41 ideas
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| 8859 | The main modal logics disagree over three key formulae [Yablo] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| 8492 | Relations are functions with two arguments [Frege] |
| 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] |
| 8865 | If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise? [Yablo] |
| 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] |
| 8863 | We must treat numbers as existing in order to express ourselves about the arrangement of planets [Yablo] |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| 8862 | Platonic objects are really created as existential metaphors [Yablo] |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| 8864 | We quantify over events, worlds, etc. in order to make logical possibilities clearer [Yablo] |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| 8858 | Philosophers keep finding unexpected objects, like models, worlds, functions, numbers, events, sets, properties [Yablo] |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| 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] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| 8861 | Hardly a word in the language is devoid of metaphorical potential [Yablo] |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |