46 ideas
20981 | What justifies reliance on reason? Is it just a tool? Why is it better than blind belief? [Sen] |
20982 | In politics and ethics, scrutiny from different perspectives is essential for objectivity [Sen] |
8368 | A correct definition is what can be substituted without loss of meaning [Ducasse] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
20990 | Rationality is conformity to reasons that can be sustained even after scrutiny [Sen] |
21005 | A human right is not plausible if public scrutiny might reject it [Sen] |
20983 | The original position insures that the agreements reached are fair [Sen] |
20987 | The veil of ignorance encourages neutral interests, but not a wider view of values [Sen] |
20984 | A social contract limits the pursuit of justice to members of a single society [Sen] |
20986 | A person's voice may count because of their interests, or because of their good sense [Sen] |
21001 | Famines tend to be caused by authoritarian rule [Sen] |
21002 | Effective democracy needs tolerant values [Sen] |
20999 | Democracy as 'government by discussion' now has wide support [Sen] |
20979 | Democracy needs more than some institutions; diverse sections of the people must be heard [Sen] |
20993 | Eradicating smallpox does not impoverish nature [Sen] |
20995 | Capabilities are part of freedom, involving real opportunities [Sen] |
20998 | Freedom can involve capabilities, independence and non-interference [Sen] |
20997 | The need for equality among people arises from impartiality and objectivity [Sen] |
20996 | All modern theories of justice demand equality of something [Sen] |
20988 | Freedom from torture or terrorist attacks is independent of citizenship [Sen] |
21000 | If justice needs public reasoning, which needs democracy, then justice and democracy are linked [Sen] |
20980 | You don't need a complete theory of justice to see that slavery is wrong [Sen] |
20978 | Practical justice concerns not only ideals, but ways to achieve them [Sen] |
20985 | Our institutions should promote justice, rather than embodying it [Sen] |
20994 | We must focus on removing manifest injustice, not just try to design a perfect society [Sen] |
8367 | Causation is defined in terms of a single sequence, and constant conjunction is no part of it [Ducasse] |
8372 | We see what is in common between causes to assign names to them, not to perceive them [Ducasse] |
8369 | Causes are either sufficient, or necessary, or necessitated, or contingent upon [Ducasse] |
8373 | When a brick and a canary-song hit a window, we ignore the canary if we are interested in the breakage [Ducasse] |
8370 | A cause is a change which occurs close to the effect and just before it [Ducasse] |
8371 | Recurrence is only relevant to the meaning of law, not to the meaning of cause [Ducasse] |
8374 | We are interested in generalising about causes and effects purely for practical purposes [Ducasse] |