39 ideas
19342 | Reason avoids multiplying hypotheses or principles [Leibniz] |
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] |
12711 | The immediate cause of movements is more real [than geometry] [Leibniz] |
19349 | The complete notion of a substance implies all of its predicates or attributes [Leibniz] |
7558 | Substances mirror God or the universe, each from its own viewpoint [Leibniz] |
16761 | Forms are of no value in physics, but are indispensable in metaphysics [Leibniz] |
13088 | Subjects include predicates, so full understanding of subjects reveals all the predicates [Leibniz] |
13085 | Leibniz is some form of haecceitist [Leibniz, by Cover/O'Leary-Hawthorne] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
5024 | Knowledge doesn't just come from the senses; we know the self, substance, identity, being etc. [Leibniz] |
20429 | Most of us are too close to our own motives to understand them [Fry] |
5027 | If a person's memories became totally those of the King of China, he would be the King of China [Leibniz] |
5023 | Future contingent events are certain, because God foresees them, but that doesn't make them necessary [Leibniz] |
2119 | People argue for God's free will, but it isn't needed if God acts in perfection following supreme reason [Leibniz] |
5025 | Mind and body can't influence one another, but God wouldn't intervene in the daily routine [Leibniz] |
20424 | Imaginative life requires no action, so new kinds of perception and values emerge in art [Fry] |
20427 | Everyone reveals an aesthetic attitude, looking at something which only exists to be seen [Fry] |
20433 | 'Beauty' can either mean sensuous charm, or the aesthetic approval of art (which may be ugly) [Fry] |
20430 | In life we neglect 'cosmic emotion', but it matters, and art brings it to the fore [Fry] |
20431 | Art needs a mixture of order and variety in its sensations [Fry] |
20423 | If graphic arts only aim at imitation, their works are only trivial ingenious toys [Fry] |
20428 | Popular opinion favours realism, yet most people never look closely at anything! [Fry] |
20432 | When viewing art, rather than flowers, we are aware of purpose, and sympathy with its creator [Fry] |
20425 | In the cinema the emotions are weaker, but much clearer than in ordinary life [Fry] |
20426 | For pure moralists art must promote right action, and not just be harmless [Fry] |
5026 | Animals lack morality because they lack self-reflection [Leibniz] |