45 ideas
| 3750 | "It is true that x" means no more than x [Ramsey] |
| 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] |
| 13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
| 13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
| 16728 | Logicians acknowledge too few things, while others acknowledge too many [Fitzralph] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
| 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] |
| 13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
| 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] |
| 6409 | The 'simple theory of types' distinguishes levels among properties [Ramsey, by Grayling] |
| 13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
| 13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
| 8495 | The distinction between particulars and universals is a mistake made because of language [Ramsey] |
| 8493 | We could make universals collections of particulars, or particulars collections of their qualities [Ramsey] |
| 8494 | Obviously 'Socrates is wise' and 'Socrates has wisdom' express the same fact [Ramsey] |
| 13766 | 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey] |
| 10993 | Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read] |
| 14279 | Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey] |
| 3212 | Beliefs are maps by which we steer [Ramsey] |
| 22328 | I just confront the evidence, and let it act on me [Ramsey] |
| 22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |
| 19724 | Belief is knowledge if it is true, certain, and obtained by a reliable process [Ramsey] |
| 6894 | Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 19143 | Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson] |
| 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] |
| 18818 | Sentence meaning is given by the actions to which it would lead [Ramsey] |
| 9418 | All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey] |
| 9420 | Causal laws result from the simplest axioms of a complete deductive system [Ramsey] |