25 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] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [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] |
22180 | Multiple realisability is said to make reduction impossible [Okasha] |
20921 | How can we state relativism of sweet and sour, if they have no determinate nature? [Theophrastus] |
22172 | Not all sciences are experimental; astronomy relies on careful observation [Okasha] |
22177 | Randomised Control Trials have a treatment and a control group, chosen at random [Okasha] |
22174 | The discoverers of Neptune didn't change their theory because of an anomaly [Okasha] |
22175 | Science mostly aims at confirming theories, rather than falsifying them [Okasha] |
22182 | Theories with unobservables are underdetermined by the evidence [Okasha] |
22185 | Two things can't be incompatible if they are incommensurable [Okasha] |
22176 | Induction is inferences from examined to unexamined instances of a given kind [Okasha] |
22178 | If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha] |
5990 | Theophrastus doubted whether nature could be explained teleologically [Theophrastus, by Gottschalk] |
22173 | Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha] |
17366 | Virtually all modern views of speciation rest on relational rather than intrinsic features [Okasha] |