33 ideas
| 1813 | All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius] |
| Full Idea: Twelfth mode: all reasoning leads on to further reasoning, and this process goes on forever. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 1811 | Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius] |
| Full Idea: Fifteenth mode: proofs often presuppose the thing to be proved. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 1815 | Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius] |
| Full Idea: Fourteenth mode: reasoning requires arbitrary faith in preliminary hypotheses. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 1812 | All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius] |
| Full Idea: Eleventh mode: all topics of discussion are full of uncertainty and contradiction. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| Full Idea: Many axioms have been proposed, not on the grounds that they can be directly known, but rather because they produce a desired body of previously recognised results. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.5.1) | |
| A reaction: This is the perennial problem with axioms - whether we start from them, or whether we deduce them after the event. There is nothing wrong with that, just as we might infer the existence of quarks because of their results. |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| Full Idea: Mathematical realism is the doctrine that mathematical objects exist, that much contemporary mathematics is true, and that the existence and truth in question is independent of our constructions, beliefs and proofs. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.12.9) | |
| A reaction: As thus defined, I would call myself a mathematical realist, but everyone must hesitate a little at the word 'exist' and ask, how does it exist? What is it 'made of'? To say that it exists in the way that patterns exist strikes me as very helpful. |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| Full Idea: In maths the primary subject-matter is not mathematical objects but structures in which they are arranged; our constants and quantifiers denote atoms, structureless points, or positions in structures; they have no identity outside a structure or pattern. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.1) | |
| A reaction: This seems to me a very promising idea for the understanding of mathematics. All mathematicians acknowledge that the recognition of patterns is basic to the subject. Even animals recognise patterns. It is natural to invent a language of patterns. |
| 6303 | Sets are positions in patterns [Resnik] |
| Full Idea: On my view, sets are positions in certain patterns. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.5) | |
| A reaction: I have always found the ontology of a 'set' puzzling, because they seem to depend on prior reasons why something is a member of a given set, which cannot always be random. It is hard to explain sets without mentioning properties. |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| Full Idea: An objection is that structuralism fails to explain why certain mathematical patterns are unified wholes while others are not; for instance, some think that an ontological account of mathematics must explain why a triangle is not a 'random' set of points. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.4) | |
| A reaction: This is an indication that we are not just saying that we recognise patterns in nature, but that we also 'see' various underlying characteristics of the patterns. The obvious suggestion is that we see meta-patterns. |
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| Full Idea: If we take mathematics at its word, there are too many mathematical objects for it to be plausible that they are all mental or physical objects. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1) | |
| A reaction: No one, of course, has ever claimed that they are, but this is a good starting point for assessing the ontology of mathematics. We are going to need 'rules', which can deduce the multitudinous mathematical objects from a small ontology. |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| Full Idea: I argue that mathematical knowledge has its roots in pattern recognition and representation, and that manipulating representations of patterns provides the connection between the mathematical proof and mathematical truth. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1) | |
| A reaction: The suggestion that patterns are at the basis of the ontology of mathematics is the most illuminating thought I have encountered in the area. It immediately opens up the possibility of maths being an entirely empirical subject. |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| Full Idea: Of the equivalence relationships which occur between patterns, congruence is the strongest, equivalence the next, and mutual occurrence the weakest. None of these is identity, which would require the same position. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.3) | |
| A reaction: This gives some indication of how an account of mathematics as a science of patterns might be built up. Presumably the recognition of these 'degrees of strength' cannot be straightforward observation, but will need an a priori component? |
| 8850 | Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M] |
| Full Idea: Agrippa's Trilemma offers three possible outcomes for a regress of justification: the chain goes on for ever (infinite); or the chain stops at an unjustified proposition (arbitrary); or the chain eventually includes the original proposition (circular). | |
