14788 | Mathematics is close to logic, but is even more abstract [Peirce] |
8628 | I hold that algebra and number are developments of logic [Jevons] |
8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
18165 | My Basic Law V is a law of pure logic [Frege] |
9945 | Logicism shows that no empirical truths are needed to justify arithmetic [George/Velleman on Frege] |
8782 | Frege offered a Platonist version of logicism, committed to cardinal and real numbers [Hale/Wright on Frege] |
5658 | Numbers are definable in terms of mapping items which fall under concepts [Scruton on Frege] |
7739 | Arithmetic is analytic [Weiner on Frege] |
16905 | Arithmetic must be based on logic, because of its total generality [Jeshion on Frege] |
8655 | Arithmetic is analytic and a priori, and thus it is part of logic [Frege] |
18166 | The loss of my Rule V seems to make foundations for arithmetic impossible [Frege] |
16880 | Frege aimed to discover the logical foundations which justify arithmetical judgements [Burge on Frege] |
8689 | Eventually Frege tried to found arithmetic in geometry instead of in logic [Friend on Frege] |
13414 | For Russell, numbers are sets of equivalent sets [Benacerraf on Russell] |
6108 | Maths can be deduced from logical axioms and the logic of relations [Russell] |
6423 | We tried to define all of pure maths using logical premisses and concepts [Russell] |
10025 | Russell and Whitehead took arithmetic to be higher-order logic [Hodes on Russell/Whitehead] |
10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Friend on Russell/Whitehead] |
14103 | Pure mathematics is the class of propositions of the form 'p implies q' [Russell] |
17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell] |
8748 | Logical positivists incorporated geometry into logicism, saying axioms are just definitions [Shapiro on Carnap] |
13936 | Questions about numbers are answered by analysis, and are analytic, and hence logically true [Carnap] |
11073 | Two and one making three has the necessity of logical inference [Wittgenstein] |
5202 | Maths and logic are true universally because they are analytic or tautological [Ayer] |
8993 | If mathematics follows from definitions, then it is conventional, and part of logic [Quine] |
13608 | Mathematics has no special axioms of its own, but follows from principles of logic (with definitions) [Bostock] |
8788 | Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright] |
10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
8473 | The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein] |