55 ideas
| 7623 | For ancient Greeks being wise was an ethical value [Putnam] |
| 6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
| 6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
| 4714 | Putnam's epistemic notion of truth replaces the realism of correspondence with ontological relativism [Putnam, by O'Grady] |
| 7617 | Before Kant, all philosophers had a correspondence theory of truth [Putnam] |
| 4716 | The correspondence theory is wrong, because there is no one correspondence between reality and fact [Putnam, by O'Grady] |
| 7616 | Truth is an idealisation of rational acceptability [Putnam] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 14203 | Intension is not meaning, as 'cube' and 'square-faced polyhedron' are intensionally the same [Putnam] |
| 14207 | If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth [Putnam] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 21492 | Realism is basic to the scientific method [Peirce] |
| 6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
| 14214 | If we try to cure the abundance of theories with causal links, this is 'just more theory' [Putnam, by Lewis] |
| 14205 | The sentence 'A cat is on a mat' remains always true when 'cat' means cherry and 'mat' means tree [Putnam] |
| 7610 | A fact is simply what it is rational to accept [Putnam] |
| 7618 | Very nominalistic philosophers deny properties, though scientists accept them [Putnam] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 4718 | If necessity is always relative to a description in a language, then there is only 'de dicto' necessity [Putnam, by O'Grady] |
| 6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
| 6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
| 6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
| 6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
| 6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
| 6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
| 6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
| 6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
| 7620 | Some kind of objective 'rightness' is a presupposition of thought itself [Putnam] |
| 14204 | Naïve operationalism would have meanings change every time the tests change [Putnam] |
| 7611 | Rationality is one part of our conception of human flourishing [Putnam] |
| 14200 | 'Water' on Twin Earth doesn't refer to water, but no mental difference can account for this [Putnam] |
| 7612 | Reference is social not individual, because we defer to experts when referring to elm trees [Putnam] |
| 7613 | Concepts are (at least in part) abilities and not occurrences [Putnam] |
| 14202 | Neither individual nor community mental states fix reference [Putnam] |
| 14201 | Maybe the total mental state of a language community fixes the reference of a term [Putnam] |
| 14206 | There are infinitely many interpretations of a sentence which can all seem to be 'correct' [Putnam] |
| 7624 | The word 'inconsiderate' nicely shows the blurring of facts and values [Putnam] |
| 6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
| 6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
| 6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |