35 ideas
| 2510 | Traditionally philosophy is an a priori enquiry into general truths about reality [Katz] |
| 2516 | Most of philosophy begins where science leaves off [Katz] |
| 6118 | Philosophy is logical analysis, followed by synthesis [Russell] |
| 6116 | A logical language would show up the fallacy of inferring reality from ordinary language [Russell] |
| 6117 | Philosophy should be built on science, to reduce error [Russell] |
| 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] |
| 6110 | Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell] |
| 6107 | It is logic, not metaphysics, that is fundamental to philosophy [Russell] |
| 6115 | Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell] |
| 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] |
| 6109 | Some axioms may only become accepted when they lead to obvious conclusions [Russell] |
| 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] |
| 2521 | 'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz] |
| 6108 | Maths can be deduced from logical axioms and the logic of relations [Russell] |
| 10968 | Russell gave up logical atomism because of negative, general and belief propositions [Russell, by Read] |
| 6113 | To mean facts we assert them; to mean simples we name them [Russell] |
| 6114 | 'Simples' are not experienced, but are inferred at the limits of analysis [Russell] |
| 21722 | Better to construct from what is known, than to infer what is unknown [Russell] |
| 6111 | As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form [Russell] |
| 2513 | We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz] |
| 2522 | Experience cannot teach us why maths and logic are necessary [Katz] |
| 6112 | Meaning takes many different forms, depending on different logical types [Russell] |
| 2517 | Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz] |
| 2519 | It is generally accepted that sense is defined as the determiner of reference [Katz] |
| 2520 | Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz] |
| 2518 | Sentences are abstract types (like musical scores), not individual tokens [Katz] |