| From: report of Agrippa (fragments/reports [c.60], §2) by Michael Williams - Without Immediate Justification §2 | |
| A reaction: This summarises Ideas 1911, 1913 and 1914. Agrippa's Trilemma is now a standard starting point for modern discussions of foundations. Personally I reject 2, and am torn between 1 (+ social consensus) and 3 (with a benign, coherent circle). |
| 1814 | Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius] |
| Full Idea: Thirteenth mode: everything is always perceived in relation to something else. | |
| From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10 |
| 23125 | Most good social changes are incremental, rather than revolutionary [Gopnik] |
| Full Idea: More permanent positive social change is made incrementally rather than by revolutionary transformation. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 1) | |
| A reaction: This is the standard liberal response to revolution. Revolutionaries obviously consider such a claim to be very naïve, and a failure to grasp how deep the changes need to go. |
| 23126 | Conservatives often want peace, prosperity and tolerance, but not social fairness [Gopnik] |
| Full Idea: Many conservatives want their world to be peaceful, properous, and pluralist, just as liberals do, but they don't particularly care that it be fair. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 1) | |
| A reaction: Every conservative will have a sense of what is fair (such as appropriate punishments, and keeping of contracts), but they are more inclined to think that fairness must be fought for by individuals, not imposed by governments. |
| 23132 | Conservatives believe obedience and rank are essential to social order [Gopnik] |
| Full Idea: The idea that the appearance of submission and obedience and rank are essential to order is at the heart of the conservative ideal. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 2) | |
| A reaction: [He has just quoted Edmund Burke writing of Marie Antoinette] I once heard Richard Hare say that he thought social order would be best modelled on the army. A colleague once told me that obedience is a prime duty of a school teacher. |
| 23128 | The opposite of liberalism is dogmatism [Gopnik] |
| Full Idea: The opposite of liberalism is not conservatism but dogmatism. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 1) | |
| A reaction: Nice. It pinpoints the liberal opposition to both extremes of normal politics. It might make anarchists their allies, though! |
| 23142 | People are fallible, so liberalism tries to distribute power [Gopnik] |
| Full Idea: Liberalism makes the idea of fallibility into a political practice by trying not to have too much power concentrated in one place or part of the system. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: There is a potential inefficiency and failure to focus on key goals implicit in this aim. It may be a good idea for a peacetime democracy, but a terrible idea for a wartime army. To stop corruption, don't let anyone do anything? |
| 23143 | Liberals have tried very hard to build a conscience into their institutions [Gopnik] |
| Full Idea: What liberalism can say on its own behalf is that no system of power in human history has tried harder to insert a corrective conscience into its institutions. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: What we are learning in recent years is that wonderful liberal institutions can be quietly eroded by the forces of darkness, once those forces have sufficient control of the media to hide what they are doing. The 'rule of law' is wobbling. |
| 23141 | Left-wingers are inconsistent in their essentialist descriptions of social groups [Gopnik] |
| Full Idea: A criticism of the left is that it is essentialist at some moments, and wildly anti-essentialist at others. We can call this opportunistic essentialism. Gender is fluid - except for transgender kids. Race is a construction - except for white races. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: [compressed] Interesting. Gopnik's solution seems to be to abandon all social essentialism as wicked. In this context he is probably right, but I am firmly committed to the idea that many entities in the world have essential natures. 'Bourgeois'. |
| 23124 | Liberal community is not blood ties or tradition, but shared choices, and sympathy for the losers [Gopnik] |
| Full Idea: The liberal idea of community is not one, as it is for many conservatives, of blood ties or traditional authority. It rest on the idea of shared choices …including even a sense of sympathy for those caught on the losing side of the argument. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 1) | |
| A reaction: The key point is that most liberals (other than extreme libertarians) have a strong sense of community, contrary to the standard criticisms offered by communitarians. |
| 23127 | Liberal community includes flight from the family, into energetic reforming groups [Gopnik] |
| Full Idea: Where conservatives believe in the renewal of traditional community, liberals believe as well in the flight from family and tradition into new kinds of communal order. …It is an idea of assembling confidence and energies for reform. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 1) | |
| A reaction: He cites Greenwich Village as an example. This suggests that his vision is a little narrow. His communities are for radicals who flee to join like minds in big cities. Politics must care about community for those left behind. Pubs, sport and pets. |
