Settlement of a Mathematical Dispute Based on a Misunderstanding
Kant answers Reimarus concerning integer ratios of a right triangle’s sides. He distinguishes consecutive numbers from the wider set of possible integer triples.
Understanding the text
Published in the Berlinische Monatsschrift in 1796, the clarification revisits an example used in a previous essay.
Key points
- 01
Example
The triple 3, 4, 5 satisfies the Pythagorean theorem, but other integer triples also exist.
- 02
Interpretation
Kant presents his restriction as applying to three immediately consecutive numbers, while Reimarus considers a wider set.
- 03
Disagreement
Ambiguous wording can create the appearance of contradiction between different propositions.
How to read it
Check both formulations mathematically and consider whether this clarification answers the original statement.
Editions & sources
Summaries and key points are original editorial interpretations. They accompany reading the work and do not replace an edition of the text. Editorial method ↗