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Recall that for Du Châtelet, these first principles include epistemological principles the principles of contradiction and sufficient reason (IP §4 and §8).
Leśniewski's early works are mainly reactions to work by others, whether Brentano and Cornelius on existential propositions, Łukasiewicz on the Principles of Contradiction and Excluded Middle, Twardowski on universals, or Kotarbiński on the timelessness of truth.
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He saw clearly that, as the first kind of proposition is governed by the principle of contradiction (a proposition and its negation cannot both be true), the second is governed by the principle of sufficient reason (nothing exists or is the case without a sufficient reason).
Second, the Principle of Contradiction is too strong.
Otherwise it could never have been derived from it by means of the principle of contradiction.
Absolute necessity, he argued, is governed by the principle of contradiction.
This was the 1910 monograph On the Principle of Contradiction in Aristotle.
In impossible worlds, however, the principle of contradiction does not hold.
Whereas mathematics is said to be grounded on the principle of contradiction, this is not the case for philosophy.
Leibniz also follows Aristotle (cf. Metaphysics IV.3), in placing great emphasis on the Principle of Identity or the Principle of Contradiction (PC).
"The contradiction is the nonidentical under the aspect of [conceptual] identity; the primacy of the principle of contradiction in dialectics tests the heterogeneous according to unitary thought [Einheitsdenken].
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