Kronecker’s finitism
E100231
Kronecker’s finitism is a philosophical and mathematical stance asserting that only finite, constructible mathematical objects and proofs are legitimate, rejecting the existence of actual infinities.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Kronecker’s finitism canonical | 1 |
| constructivism in mathematics | 1 |
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical foundational stance
ⓘ
philosophy of mathematics position ⓘ |
| accepts |
explicit constructions in proofs
ⓘ
finite sequences of integers ⓘ natural numbers as finite objects ⓘ |
| associatedWith |
Kronecker’s finitism
self-linksurface differs
ⓘ
surface form:
constructivism in mathematics
intuitionism in mathematics ⓘ |
| contrastsWith |
Platonism
ⓘ
surface form:
Platonism in mathematics
formalism that allows ideal infinite objects ⓘ logicism in mathematics ⓘ |
| corePrinciple |
infinite sets are not completed objects
ⓘ
mathematical existence requires explicit construction ⓘ only finite, effectively constructible objects are legitimate ⓘ |
| criticizes |
non-constructive existence theorems in classical analysis
ⓘ
use of completed infinite sets in analysis ⓘ |
| differsFrom | Hilbert’s finitism by stronger rejection of ideal elements ⓘ |
| domain |
foundations of analysis
ⓘ
foundations of arithmetic ⓘ |
| emphasizes |
constructible mathematical objects
ⓘ
finite mathematical objects ⓘ |
| epistemicAttitude | mathematical knowledge must be grounded in finite operations ⓘ |
| focusesOn | arithmetic rather than abstract set-theoretic entities ⓘ |
| historicalContext |
19th-century debates on foundations of analysis
ⓘ
early criticism of transfinite methods ⓘ |
| historicallyArticulatedBy | Leopold Kronecker’s writings and remarks ⓘ |
| influenced | later constructive and finitist schools ⓘ |
| influencedBy | Leopold Kronecker’s arithmeticism ⓘ |
| influencedDiscussionOf |
legitimacy of transfinite numbers
ⓘ
role of constructive methods in mathematics ⓘ |
| motivatedBy |
desire for arithmetic foundations of mathematics
ⓘ
suspicion of non-constructive methods ⓘ |
| namedAfter | Leopold Kronecker ⓘ |
| opposes |
set theory
ⓘ
surface form:
Cantorian set theory
classical set theory with actual infinities ⓘ unrestricted use of the law of excluded middle in infinite contexts ⓘ |
| philosophicalClaim |
mathematics is grounded in the intuition of finite integers
ⓘ
only computable or effectively given objects are acceptable ⓘ |
| rejects |
actual infinities
ⓘ
completed infinite totalities ⓘ non-constructive existence proofs ⓘ |
| relatedTo |
Hilbert’s finitism (as a later, distinct development)
ⓘ
finitism in proof theory ⓘ |
| stanceOnProofs |
prefers algorithmic or constructive proofs
ⓘ
rejects proofs that assert existence without construction ⓘ |
| viewOnInfinity | accepts only potential infinity, not actual infinity ⓘ |
| viewOnRealNumbers | skeptical of non-constructively defined real numbers ⓘ |
| viewOnSets | accepts only finite sets as completed objects ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
constructivism in mathematics