaction: Of all the accounts of hell in the Koran, this strikes me as the most alarming. I cannot think of a worse infliction, because here every nerve which can experience pain will suffer it (though the drinking of boiling water, Idea 6816, will make it worse). |
| 6816 | The unbelievers shall drink boiling water [Mohammed] |
| Full Idea: As for the unbelievers, they shall drink boiling water. | |
| From: Mohammed (The Koran [c.622], Ch.10) | |
| A reaction: This seems to be presented not only as a threat to unbelievers, but also as a satisfaction to believers. |