25 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] |
| 13074 | Only natural kinds and their members have real essences [Suárez, by Cover/O'Leary-Hawthorne] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 19451 | When absorbed in deep reflection, is your reason in control, or is it you? [Feuerbach] |
| 19450 | Reason, love and will are the highest perfections and essence of man - the purpose of his life [Feuerbach] |
| 7563 | The old 'influx' view of causation says it is a flow of accidental properties from A to B [Suárez, by Jolley] |
| 19448 | Consciousness is said to distinguish man from animals - consciousness of his own species [Feuerbach] |
| 19454 | A God needs justice, kindness and wisdom, but those concepts don't depend on the concept of God [Feuerbach] |
| 19452 | The nature of God is an expression of human nature [Feuerbach] |
| 19453 | If love, goodness and personality are human, the God who is their source is anthropomorphic [Feuerbach] |
| 19449 | Religion is the consciousness of the infinite [Feuerbach] |
| 19455 | Today's atheism will tomorrow become a religion [Feuerbach] |