Certainty, Geometry's and Metaphysics'
Can the truths of metaphysics be made as exact as a geometer's? The Berlin Academy's prize question, answered here with a firm no and a reason that would drive everything after.
Mathematics makes its own objects — define a triangle and the definition is whole — so it builds downward from definitions with perfect distinctness. Metaphysics inherits its objects already tangled in experience and must work the other way, analysing given concepts for what is certain in them, the method Kant credits to Newton over Euclid. The essay lost the 1763 prize to Mendelssohn; its verdict, that philosophy had been failing by borrowing mathematics' method without mathematics' advantages, is the sharpest pre-critical statement of the problem the first Critique would finally resolve.
- reason
- necessity
- contradiction
- judgment
- metaphysics
- epistemology
- certainty
- mathematics
Enter a dialogue
- A student despairs that philosophy never reaches a geometer's certainty — what would you tell her to expect from it instead?
- You say metaphysics must analyse given concepts, never build from definitions — doesn't that doom it to being less sure than geometry?
- How does the geometer's power to make his own object differ from what the metaphysician is stuck doing?
- Borrowing mathematics' method got philosophy nowhere — what must a thinker surrender once they admit their objects come already tangled in experience?