| 23129 | Right-wingers attack liberal faith in reason, left-wingers attack its faith in reform [Gopnik] |
| Full Idea: The right-wing critique of liberalism is largely an attack on its overreliance on reason; the left-wing one, mostly an attack on its false faith in reform. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 2) | |
| A reaction: I doubt whether sensible liberals do rely too much on reason, though they do rely of scientific evidence (after peer review!). No one can doubt that lots of reforms have occurred, so it must be frustration with the very slow process. |
| 23133 | Cosmopolitan liberals lack national loyalty, and welcome excessive immigration [Gopnik] |
| Full Idea: Critics say liberal cosmopolitanism is indifference to national loyalty, making them easily contemplate going elsewhere and, worse still, welcoming in the world through unsifted immigration. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 2) | |
| A reaction: There is certainly some truth in this. Not all liberals are so cosmopolitan, though. It is interesting to observe whether people who retire stay in their old community or move to somewhere quite new. |
| 23138 | Modern left-wingers criticise liberalism's control of culture [Gopnik] |
| Full Idea: Most left-wing critiques of liberalism now turn more often on its cultural power and its cultural illusions. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: As opposed to older Marxists critiques of the exploitation of workers. This is certainly fertile ground for interesting studies of our culture. It is very hard to grasp the influence had by the endless stories we expose ourselves to. |
| 23139 | Liberalism's attempt to be neutral and colour-blind erases cultural identities [Gopnik] |
| Full Idea: The 'colour-blind' universe of 'neutral' liberalism is actually an attempt to erase cultural identity and history. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: This is the modern critique of liberalism [centred on the Intersectionality of Bell Hooks or Kimberlé Crenshaw], which analyses alienated minorities, and their emphasis on their difference in response. It can lead to 'identity politics'. |
| 23135 | Classic Marxists see liberalism as the ideology of the bourgeoisie [Gopnik] |
| Full Idea: The classic Marxist account shows liberalism as merely the ideology of the bourgeoisie. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: The word 'merely' does an awful lot of work in philosohy! I suspect that 'bourgeoisie' is self-defining here - as the believers in liberalism - given that lots of Marxists emerge from the middle classes. |
| 23140 | Environmental disasters result not from capitalism, but from a general drive for growth [Gopnik] |
| Full Idea: It is the drive for growth, not capitalism in particular, that makes environmental disasters happen. Those caused by the command economics of Eastern Europe were far greater than even the worst known in Western Europe. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: So the next question is whether you can have capitalism without a drive for growth. I would have thought not, given the role recycled profit plays in driving capitalism. Command economies are more easily swept away. |
| 23130 | Popular imperialism gives the poor the belief that their acts have world historical meaning [Gopnik] |
| Full Idea: Popular imperialism is the cosmopolitanism of the poor, the lever by which the small and impotent come to believe that their acts have world historical meaning. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 2) | |
| A reaction: It is not only the poor who like imperialism. The focus of this popular attitude is the armed forces, and especially the army, where personal bravery is most obvious. The army gets strong support, no matter how dubious are its activities. |
| 23131 | Patriots love their place, but nationalists have a paranoid ethnic hostility [Gopnik] |
| Full Idea: The patriot loves his place and its cheeses; …the nationalist has not particular affection for the place, but employs his obsessive sense of encirclement and grievance on behalf of acts of ethnic vengeance. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 2) | |
| A reaction: 'Vengeance' seems a bit strong. John Le Carré said nationalists are distinguished by the need to have enemies. Russia is particularly obsessed with 'encirclement'. |
| 23136 | Liberal free speech is actually paid speech [Gopnik] |
| Full Idea: What liberals call free speech or a free press is invariably paid speech. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: He give this as the left-wing view of liberalism. The much-hated social media are a substantial breech in this tendency. Sales of newspapers are declining everywhere, so the battle is for television channels. |
| 23134 | A 'free' society implies a free market, which always produces predatory capitalism and inequalities [Gopnik] |
| Full Idea: 'Free societies', as a matter of practical fact, always mean free-market societies - and free markets will never sponsor more than predatory capitalism. Inequalities always emerge. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: This is part of his account of left-wing objections to liberalism. The crux of the liberal view is a conviction that the worst of capitalism can be restrained. This began to look doubtful once huge multinational companies emerged. What to do? |