75 ideas
| 4767 | Traditionally, rational beliefs are those which are justified by reasons [Psillos] |
| 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] |
| 10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
| 10975 | Compactness does not deny that an inference can have infinitely many premisses [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] |
| 4810 | Valid deduction is monotonic - that is, it remains valid if further premises are added [Psillos] |
| 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] |
| 4768 | The 'epistemic fallacy' is inferring what does exist from what can be known to exist [Psillos] |
| 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] |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| 10989 | The standard view of conditionals is that they are truth-functional [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] |
| 4807 | A good barometer will predict a storm, but not explain it [Psillos] |
| 4808 | If we say where Mars was two months ago, we offer an explanation without a prediction [Psillos] |
| 4811 | Induction (unlike deduction) is non-monotonic - it can be invalidated by new premises [Psillos] |
| 4812 | Explanation is either showing predictability, or showing necessity, or showing causal relations [Psillos] |
| 4802 | Just citing a cause does not enable us to understand an event; we also need a relevant law [Psillos] |
| 4804 | The 'covering law model' says only laws can explain the occurrence of single events [Psillos] |
| 4805 | If laws explain the length of a flagpole's shadow, then the shadow also explains the length of the pole [Psillos] |
| 4395 | There are non-causal explanations, most typically mathematical explanations [Psillos] |
| 4806 | An explanation can just be a 'causal story', without laws, as when I knock over some ink [Psillos] |
| 4404 | Maybe explanation is entirely relative to the interests and presuppositions of the questioner [Psillos] |
| 4803 | An explanation is the removal of the surprise caused by the event [Psillos] |
| 10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
| 4769 | It is hard to analyse causation, if it is presupposed in our theory of the functioning of the mind [Psillos] |
| 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] |
| 4770 | Nothing is more usual than to apply to external bodies every internal sensation which they occasion [Psillos] |
| 15640 | Courage is not a virtue, but the form of every virtue at its testing point [Lewis,CS] |
| 4403 | We can't base our account of causation on explanation, because it is the wrong way round [Psillos] |
| 4399 | Causes clearly make a difference, are recipes for events, explain effects, and are evidence [Psillos] |
| 4400 | Theories of causation are based either on regularity, or on intrinsic relations of properties [Psillos] |
| 4789 | Three divisions of causal theories: generalist/singularist, intrinsic/extrinsic, reductive/non-reductive [Psillos] |
| 4790 | If causation is 'intrinsic' it depends entirely on the properties and relations of the cause and effect [Psillos] |
| 4402 | Empiricists tried to reduce causation to explanation, which they reduced to logic-plus-a-law [Psillos] |
| 4774 | Counterfactual claims about causation imply that it is more than just regular succession [Psillos] |
| 4793 | "All gold cubes are smaller than one cubic mile" is a true universal generalisation, but not a law [Psillos] |
| 4397 | Regularity doesn't seem sufficient for causation [Psillos] |
| 4792 | A Humean view of causation says it is regularities, and causal facts supervene on non-causal facts [Psillos] |
| 4801 | The regularity of a cock's crow is used to predict dawn, even though it doesn't cause it [Psillos] |
| 4401 | It is not a law of nature that all the coins in my pocket are euros, though it is a regularity [Psillos] |
| 4796 | Laws are sets of regularities within a simple and strong coherent system of wider regularities [Psillos] |
| 4799 | Dispositional essentialism can't explain its key distinction between essential and non-essential properties [Psillos] |
| 4780 | In some counterfactuals, the counterfactual event happens later than its consequent [Psillos] |
| 4791 | Counterfactual theories say causes make a difference - if c hadn't occurred, then e wouldn't occur [Psillos] |