28 ideas
| 2666 | Carneades' pinnacles of philosophy are the basis of knowledge (the criterion of truth) and the end of appetite (good) [Carneades, by Cicero] |
| 21390 | Future events are true if one day we will say 'this event is happening now' [Carneades] |
| 21672 | We say future things are true that will possess actuality at some following time [Carneades, by Cicero] |
| 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] |
| 15825 | Carneades denied the transitivity of identity [Carneades, by Chisholm] |
| 21389 | Carneades distinguished logical from causal necessity, when talking of future events [Long on Carneades] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 16634 | I can't be unaware of anything which is in me [Descartes] |
| 21671 | Voluntary motion is intrinsically within our power, and this power is its cause [Carneades, by Cicero] |
| 21391 | Some actions are within our power; determinism needs prior causes for everything - so it is false [Carneades, by Cicero] |
| 21674 | Even Apollo can only foretell the future when it is naturally necessary [Carneades, by Cicero] |
| 7398 | Carneades said that after a shipwreck a wise man would seize the only plank by force [Carneades, by Tuck] |
| 3635 | Essence must be known before we discuss existence [Descartes] |
| 21392 | People change laws for advantage; either there is no justice, or it is a form of self-injury [Carneades, by Lactantius] |
| 3634 | We can't prove a first cause from our inability to grasp infinity [Descartes] |