30 ideas
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
16185 | Causality indicates which properties are real [Cartwright,N] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
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] |
4377 | Intellectualism is an excessive emphasis on reasoning in moral philosophy [Burnyeat] |
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] |