37 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] |
| 16665 | There are entities, and then positive 'modes', modifying aspects outside the thing's essence [Suárez] |
| 16666 | A mode determines the state and character of a quantity, without adding to it [Suárez] |
| 16667 | Substances are incomplete unless they have modes [Suárez, by Pasnau] |
| 17007 | Forms must rule over faculties and accidents, and are the source of action and unity [Suárez] |
| 16780 | Partial forms of leaf and fruit are united in the whole form of the tree [Suárez] |
| 16758 | The best support for substantial forms is the co-ordinated unity of a natural being [Suárez] |
| 16743 | We can get at the essential nature of 'quantity' by knowing bulk and extension [Suárez] |
| 16742 | We only know essences through non-essential features, esp. those closest to the essence [Suárez] |
| 22143 | Identity does not exclude possible or imagined difference [Suárez, by Boulter] |
| 22144 | Real Essential distinction: A and B are of different natural kinds [Suárez, by Boulter] |
| 22146 | Minor Real distinction: B needs A, but A doesn't need B [Suárez, by Boulter] |
| 22145 | Major Real distinction: A and B have independent existences [Suárez, by Boulter] |
| 22147 | Conceptual/Mental distinction: one thing can be conceived of in two different ways [Suárez, by Boulter] |
| 22148 | Modal distinction: A isn't B or its property, but still needs B [Suárez, by Boulter] |
| 22149 | Scholastics assess possibility by what has actually happened in reality [Suárez, by Boulter] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 3444 | If actions are not caused by other events, and are not causeless, they must be caused by the person [Chisholm] |
| 3446 | For Hobbes (but not for Kant) a person's actions can be deduced from their desires and beliefs [Chisholm] |
| 9268 | If free will miraculously interrupts causation, animals might do that; why would we want to do it? [Frankfurt on Chisholm] |
| 3442 | Responsibility seems to conflict with events being either caused or not caused [Chisholm] |
| 3443 | Desires may rule us, but are we responsible for our desires? [Chisholm] |
| 3445 | Causation among objects relates either events or states [Chisholm] |
| 16682 | Other things could occupy the same location as an angel [Suárez] |