11 ideas
| 17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
| Full Idea: Zermelo's paper sets out to show that the standard set-theoretic axioms (what he calls the 'constitutive axioms', thus the ZF axioms minus the axiom of infinity) have an unending sequence of different models, thus that they are non-categorical. | |
| From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Michael Hallett - Introduction to Zermelo's 1930 paper p.1209 | |
| A reaction: Hallett says later that Zermelo is working with second-order set theory. The addition of an Axiom of Infinity seems to have aimed at addressing the problem, and the complexities of that were pursued by Gödel. |
| 13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
| Full Idea: Zermelo included Replacement in 1930, after it was noticed that the sequence of power sets was needed, and Replacement gave the ordinal form of the well-ordering theorem, and justification for transfinite recursion. | |
| From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Penelope Maddy - Believing the Axioms I §1.8 | |
| A reaction: Maddy says that this axiom suits the 'limitation of size' theorists very well, but is not so good for the 'iterative conception'. |
| 17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
| Full Idea: Two opposite tendencies of thought, the idea of creative advance and of collection and completion (underlying the Kantian 'antinomies') find their symbolic representation and their symbolic reconciliation in the transfinite numbers based on well-ordering. | |
| From: Ernst Zermelo (On boundary numbers and domains of sets [1930], §5) | |
| A reaction: [a bit compressed] It is this sort of idea, from one of the greatest set-theorists, that leads philosophers to think that the philosophy of mathematics may offer solutions to metaphysical problems. As an outsider, I am sceptical. |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal. | |
| From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'. |
| 21833 | Research suggest that we overrate conscious experience [Flanagan] |
| Full Idea: The emerging consensus is that we probably overrate the power of conscious experience in our lives. Freud, of course, said the same thing for different reasons. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 3 'Ontology') | |
| A reaction: [He cites Pockett, Banks and Gallagher 2006]. Freud was concerned with big deep secrets, but the modern view concerns ordinary decisions and perceptions. An important idea, which should incline us all to become Nietzscheans. |
| 21834 | Sensations may be identical to brain events, but complex mental events don't seem to be [Flanagan] |
| Full Idea: There is still some hope for something like identity theory for sensations. But almost no one believes that strict identity theory will work for more complex mental states. Strict identity is stronger than type neurophysicalism. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 3 'Ontology') | |
| A reaction: It is so hard to express the problem. What needs to be explained? How can one bunch of neurons represent many different things? It's not like computing. That just transfers the data to brains, where the puzzling stuff happens. |
| 21837 | Morality is normative because it identifies best practices among the normal practices [Flanagan] |
| Full Idea: Morality is 'normative' in the sense that it consists of the extraction of ''good' or 'excellent' practices from common practices. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 4 'Naturalism') |
| 21830 | For Darwinians, altruism is either contracts or genetics [Flanagan] |
| Full Idea: Two explanations came forward in the neo-Darwinian synthesis. Altruism is either 1) person-based reciprocal altruism, or 2) gene-based kin altruism. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 2 'Darwin') | |
| A reaction: Flanagan obviously thinks there is also 'genuine psychological atruism'. Presumably we don't explain mathematics or music or the desire to travel as either contracts or genetics, so we have other explanations available. |
| 21835 | We need Eudaimonics - the empirical study of how we should flourish [Flanagan] |
| Full Idea: It would be nice if I could advance the case for Eudaimonics - empirical enquiry into the nature, causes, and constituents of flourishing, …and the case for some ways of living and being as better than others. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 4 'Normative') | |
| A reaction: Things seem to be moving in that direction. Lots of statistics about happiness have been appearing. |
| 21831 | Alienation is not finding what one wants, or being unable to achieve it [Flanagan] |
| Full Idea: What Marx called 'alienation' is the widespread condition of not being able to discover what one wants, or not being remotely positioned to achieve. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 2 'Expanding') | |
| A reaction: I took alienation to concern people's relationship to the means of production in their trade. On Flanagan's definition I would expect almost everyone aged under 20 to count as alienated. |
| 21832 | Buddhists reject God and the self, and accept suffering as key, and liberation through wisdom [Flanagan] |
| Full Idea: Buddhism rejected the idea of a creator God, and the unchanging self [atman]. They accept the appearance-reality distinction, reward for virtue [karma], suffering defining our predicament, and that liberation [nirvana] is possible through wisdom. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 3 'Buddhism') | |
| A reaction: [Compressed] Flanagan is an analytic philosopher and a practising Buddhist. Looking at a happiness map today which shows Europeans largely happy, and Africans largely miserable, I can see why they thought suffering was basic. |