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Single Idea 6849
[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
]
Full Idea
Wittgenstein didn't just have an arguments against logicism; he hated logicism, and described is as a cancerous growth.
Gist of Idea
Wittgenstein hated logicism, and described it as a cancerous growth
Source
report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Ray Monk - Interview with Baggini and Stangroom p.12
Book Ref
Baggini,J/Stangroom,J: 'New British Philosophy' [Routledge 2002], p.12
A Reaction
This appears to have been part of an inexplicable personal antipathy towards Russell. Wittgenstein appears to have developed a dislike of all reductionist ideas in philosophy.
The
40 ideas
with the same theme
[objections to the logicism view of maths]:
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]
|
10831
|
Frege only managed to prove that arithmetic was analytic with a logic that included set-theory
[Quine on Frege]
|
10010
|
Frege's belief in logicism and in numerical objects seem uncomfortable together
[Hodes on Frege]
|
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]
|
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]
|
23509
|
The logic of the world is shown by tautologies in logic, and by equations in mathematics
[Wittgenstein]
|
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]
|
23441
|
Logical truth is true in all models, so mathematical objects can't be purely logical
[Linnebo]
|
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]
|