How is pure mathematics possible?
E91455
"How is pure mathematics possible?" is a central guiding question in Immanuel Kant’s *Prolegomena to Any Future Metaphysics*, where he investigates the conditions that make synthetic a priori knowledge in mathematics possible.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
Kantian concept
ⓘ
epistemological problem ⓘ philosophical question ⓘ |
| addresses |
ground of the certainty of mathematical knowledge
ⓘ
problem of the applicability of mathematics to appearances ⓘ |
| aimsToExplain |
how mathematical judgments can be necessary and universally valid
ⓘ
how mathematical knowledge extends our cognition ⓘ |
| answerAccordingToKant |
arithmetic is grounded in the pure intuition of time
ⓘ
geometry is grounded in the pure intuition of space ⓘ pure mathematics is possible because its objects are constructed in pure intuition ⓘ |
| asksAbout |
a priori foundations of arithmetic
ⓘ
a priori foundations of geometry ⓘ possibility of pure mathematics as a science ⓘ relation between mathematics and pure intuition ⓘ |
| author | Immanuel Kant ⓘ |
| centralTheme | synthetic a priori knowledge ⓘ |
| concerns |
conditions of possibility of mathematical knowledge
ⓘ
justification of synthetic a priori judgments in mathematics ⓘ status of mathematical propositions ⓘ |
| discussedIn | Prolegomena to Any Future Metaphysics ⓘ |
| field |
epistemology
ⓘ
philosophy of mathematics ⓘ |
| historicalContext | late 18th century ⓘ |
| influenced |
neo-Kantian philosophy
ⓘ
phenomenology of mathematics ⓘ subsequent philosophy of mathematics ⓘ |
| keyConcept |
a priori versus a posteriori knowledge
ⓘ
distinction between analytic and synthetic judgments ⓘ forms of sensibility ⓘ pure intuition of space ⓘ pure intuition of time ⓘ synthetic a priori judgments ⓘ transcendental ideality of space and time ⓘ |
| language | German ⓘ |
| mainWork | Prolegomena to Any Future Metaphysics ⓘ |
| method | transcendental investigation ⓘ |
| originalTitleContext |
Prolegomena to Any Future Metaphysics
ⓘ
surface form:
Prolegomena zu einer jeden künftigen Metaphysik, die als Wissenschaft wird auftreten können
|
| philosophicalPeriod |
Age of Enlightenment
ⓘ
surface form:
Enlightenment
|
| philosophicalTradition | transcendental idealism ⓘ |
| relatedDoctrine |
Kant’s doctrine of sensibility
ⓘ
Kant’s doctrine of the transcendental aesthetic ⓘ |
| relatedQuestion |
How is metaphysics as a science possible?
ⓘ
How is pure natural science possible? ⓘ |
| relatedWork | Critique of Pure Reason ⓘ |
| statusInWork | central guiding question of the Prolegomena ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.