36 ideas
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
16185 | Causality indicates which properties are real [Cartwright,N] |
8361 | What is true used to be possible, but it may no longer be so [Wright,GHv] |
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] |
16171 | The covering law view assumes that each phenomenon has a 'right' explanation [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] |
16183 | In science, best explanations have regularly turned out to be false [Cartwright,N] |
8363 | p is a cause and q an effect (not vice versa) if manipulations of p change q [Wright,GHv] |
8364 | We can imagine controlling floods by controlling rain, but not vice versa [Wright,GHv] |
8366 | The very notion of a cause depends on agency and action [Wright,GHv] |
8362 | We give regularities a causal character by subjecting them to experiment [Wright,GHv] |
8360 | We must further analyse conditions for causation, into quantifiers or modal concepts [Wright,GHv] |
16175 | A cause won't increase the effect frequency if other causes keep interfering [Cartwright,N] |
8365 | Some laws are causal (Ohm's Law), but others are conceptual principles (conservation of energy) [Wright,GHv] |
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] |
16178 | There are few laws for when one theory meets another [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] |