28 ideas
343 | The unexamined life is not worth living for men [Socrates] |
18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
13344 | X follows from sentences K iff every model of K also models X [Tarski] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
344 | If death is like a night of dreamless sleep, such nights are very pleasant [Socrates] |
339 | Men fear death as a great evil when it may be a great blessing [Socrates] |
2 | We should not even harm someone who harms us [Socrates] |
345 | A good man cannot be harmed, either in life or in death [Socrates] |
346 | One ought not to return a wrong or injury to any person, whatever the provocation [Socrates] |
341 | Wealth is good if it is accompanied by virtue [Socrates] |
347 | Will I stand up against the law, simply because I have been unjustly judged? [Socrates] |
338 | Socrates is accused of denying the gods, saying sun is stone and moon is earth [Socrates, by Plato] |