55 ideas
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
21032 | Speak truth only to those who deserve the truth [Sandel] |
21033 | Careful evasions of truth at least show respect for it [Sandel] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
21036 | Not all deals are fair deals [Sandel] |
21038 | Does consent create the obligation, or must there be some benefit? [Sandel] |
21039 | Moral contracts involve both consent and reciprocity; making the deal, and keeping it [Sandel] |
21030 | The categorical imperative is not the Golden Rule, which concerns contingent desires [Sandel] |
22262 | Kant's moral law has no foundation - because that would undermine its priority [Sandel] |
21031 | Man cannot dispose of himself, because he is not a thing to be owned [Sandel] |
20594 | Choosers in the 'original position' have been stripped of most human characteristics [Sandel, by Tuckness/Wolf] |
21035 | Just visiting (and using roads) is hardly ratifying the Constitution [Sandel] |
21037 | A ratified constitution may not be a just constitution [Sandel] |
21034 | A just constitution harmonises the different freedoms [Sandel] |
22258 | Passion for progress is always short-lived [Sandel] |
22259 | Conservatives are either individualistic, or communal [Sandel] |
22264 | Modern liberal rights in democracies protect individuals against the majority [Sandel] |
22261 | Liberals say rights always come first, and justice is neutral on social values [Sandel] |
21120 | The self is 'unencumbered' if it can abandon its roles and commitments without losing identity [Sandel, by Shorten] |
22263 | Liberal justice means the withdrawal of the self, as transcendental or as unencumbered [Sandel] |
21049 | Liberal freedom was a response to assigned destinies like caste and class [Sandel] |
22805 | Liberalism concerns rights, and communitarianism concerns the common good [Sandel, by Avineri/De-Shalit] |
22260 | Modern liberalism fails to articulate a vision of the common good [Sandel] |
22265 | I can't defend the view that the majority values of a community are thereby right [Sandel] |
22268 | If persons define themselves by a group membership, insults to that group are a real harm [Sandel] |
22267 | In the liberal view an insult to my group doesn't hurt me, since I'm defined by choices not groups [Sandel] |
21040 | Libertarians just want formal equality in a free market; the meritocratic view wants fair equality [Sandel] |
21028 | We can approach justice through welfare, or freedom, or virtue [Sandel] |
21027 | Justice concerns how a society distributes what it prizes - wealth, rights, power and honours [Sandel] |
21042 | Should we redress wrongs done by a previous generation? [Sandel] |
21043 | Distributive justice concern deserts, as well as who gets what [Sandel] |
21052 | Justice is about how we value things, and not just about distributions [Sandel] |
21048 | Work is not fair if it is negotiated, even in a fair situation, but if it suits the nature of the worker [Sandel] |
22266 | The case for religious liberty depends on the religion contributing to a morally good life [Sandel] |
21045 | Teleological thinking is essential for social and political issues [Sandel] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |