24 ideas
18859 | Metaphysics is a quest for truthmakers [Tallant] |
18861 | Maybe number statements can be paraphrased into quantifications plus identities [Tallant] |
18866 | Maybe only 'positive' truths need truth-makers [Tallant] |
18860 | A truthmaker is the minimal portion of reality that will do the job [Tallant] |
18863 | What is the truthmaker for a possible new power? [Tallant] |
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] |
18864 | The wisdom of Plato and of Socrates are not the same property [Tallant] |
18865 | Substance must have two properties: individuation, and property-bearing [Tallant] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
18862 | Are propositions all the thoughts and sentences that are possible? [Tallant] |
20746 | One is not born, but rather becomes a woman [Beauvoir] |