39 ideas
| 18851 | Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen] |
| Full Idea: In conjunction with Extensionality, Pairing entails that given a single non-set, infinitely many sets exist. | |
| From: Gideon Rosen (The Limits of Contingency [2006], 04) |
| 18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
| Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1) | |
| A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark. |
| 18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
| Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise. |
| 18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
| Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea. |
| 18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
| Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting. |
| 18852 | A Meinongian principle might say that there is an object for any modest class of properties [Rosen] |
| Full Idea: Meinongian abstraction principles say that for any (suitably restricted) class of properties, there exists an abstract entity (arbitrary object, subsistent entity) that possesses just those properties. | |
| From: Gideon Rosen (The Limits of Contingency [2006], 04) | |
| A reaction: This is 'Meinongian' because there will be an object which is circular and square. The nub of the idea presumably resides in what is meant by 'restricted'. An object possessing every conceivable property is, I guess, a step too far. |
| 18849 | Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant [Rosen] |
| Full Idea: If P is metaphysically necessary, then it is absolutely necessary, and necessary in every real (non-epistemic) sense; and if P is possible in any sense, then it's possible in the metaphysical sense. | |
| From: Gideon Rosen (The Limits of Contingency [2006], 02) | |
| A reaction: Rosen's shot at defining metaphysical necessity and possibility, and it looks pretty good to me. In my terms (drawing from Kit Fine) it is what is necessitated or permitted 'by everything'. So if it is necessitated by logic or nature, that's included. |
| 18850 | 'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting [Rosen] |
| Full Idea: 'Metaphysical' modality is the sort of modality relative to which it is an interesting question whether the laws of nature are necessary or contingent. | |
| From: Gideon Rosen (The Limits of Contingency [2006], 02) | |
| A reaction: Being an essentialist here, I take it that the stuff of the universe necessitates the so-called 'laws'. The metaphysically interesting question is whether the stuff might have been different. Search me! A nice test of metaphysical modality though. |
| 18858 | Sets, universals and aggregates may be metaphysically necessary in one sense, but not another [Rosen] |
| Full Idea: It may be metaphysically necessary in one sense that sets or universals or mereological aggregates exist, while in another sense existence is always a contingent matter. | |
| From: Gideon Rosen (The Limits of Contingency [2006], 10) | |
| A reaction: This idea depends on Idea 18856 and 18857. Personally I only think mereological aggregates and sets exist when people decide that they exist, so I don't see how they could ever be necessary. I'm unconvinced about his two concepts. |
| 18857 | Standard Metaphysical Necessity: P holds wherever the actual form of the world holds [Rosen] |
| Full Idea: According to the Standard Conception of Metaphysical Necessity, P is metaphysically necessary when it holds in every possible world in which the laws of metaphysics (about the form or structure of the actual world) hold | |
| From: Gideon Rosen (The Limits of Contingency [2006], 10) | |
| A reaction: Rosen has a second meaning, in Idea 18856. He thinks it is crucial to see that there are two senses, because many things come out as metaphysically necessary on one concept, but contingent on the other. Interesting.... |
| 18856 | Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things [Rosen] |
| Full Idea: According to the Non-Standard conception of Metaphysical Necessity, P is metaphysically necessary when its negation is logically incompatible with the nature of things. | |
| From: Gideon Rosen (The Limits of Contingency [2006], 10) | |
| A reaction: Rosen's new second meaning of the term. My immediate problem is with it resting on being 'logically' incompatible. Are squares 'logically' incompatible with circles? I like the idea that it rests on 'the nature of things'. (Psst! natures = essences) |
| 18848 | Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen] |
| Full Idea: It is one thing to say that P is necessary in some generic sense because it is a truth of logic (true in all models of a language, perhaps). It is something else to say that P therefore enjoys a special sort of necessity. | |
| From: Gideon Rosen (The Limits of Contingency [2006], 02) | |
| A reaction: This encourages my thought that there is only one sort of necessity (what must be), and the variety comes from the different types of necessity makers (everything there could be, nature, duties, promises, logics, concepts...). |
| 18855 | Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen] |
| Full Idea: Combinatorial theories of possibility take it for granted ....that possible worlds in general share a syntax, as it were, differing only in the constituents from which they are generated, or in the particular manner of their arrangements. | |
| From: Gideon Rosen (The Limits of Contingency [2006], 08) | |
| A reaction: For instance, it might assume that every world has 'objects', to which 'properties' and 'relations' can be attached, or to which 'functions' can apply. |
| 18853 | A proposition is 'correctly' conceivable if an ominiscient being could conceive it [Rosen] |
| Full Idea: To a first approximation, P is correctly conceivable iff it would be conceivable for a logically ominiscient being who was fully informed about the nature of things. | |
| From: Gideon Rosen (The Limits of Contingency [2006], 05) | |
| A reaction: Isn't the last bit covered by 'ominiscient'? Ah, I think the 'logically' only means they have a perfect grasp of what is consistent. This is to meet the standard problem, of ill-informed people 'conceiving' of things which are actually impossible. |
| 18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
| Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory. |
| 18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
| Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions. |
| 18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
| Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular). |
| 18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
| Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds. |
| 18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
| Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5) | |
| A reaction: They accept lots of successes in modelling necessity and time. |
| 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. |
| 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. |
| 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! |
| 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? |
| 18854 | The MRL view says laws are the theorems of the simplest and strongest account of the world [Rosen] |
| Full Idea: According to the Mill-Ramsey-Lewis account of the laws of nature, a generalisation is a law just in case it is a theorem of every true account of the actual world that achieves the best overall balance of simplicity and strength. | |
| From: Gideon Rosen (The Limits of Contingency [2006], 08) | |
| A reaction: The obvious objection is that many of the theorems will be utterly trivial, and that is one thing that the laws of nature are not. Unless you are including 'metaphysical laws' about very very fundamental things, like objects, properties, relations. |