67 ideas
| 21032 | Speak truth only to those who deserve the truth [Sandel] |
| 21033 | Careful evasions of truth at least show respect for it [Sandel] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 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] |