33 ideas
| 1642 | We must fight fiercely for knowledge, understanding and intelligence [Plato] |
| 1645 | The desire to split everything into its parts is unpleasant and unphilosophical [Plato] |
| 287 | Good analysis involves dividing things into appropriate forms without confusion [Plato] |
| 1644 | Dialectic should only be taught to those who already philosophise well [Plato] |
| 20478 | In discussion a person's opinions are shown to be in conflict, leading to calm self-criticism [Plato] |
| 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] |
| 11278 | What does 'that which is not' refer to? [Plato] |
| 1643 | If statements about non-existence are logically puzzling, so are statements about existence [Plato] |
| 7022 | To be is to have a capacity, to act on other things, or to receive actions [Plato] |
| 1641 | Some alarming thinkers think that only things which you can touch exist [Plato] |
| 10784 | Whenever there's speech it has to be about something [Plato] |
| 16122 | Good thinkers spot forms spread through things, or included within some larger form [Plato] |
| 10422 | The not-beautiful is part of the beautiful, though opposed to it, and is just as real [Plato] |
| 15855 | If we see everything as separate, we can then give no account of it [Plato] |
| 16285 | A possible world can be seen as a complete and consistent novel [Jeffrey] |
| 1637 | A soul without understanding is ugly [Plato] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 19155 | Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey, by Davidson] |
| 1636 | Wickedness is an illness of the soul [Plato] |
| 1638 | Didactic education is hard work and achieves little [Plato] |