37 ideas
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
15592 | The usual Tarskian interpretation of variables is to specify their range of values [Fine,K] |
15593 | Variables can be viewed as special terms - functions taking assignments into individuals [Fine,K] |
15590 | It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that [Fine,K] |
15591 | In separate expressions variables seem identical in role, but in the same expression they aren't [Fine,K] |
15595 | The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K] |
15594 | 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K] |
15599 | Cicero/Cicero and Cicero/Tully may differ in relationship, despite being semantically the same [Fine,K] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
15603 | I can only represent individuals as the same if I do not already represent them as the same [Fine,K] |
15604 | If Cicero=Tully refers to the man twice, then surely Cicero=Cicero does as well? [Fine,K] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
15602 | Mental files are devices for keeping track of basic coordination of objects [Fine,K] |
15588 | You cannot determine the full content from a thought's intrinsic character, as relations are involved [Fine,K] |
15596 | The standard aim of semantics is to assign a semantic value to each expression [Fine,K] |
15587 | That two utterances say the same thing may not be intrinsic to them, but involve their relationships [Fine,K] |
15589 | The two main theories are Holism (which is inferential), and Representational (which is atomistic) [Fine,K] |
15598 | We should pursue semantic facts as stated by truths in theories (and not put the theories first!) [Fine,K] |
15600 | Referentialist semantics has objects for names, properties for predicates, and propositions for connectives [Fine,K] |
15601 | Fregeans approach the world through sense, Referentialists through reference [Fine,K] |
15605 | I take indexicals such as 'this' and 'that' to be linked to some associated demonstration [Fine,K] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |