32 ideas
| 1606 | You have to be a Platonist to debate about reality, so every philosopher is a Platonist [Roochnik] |
| 1595 | Philosophy aims to satisfy the chief human desire - the articulation of beauty itself [Roochnik] |
| 1571 | 'Logos' ranges from thought/reasoning, to words, to rational structures outside thought [Roochnik] |
| 1572 | In the seventeenth century the only acceptable form of logos was technical knowledge [Roochnik] |
| 1573 | The hallmark of a person with logos is that they give reasons why one opinion is superior to another [Roochnik] |
| 1592 | Logos cannot refute the relativist, and so must admit that it too is a matter of desire (for truth and agreement) [Roochnik] |
| 1593 | Human desire has an ordered structure, with logos at the pinnacle [Roochnik] |
| 1603 | Logos is not unconditionally good, but good if there is another person willing to engage with it [Roochnik] |
| 1598 | We prefer reason or poetry according to whether basics are intelligible or not [Roochnik] |
| 1584 | Modern science, by aiming for clarity about the external world, has abandoned rationality in the human world [Roochnik] |
| 1591 | Unfortunately for reason, argument can't be used to establish the value of argument [Roochnik] |
| 1599 | Attempts to suspend all presuppositions are hopeless, because a common ground must be agreed for the process [Roochnik] |
| 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] |
| 1605 | Reality can be viewed neutrally, or as an object of desire [Roochnik] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 1577 | Relativism is a disease which destroys the possibility of rational debate [Roochnik] |
| 1578 | If relativism is the correct account of human values, then rhetoric is more important than reasoning [Roochnik] |
| 1596 | Reasoning aims not at the understanding of objects, but at the desire to give beautiful speeches [Roochnik] |
| 14409 | I am a presentist, and all language and common sense supports my view [Bigelow] |