68 ideas
| 6961 | An analogy begins to break down as soon as the two cases differ [Hume] |
| 10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
| 11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
| 11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
| 11011 | Same say there are positive, negative and neuter free logics [Read] |
| 11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
| 10986 | Not all validity is captured in first-order logic [Read] |
| 10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
| 11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
| 10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
| 10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
| 10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
| 10973 | A theory is logically closed, which means infinite premisses [Read] |
| 11007 | Quantifiers are second-order predicates [Read] |
| 10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
| 10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
| 10988 | Any first-order theory of sets is inadequate [Read] |
| 10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
| 10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
| 10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
| 10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
| 11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
| 11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
| 10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
| 10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
| 10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
| 11016 | Would a language without vagueness be usable at all? [Read] |
| 11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
| 11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
| 11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
| 10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
| 11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
| 10989 | The standard view of conditionals is that they are truth-functional [Read] |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| 11017 | Some people even claim that conditionals do not express propositions [Read] |
| 10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
| 10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
| 10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
| 10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
| 11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
| 21285 | Events are baffling before experience, and obvious after experience [Hume] |
| 10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
| 16369 | There is a single file per object, memorised, reactivated, consolidated and expanded [Papineau, by Recanati] |
| 11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
| 10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
| 6959 | We can't assume God's perfections are like our ideas or like human attributes [Hume] |
| 6957 | The objects of theological reasoning are too big for our minds [Hume] |
| 21255 | No being's non-existence can imply a contradiction, so its existence cannot be proved a priori [Hume] |
| 21254 | A chain of events requires a cause for the whole as well as the parts, yet the chain is just a sum of parts [Hume] |
| 1435 | If something must be necessary so that something exists rather than nothing, why can't the universe be necessary? [Hume] |
| 6962 | The thing which contains order must be God, so see God where you see order [Hume] |
| 6960 | Analogy suggests that God has a very great human mind [Hume] |
| 6958 | How can we pronounce on a whole after a brief look at a very small part? [Hume] |
| 21279 | If the divine cause is proportional to its effects, the effects are finite, so the Deity cannot be infinite [Hume] |
| 21282 | Design cannot prove a unified Deity. Many men make a city, so why not many gods for a world? [Hume] |
| 21280 | From a ship you would judge its creator a genius, not a mere humble workman [Hume] |
| 6966 | Creation is more like vegetation than human art, so it won't come from reason [Hume] |
| 21281 | This excellent world may be the result of a huge sequence of trial-and-error [Hume] |
| 21283 | Humans renew their species sexually. If there are many gods, would they not do the same? [Hume] |
| 21284 | This Creator god might be an infant or incompetent or senile [Hume] |
| 6967 | Order may come from an irrational source as well as a rational one [Hume] |
| 21286 | Motion often begins in matter, with no sign of a controlling agent [Hume] |
| 21287 | The universe could settle into superficial order, without a designer [Hume] |
| 21288 | Ideas arise from objects, not vice versa; ideas only influence matter if they are linked [Hume] |
| 21256 | A surprise feature of all products of 9 looks like design, but is actually a necessity [Hume] |
| 6965 | The universe may be the result of trial-and-error [Hume] |
| 6964 | From our limited view, we cannot tell if the universe is faulty [Hume] |
| 6963 | Why would we infer an infinite creator from a finite creation? [Hume] |