This paper is based on a semantic foundation of quantum logic which makes use of dialog-games. In the first part of the paper the dialogic method is introduced and under the conditions of quantum mechanical measurements the rules of a dialog-game about quantum mechanical propositions are established. In the second part of the paper the quantum mechanical dialog-game is replaced by a calculus of quantum logic. As the main part of the paper we show that the calculus of quantum logic (...) is complete and consistent with respect to the dialogic semantics. Since the dialoggame does not involve the 'excluded middle' the calculus represents a calculus of effective (intuitionistic) quantum logic. In a forthcoming paper it is shown that this calculus is equivalent to a calculus of sequents and more interestingly to a calculus of propositions. With the addition of the 'excluded middle' the latter calculus is a model for the lattice of subspaces of a Hilbert space. (shrink)

‘And now invoking as our helper overseas Zeus' calf and the son of the flower-browsing ancestress cow by conception from the on-breathing of Zeus—’: so begins the appeal of Danaos' daughters to their forefather Epaphos; the opening sentence is interrupted by a digression and never completed. In 43 M reads is almost universally adopted. However, is printed in the current Oxford text . Porson's emendation was attacked by Tucker on various grounds: it was palaeographically unsatisfactory, it added an otiose epithet (...) to but left unqualified, it involved a ‘scarcely Greek’ use of the participle, and it coined a form in having the unique sense ‘graze’ instead of ‘handle’. My purpose is to defend as the true reading and to explore its contextual significance. I begin by taking Tucker's objections in order. (shrink)