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 start from concepts we already half understand and break them down, not build from definitions as geometry does. Doesn't that make it less certain?
- Augustine said he knows what time is until someone asks him. Why do you think a real definition of time comes last, not first?
- You suggest knowledge of God, a being that must exist, could be surer than most other philosophy. Why would the highest subject be the most certain one?
- You want a table of the truths metaphysics must take as unprovable, and rank finding them first among philosophy's tasks. Why is finding what cannot be proved progress?