Was sind und was sollen die Zahlen?
E634839
*Was sind und was sollen die Zahlen?* is a foundational work in the philosophy of mathematics by Richard Dedekind that rigorously investigates the nature and logical basis of numbers.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Was sind und was sollen die Zahlen? canonical | 1 |
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics monograph ⓘ philosophy of mathematics work ⓘ |
| author | Richard Dedekind NERFINISHED ⓘ |
| centralQuestion |
How can numbers be defined purely logically?
ⓘ
What are numbers? ⓘ What is the logical foundation of arithmetic? ⓘ |
| countryOfOrigin | Germany ⓘ |
| focusesOn |
concept of infinity
ⓘ
construction of real numbers ⓘ definition of natural numbers ⓘ logical basis of arithmetic ⓘ set-theoretic methods in arithmetic ⓘ |
| genre |
mathematical treatise
ⓘ
non-fiction ⓘ |
| hasPart |
axiomatic characterization of natural numbers
ⓘ
definition of real numbers via Dedekind cuts ⓘ |
| historicalPeriod | 19th-century mathematics ⓘ |
| influenced |
20th-century foundations of mathematics
ⓘ
Peano arithmetic NERFINISHED ⓘ axiomatic set theory ⓘ logicism in the philosophy of mathematics ⓘ |
| introducesConcept |
Dedekind cut
NERFINISHED
ⓘ
simply infinite system ⓘ |
| mainSubject |
axiomatic foundations
ⓘ
foundations of arithmetic NERFINISHED ⓘ logic of number ⓘ natural numbers ⓘ philosophy of mathematics ⓘ real numbers ⓘ set-theoretic construction of numbers ⓘ |
| mathematicalDiscipline |
analysis
ⓘ
number theory NERFINISHED ⓘ set theory ⓘ |
| notableFor |
influence on modern mathematical logic
ⓘ
introduction of Dedekind cuts ⓘ rigorous logical treatment of number ⓘ set-theoretic construction of the reals ⓘ |
| originalLanguage | German ⓘ |
| philosophicalPosition | logicist approach to arithmetic ⓘ |
| publicationYear | 1888 ⓘ |
| relatedThinker |
Bertrand Russell
NERFINISHED
ⓘ
Giuseppe Peano NERFINISHED ⓘ Gottlob Frege NERFINISHED ⓘ |
| relatedWork | Grundlagen der Arithmetik NERFINISHED ⓘ |
| titleTranslation | What are numbers and what should they be? ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.