44 ideas
| 6575 | Philosophy may never find foundations, and may undermine our lives in the process [Fogelin] |
| 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] |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| 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] |