44 ideas
| 7689 | The modal logic of C.I.Lewis was only interpreted by Kripke and Hintikka in the 1960s [Jacquette] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 7681 | Logic describes inferences between sentences expressing possible properties of objects [Jacquette] |
| 7682 | Logic is not just about signs, because it relates to states of affairs, objects, properties and truth-values [Jacquette] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 7697 | On Russell's analysis, the sentence "The winged horse has wings" comes out as false [Jacquette] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 7701 | Can a Barber shave all and only those persons who do not shave themselves? [Jacquette] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 7707 | To grasp being, we must say why something exists, and why there is one world [Jacquette] |
| 7687 | Existence is completeness and consistency [Jacquette] |
| 7692 | Being is maximal consistency [Jacquette] |
| 7679 | Ontology is the same as the conceptual foundations of logic [Jacquette] |
| 7678 | Ontology must include the minimum requirements for our semantics [Jacquette] |
| 7683 | Logic is based either on separate objects and properties, or objects as combinations of properties [Jacquette] |
| 7684 | Reduce states-of-affairs to object-property combinations, and possible worlds to states-of-affairs [Jacquette] |
| 7703 | If classes can't be eliminated, and they are property combinations, then properties (universals) can't be either [Jacquette] |
| 7685 | An object is a predication subject, distinguished by a distinctive combination of properties [Jacquette] |
| 7699 | Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals [Jacquette] |
| 7691 | The actual world is a consistent combination of states, made of consistent property combinations [Jacquette] |
| 7688 | The actual world is a maximally consistent combination of actual states of affairs [Jacquette] |
| 7695 | Do proposition-structures not associated with the actual world deserve to be called worlds? [Jacquette] |
| 7694 | We must experience the 'actual' world, which is defined by maximally consistent propositions [Jacquette] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 7706 | If qualia supervene on intentional states, then intentional states are explanatorily fundamental [Jacquette] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 7704 | Reduction of intentionality involving nonexistent objects is impossible, as reduction must be to what is actual [Jacquette] |
| 7702 | The extreme views on propositions are Frege's Platonism and Quine's extreme nominalism [Jacquette] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |