40 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. |
| 8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
| Full Idea: Euclid gives proofs of many things which anyone would concede to him without question. ...The aim of proof is not merely to place the truth of a proposition beyond doubt, but also to afford us insight into the dependence of truths upon one another. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §02 | |
| A reaction: This connects nicely with Shoemaker's view of analysis (Idea 8559), which I will adopt as my general view. I've always thought of philosophy as the aspiration to wisdom through the cartography of concepts. |
| 13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
| Full Idea: Euclid begins proofs about all triangles with 'let ABC be a triangle', but ABC is not a proper name. It names an arbitrarily selected triangle, and if that has a property, then we can conclude that all triangles have the property. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by E.J. Lemmon - Beginning Logic 3.2 | |
| A reaction: Lemmon adds the proviso that there must be no hidden assumptions about the triangle we have selected. You must generalise the properties too. Pick a triangle, any triangle, say one with three angles of 60 degrees; now generalise from it. |
| 6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
| Full Idea: Euclid's geometry is a synthetic geometry; Descartes supplied an analytic version of Euclid's geometry, and we now have analytic versions of the early non-Euclidean geometries. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michael D. Resnik - Maths as a Science of Patterns One.4 | |
| A reaction: I take it that the original Euclidean axioms were observations about the nature of space, but Descartes turned them into a set of pure interlocking definitions which could still function if space ceased to exist. |
| 9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
| Full Idea: Assume a largest prime, then multiply the primes together and add one. The new number isn't prime, because we assumed a largest prime; but it can't be divided by a prime, because the remainder is one. So only a larger prime could divide it. Contradiction. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by James Robert Brown - Philosophy of Mathematics Ch.1 | |
| A reaction: Not only a very elegant mathematical argument, but a model for how much modern logic proceeds, by assuming that the proposition is false, and then deducing a contradiction from it. |
| 9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
| Full Idea: A unit is that according to which each existing thing is said to be one. | |
| From: Euclid (Elements of Geometry [c.290 BCE], 7 Def 1) | |
| A reaction: See Frege's 'Grundlagen' §29-44 for a sustained critique of this. Frege is good, but there must be something right about the Euclid idea. If I count stone, paper and scissors as three, each must first qualify to be counted as one. Psychology creeps in. |
| 8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
| Full Idea: Euclid's Postulate 2 says the geometer can 'produce a finite straight line continuously in a straight line'. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Thinking About Mathematics 4.2 | |
| A reaction: The point being that this takes infinity for granted, especially if you start counting how many points there are on the line. The Einstein idea that it might eventually come round and hit you on the back of the head would have charmed Euclid. |
| 22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
| Full Idea: Euclid's axioms were insufficient to derive all the theorems of geometry: at various points in his proofs he appealed to properties that are obvious from the diagrams but do not follow from the stated axioms. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'aim' | |
| A reaction: I suppose if the axioms of a system are based on self-evidence, this would licence an appeal to self-evidence elsewhere in the system. Only pedants insist on writing down what is obvious to everyone! |
| 8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
| Full Idea: Euclid's fifth 'parallel' postulate says if there is an infinite straight line and a point, then there is only one straight line through the point which won't intersect the first line. This axiom is independent of Euclid's first four (agreed) axioms. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 2.2 | |
| A reaction: This postulate was challenged in the nineteenth century, which was a major landmark in the development of modern relativist views of knowledge. |
| 10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
| Full Idea: Euclid gives no principle of continuity, which would sanction an inference that if a line goes from the outside of a circle to the inside of circle, then it must intersect the circle at some point. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Philosophy of Mathematics 6.1 n2 | |
| A reaction: Cantor and Dedekind began to contemplate discontinuous lines. |
| 10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
| Full Idea: Euclid postulates: One can join two points by a straight line; Hilbert states the axiom: Given any two points, there exists a straight line on which both are situated. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Paul Bernays - On Platonism in Mathematics p.259 |
| 14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
| Full Idea: In descriptive geometry the first 26 propositions of Euclid hold. In projective geometry the 1st, 7th, 16th and 17th require modification (as a straight line is not a closed series). Those after 26 depend on the postulate of parallels, so aren't assumed. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Bertrand Russell - The Principles of Mathematics §388 |
| 1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
| Full Idea: The best known example of Euclid's 'common notions' is "If equals are subtracted from equals the remainders are equal". These can be called axioms, and are what "the man who is to learn anything whatever must have". | |
| From: report of Euclid (Elements of Geometry [c.290 BCE], 72a17) by David Roochnik - The Tragedy of Reason p.149 |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 21277 | Even an imperfect machine can exhibit obvious design [Paley] |
| Full Idea: It is not necessary that a machine be perfect, in order to show with what design it was made. | |
| From: William Paley (Natural Theology [1802], Ch 1) | |
| A reaction: This encounters Hume's point that you will then have to infer that the designer contains similar imperfections. If you look at plagues, famines and mothers dying in childbirth (see Mill), you might wish the designer had never started. |
| 21275 | Unlike a stone, the parts of a watch are obviously assembled in order to show the time [Paley] |
| Full Idea: When we come to inspect a watch we perceive (what we could not discover in a stone) that its several parts are put together for a purpose, to produce motion, and that motion so regulated as to point out the hour of the day. | |
| From: William Paley (Natural Theology [1802], Ch 1) | |
| A reaction: Microscopic examination of the stone would have surprised Paley. Should we infer a geometer because the sun is spherical? Crytals look designed, but are explained by deeper chemistry. |
| 21276 | From the obvious purpose and structure of a watch we must infer that it was designed [Paley] |
| Full Idea: The inference is inevitable that the watch had a maker; that there must have existed, at some time, an artificer or artificers who formed it for the purpose which we find it actually to answer, who designed its use. | |
| From: William Paley (Natural Theology [1802], Ch 1) | |
| A reaction: It rather begs the question to refer to an ordered structure as a 'design'. Why do we think it is absurd to think the the 'purpose' of the sun is to benefit mankind? Suppose we found a freakish natural sundial in the woods. |
| 21357 | No organ shows purpose more obviously than the eyelid [Paley] |
| Full Idea: The eyelid defends the eye; it wipes it; it closes it in sleep. Are there, in any work of art whatever, purposes more evident than those which this organ fulfils? | |
| From: William Paley (Natural Theology [1802], p.24), quoted by Armand Marie LeRoi - The Lagoon: how Aristotle invented science 031 | |
| A reaction: Nice to have another example, in addition to the watch. He is not wholly wrong, because it is impossible to give an evolutionary account of the development of the eyelid without referring to some sort of teleological aspect. The eyelid has a function. |
| 21278 | All the signs of design found in a watch are also found in nature [Paley] |
| Full Idea: Every indication of contrivance, every manifestation of design, which existed in the watch, exists in the works of nature. | |
| From: William Paley (Natural Theology [1802], Ch.3) | |
| A reaction: This is far from obvious. It was crucial to the watch analogy that we immediately see its one self-evident purpose. No one looks at nature and says 'Aha, I know what this is all for'. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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). |