12458 | Kant taught that mathematics is independent of logic, and cannot be grounded in it [Kant, by Hilbert] |
2795 | If 7+5=12 is analytic, then an infinity of other ways to reach 12 have to be analytic [Kant, by Dancy,J] |
13864 | Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects [Wright,C on Frege] |
10033 | Why should the existence of pure logic entail the existence of objects? [George/Velleman on Frege] |
10010 | Frege's belief in logicism and in numerical objects seem uncomfortable together [Hodes on Frege] |
10831 | Frege only managed to prove that arithmetic was analytic with a logic that included set-theory [Quine on Frege] |
9545 | Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara] |
17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
6849 | Wittgenstein hated logicism, and described it as a cancerous growth [Wittgenstein, by Monk] |
9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
1635 | Mathematics reduces to set theory (which is a bit vague and unobvious), but not to logic proper [Quine] |
1613 | Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine] |
8754 | Logic is dependent on mathematics, not the other way round [Heyting, by Shapiro] |
17808 | Saying mathematics is logic is merely replacing one undefined term by another [Curry] |
9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
12331 | Logic is definitional, but real mathematics is axiomatic [Badiou] |
18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C] |
13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C] |
18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
12224 | Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright] |
13625 | Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
21713 | Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B] |
21715 | For those who abandon logicism, standard set theory is a rival option [Linsky,B] |
17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
11063 | Logicism struggles because there is no decent theory of analyticity [Hanna] |
17724 | It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins] |