31 ideas
| 13070 | If definitions must be general, and general terms can't individuate, then Socrates can't be defined [Aquinas, by Cover/O'Leary-Hawthorne] |
| 11197 | The definitions expressing identity are used to sort things [Aquinas] |
| 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] |
| 11195 | If affirmative propositions express being, we affirm about what is absent [Aquinas] |
| 11201 | Properties have an incomplete essence, with definitions referring to their subject [Aquinas] |
| 11205 | If the form of 'human' contains 'many', Socrates isn't human; if it contains 'one', Socrates is Plato [Aquinas] |
| 13090 | The principle of diversity for corporeal substances is their matter [Aquinas, by Cover/O'Leary-Hawthorne] |
| 11202 | It is by having essence that things exist [Aquinas] |
| 11203 | Specific individual essence is defined by material, and generic essence is defined by form [Aquinas] |
| 11200 | The definition of a physical object must include the material as well as the form [Aquinas] |
| 11196 | Essence is something in common between the natures which sort things into categories [Aquinas] |
| 11208 | A simple substance is its own essence [Aquinas] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 11198 | Definition of essence makes things understandable [Aquinas] |
| 11206 | The mind constructs complete attributions, based on the unified elements of the real world [Aquinas] |
| 12165 | Romantics say music expresses ideas, or the Will, or intuitions, or feelings [Scruton] |
| 12164 | Expressing melancholy is a good thing, but arousing it is a bad thing [Scruton] |
| 11207 | A cause can exist without its effect, but the effect cannot exist without its cause [Aquinas] |