55 ideas
| 21032 | Speak truth only to those who deserve the truth [Sandel] |
| 21033 | Careful evasions of truth at least show respect for it [Sandel] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 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] |