31 ideas
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [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] |
| 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] |
| 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] |
| 16185 | Causality indicates which properties are real [Cartwright,N] |
| 14221 | Serious essentialism says everything has essences, they're not things, and they ground necessities [Shalkowski] |
| 14222 | Essences are what it is to be that (kind of) thing - in fact, they are the thing's identity [Shalkowski] |
| 14226 | We distinguish objects by their attributes, not by their essences [Shalkowski] |
| 14225 | Critics say that essences are too mysterious to be known [Shalkowski] |
| 14223 | De dicto necessity has linguistic entities as their source, so it is a type of de re necessity [Shalkowski] |
| 16182 | Two main types of explanation are by causes, or by citing a theoretical framework [Cartwright,N] |
| 16184 | An explanation is a model that fits a theory and predicts the phenomenological laws [Cartwright,N] |
| 16167 | Laws get the facts wrong, and explanation rests on improvements and qualifications of laws [Cartwright,N] |
| 16169 | Laws apply to separate domains, but real explanations apply to intersecting domains [Cartwright,N] |
| 16176 | Covering-law explanation lets us explain storms by falling barometers [Cartwright,N] |
| 16177 | I disagree with the covering-law view that there is a law to cover every single case [Cartwright,N] |
| 16180 | You can't explain one quail's behaviour by just saying that all quails do it [Cartwright,N] |
| 16171 | The covering law view assumes that each phenomenon has a 'right' explanation [Cartwright,N] |
| 16183 | In science, best explanations have regularly turned out to be false [Cartwright,N] |
| 14224 | Equilateral and equiangular aren't the same, as we have to prove their connection [Shalkowski] |
| 16175 | A cause won't increase the effect frequency if other causes keep interfering [Cartwright,N] |
| 6781 | There are fundamental explanatory laws (false!), and phenomenological laws (regularities) [Cartwright,N, by Bird] |
| 16166 | Laws of appearances are 'phenomenological'; laws of reality are 'theoretical' [Cartwright,N] |
| 16179 | Good organisation may not be true, and the truth may not organise very much [Cartwright,N] |
| 16170 | To get from facts to equations, we need a prepared descriptions suited to mathematics [Cartwright,N] |
| 16181 | Simple laws have quite different outcomes when they act in combinations [Cartwright,N] |
| 16178 | There are few laws for when one theory meets another [Cartwright,N] |