47 ideas
| 8166 | Truth is part of semantics, since valid inference preserves truth [Dummett] |
| 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] |
| 8173 | Language can violate bivalence because of non-referring terms or ill-defined predicates [Dummett] |
| 8179 | The law of excluded middle is the logical reflection of the principle of bivalence [Dummett] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 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] |
| 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] |
| 8184 | Philosophers should not presume reality, but only invoke it when language requires it [Dummett] |
| 8185 | We can't make sense of a world not apprehended by a mind [Dummett] |
| 8163 | Since 'no bird here' and 'no squirrel here' seem the same, we must talk of 'atomic' facts [Dummett] |
| 8161 | We know we can state facts, with true statements [Dummett] |
| 8180 | 'That is red or orange' might be considered true, even though 'that is red' and 'that is orange' were not [Dummett] |
| 8178 | Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale [Dummett] |
| 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] |
| 8175 | A theory of thought will include propositional attitudes as well as propositions [Dummett] |
| 8174 | The theories of meaning and understanding are the only routes to an account of thought [Dummett] |
| 8165 | To 'abstract from' is a logical process, as opposed to the old mental view [Dummett] |
| 8168 | To know the truth-conditions of a sentence, you must already know the meaning [Dummett] |
| 8181 | A justificationist theory of meaning leads to the rejection of classical logic [Dummett] |
| 8182 | Verificationism could be realist, if we imagined the verification by a superhuman power [Dummett] |
| 8183 | If truths about the past depend on memories and current evidence, the past will change [Dummett] |
| 8176 | We could only guess the meanings of 'true' and 'false' when sentences were used [Dummett] |
| 8170 | Sentences are the primary semantic units, because they can say something [Dummett] |
| 8169 | We can't distinguish a proposition from its content [Dummett] |
| 22410 | Maybe the unthinkable is a moral category, and considering some options is dishonourable or absurd [Williams,B] |
| 22408 | Consequentialism assumes that situations can be compared [Williams,B] |
| 22411 | For a consequentialist massacring 7 million must be better than massacring 7 million and one [Williams,B] |
| 22409 | We don't have a duty to ensure that others do their duty [Williams,B] |
| 22407 | Utilitarianism cannot make any serious sense of integrity [Williams,B] |
| 8186 | Time is the measure of change, so we can't speak of time before all change [Dummett] |
| 8167 | If Presentism is correct, we cannot even say that the present changes [Dummett] |