Actuality, and the Necessity of Distinctness and Possibility

Abstract

AbstractAn actuality operator is introduced, governed by two principles according to which p if possibly actually p, and necessarily actually p if p. With actuality added to Classicism in this way, two new principles, namely the necessity of distinctness and the necessity of possibility, become derivable. Relative to Classicism, these two principles are equivalent. Setting aside the actuality operator, this motivates extending Classicism by the necessity of possibility; the resulting view is called C5. It is shown that this leads to the strong and well-known modal logic S5.