32 ideas
| 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] |
| 16660 | Are things distinct if they are both separate, or if only one of them can be separate? [Duns Scotus, by Pasnau] |
| 16626 | Substance is only grasped under the general heading of 'being' [Duns Scotus] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 20014 | Actions include: the involuntary, the purposeful, the intentional, and the self-consciously autonomous [Wilson/Schpall] |
| 20019 | Maybe bodily movements are not actions, but only part of an agent's action of moving [Wilson/Schpall] |
| 20021 | Is the action the arm movement, the whole causal process, or just the trying to do it? [Wilson/Schpall] |
| 20022 | To be intentional, an action must succeed in the manner in which it was planned [Wilson/Schpall] |
| 20023 | If someone believes they can control the lottery, and then wins, the relevant skill is missing [Wilson/Schpall] |
| 20025 | We might intend two ways to acting, knowing only one of them can succeed [Wilson/Schpall] |
| 20031 | On one model, an intention is belief-desire states, and intentional actions relate to beliefs and desires [Wilson/Schpall] |
| 20028 | Groups may act for reasons held by none of the members, so maybe groups are agents [Wilson/Schpall] |
| 20027 | If there are shared obligations and intentions, we may need a primitive notion of 'joint commitment' [Wilson/Schpall] |
| 20016 | Strong Cognitivism identifies an intention to act with a belief [Wilson/Schpall] |
| 20017 | Weak Cognitivism says intentions are only partly constituted by a belief [Wilson/Schpall] |
| 20018 | Strong Cognitivism implies a mode of 'practical' knowledge, not based on observation [Wilson/Schpall] |
| 20012 | Maybe the explanation of an action is in the reasons that make it intelligible to the agent [Wilson/Schpall] |
| 20029 | Causalists allow purposive explanations, but then reduce the purpose to the action's cause [Wilson/Schpall] |
| 20013 | It is generally assumed that reason explanations are causal [Wilson/Schpall] |