64 ideas
| 9408 | Science studies phenomena, but only metaphysics tells us what exists [Mumford] |
| 6575 | Philosophy may never find foundations, and may undermine our lives in the process [Fogelin] |
| 9429 | Many forms of reasoning, such as extrapolation and analogy, are useful but deductively invalid [Mumford] |
| 6585 | Rationality is threatened by fear of inconsistency, illusions of absolutes or relativism, and doubt [Fogelin] |
| 6557 | Humans may never be able to attain a world view which is both rich and consistent [Fogelin] |
| 6568 | A game can be played, despite having inconsistent rules [Fogelin] |
| 6560 | The law of noncontradiction is traditionally the most basic principle of rationality [Fogelin] |
| 6565 | The law of noncontradiction makes the distinction between asserting something and denying it [Fogelin] |
| 6574 | Legal reasoning is analogical, not deductive [Fogelin] |
| 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] |
| 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] |
| 9427 | For Humeans the world is a world primarily of events [Mumford] |
| 9446 | Properties are just natural clusters of powers [Mumford] |
| 9435 | A 'porridge' nominalist thinks we just divide reality in any way that suits us [Mumford] |
| 9447 | If properties are clusters of powers, this can explain why properties resemble in degrees [Mumford] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 12248 | How can we show that a universally possessed property is an essential property? [Mumford] |
| 6582 | Conventions can only work if they are based on something non-conventional [Fogelin] |
| 6576 | My view is 'circumspect rationalism' - that only our intellect can comprehend the world [Fogelin] |
| 6589 | Knowledge is legitimate only if all relevant defeaters have been eliminated [Fogelin] |
| 6596 | For coherentists, circularity is acceptable if the circle is large, rich and coherent [Fogelin] |
| 6597 | A rule of justification might be: don't raise the level of scrutiny without a good reason [Fogelin] |
| 6588 | Scepticism is cartesian (sceptical scenarios), or Humean (future), or Pyrrhonian (suspend belief) [Fogelin] |
| 6590 | Scepticism deals in remote possibilities that are ineliminable and set the standard very high [Fogelin] |
| 6583 | Radical perspectivism replaces Kant's necessary scheme with many different schemes [Fogelin] |
| 6555 | We are also irrational, with a unique ability to believe in bizarre self-created fictions [Fogelin] |
| 6605 | Critics must be causally entangled with their subject matter [Fogelin] |
| 6607 | The word 'beautiful', when deprived of context, is nearly contentless [Fogelin] |
| 6604 | Saying 'It's all a matter to taste' ignores the properties of the object discussed [Fogelin] |
| 6586 | Cynics are committed to morality, but disappointed or disgusted by human failings [Fogelin] |
| 6572 | Deterrence, prevention, rehabilitation and retribution can come into conflict in punishments [Fogelin] |
| 6573 | Retributivists say a crime can be 'paid for'; deterrentists still worry about potential victims [Fogelin] |
| 9430 | Singular causes, and identities, might be necessary without falling under a law [Mumford] |
| 9445 | We can give up the counterfactual account if we take causal language at face value [Mumford] |
| 9443 | It is only properties which are the source of necessity in the world [Mumford] |
| 9444 | There are four candidates for the logical form of law statements [Mumford] |
| 9441 | Regularity laws don't explain, because they have no governing role [Mumford] |
| 9431 | Pure regularities are rare, usually only found in idealized conditions [Mumford] |
| 9416 | Regularities are more likely with few instances, and guaranteed with no instances! [Mumford] |
| 9415 | Would it count as a regularity if the only five As were also B? [Mumford] |
| 9422 | If the best system describes a nomological system, the laws are in nature, not in the description [Mumford] |
| 9421 | The best systems theory says regularities derive from laws, rather than constituting them [Mumford] |
| 9432 | Laws of nature are necessary relations between universal properties, rather than about particulars [Mumford] |
| 9433 | If laws can be uninstantiated, this favours the view of them as connecting universals [Mumford] |
| 9434 | Laws of nature are just the possession of essential properties by natural kinds [Mumford] |
| 9437 | To distinguish accidental from essential properties, we must include possible members of kinds [Mumford] |
| 9439 | The Central Dilemma is how to explain an internal or external view of laws which govern [Mumford] |
| 9412 | You only need laws if you (erroneously) think the world is otherwise inert [Mumford] |
| 9411 | There are no laws of nature in Aristotle; they became standard with Descartes and Newton [Mumford] |