67 ideas
| 4767 | Traditionally, rational beliefs are those which are justified by reasons [Psillos] |
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
| 10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
| 10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
| 10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 4810 | Valid deduction is monotonic - that is, it remains valid if further premises are added [Psillos] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 4768 | The 'epistemic fallacy' is inferring what does exist from what can be known to exist [Psillos] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| 10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
| 10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 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] |
| 10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
| 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] |
| 4769 | It is hard to analyse causation, if it is presupposed in our theory of the functioning of the mind [Psillos] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 4770 | Nothing is more usual than to apply to external bodies every internal sensation which they occasion [Psillos] |
| 20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
| 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] |