31 ideas
| 22094 | Subjective truth can only be sustained by repetition [Kierkegaard, by Carlisle] |
| 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] |
| 18680 | To avoid misunderstandings supervenience is often expressed negatively: no A-change without B-change [Orsi] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 18684 | Rather than requiring an action, a reason may 'entice' us, or be 'eligible', or 'justify' it [Orsi] |
| 18666 | Value-maker concepts (such as courageous or elegant) simultaneously describe and evaluate [Orsi] |
| 18667 | The '-able' concepts (like enviable) say this thing deserves a particular response [Orsi] |
| 18685 | Final value is favoured for its own sake, and personal value for someone's sake [Orsi] |
| 18679 | Things are only valuable if something makes it valuable, and we can ask for the reason [Orsi] |
| 18682 | A complex value is not just the sum of the values of the parts [Orsi] |
| 18683 | Trichotomy Thesis: comparable values must be better, worse or the same [Orsi] |
| 18686 | The Fitting Attitude view says values are fitting or reasonable, and values are just byproducts [Orsi] |
| 18672 | Values from reasons has the 'wrong kind of reason' problem - admiration arising from fear [Orsi] |
| 18677 | A thing may have final value, which is still derived from other values, or from relations [Orsi] |
| 18668 | Truths about value entail normative truths about actions or attitudes [Orsi] |
| 18670 | The Buck-Passing view of normative values says other properties are reasons for the value [Orsi] |
| 18669 | Values can be normative in the Fitting Attitude account, where 'good' means fitting favouring [Orsi] |
| 22093 | Life is a repetition when what has been now becomes [Kierkegaard] |