54 ideas
4767 | Traditionally, rational beliefs are those which are justified by reasons [Psillos] |
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
4810 | Valid deduction is monotonic - that is, it remains valid if further premises are added [Psillos] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
4768 | The 'epistemic fallacy' is inferring what does exist from what can be known to exist [Psillos] |
14933 | Scientific properties are defined by the laws that embody them [Psillos, by Ladyman/Ross] |
17996 | Powers are claimed to be basic because fundamental particles lack internal structure [Psillos] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
4808 | If we say where Mars was two months ago, we offer an explanation without a prediction [Psillos] |
4807 | A good barometer will predict a storm, but not explain it [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] |
4769 | It is hard to analyse causation, if it is presupposed in our theory of the functioning of the mind [Psillos] |
4770 | Nothing is more usual than to apply to external bodies every internal sensation which they occasion [Psillos] |
3015 | The virtue of man is thoughtful foresight of future events [Chilo, by Diog. Laertius] |
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] |