27 ideas
| 22358 | Scientific objectivity lies in inter-subjective testing [Popper] |
| 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] |
| 16659 | Relations do not add anything to reality, though they are real aspects of the world [Olivi] |
| 16673 | Quantity just adds union and location to the extension of parts [Olivi] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 22188 | Give Nobel Prizes for really good refutations? [Gorham on Popper] |
| 7780 | Falsification is the criterion of demarcation between science and non-science [Popper, by Magee] |
| 16830 | We don't only reject hypotheses because we have falsified them [Lipton on Popper] |
| 6794 | If falsification requires logical inconsistency, then probabilistic statements can't be falsified [Bird on Popper] |
| 6795 | When Popper gets in difficulties, he quietly uses induction to help out [Bird on Popper] |
| 3856 | Good theories have empirical content, explain a lot, and are not falsified [Popper, by Newton-Smith] |
| 7779 | There is no such thing as induction [Popper, by Magee] |
| 3860 | Science cannot be shown to be rational if induction is rejected [Newton-Smith on Popper] |
| 16663 | Things are limited by the species to certain modes of being [Olivi] |