The present paper aims at integrating the phenomenological reading of Brouwerian intuitionism into the domain of semantics, by challenging the claim that the very meaning of mathematical expressions—expressions of free choice sequences included—is invariable and objectively determinable and that, accordingly, any deictic expression should be removed from mathematics. By introducing constructability into the constitution of meaning itself and by considering meaning as a “social act”, we try to map another route into intersubjectivity, based on the distinction between the play-level and the strategic level, which has been further developed in the dialogical framework, following the work of Paul Lorenzen. It is suggested that the steps towards such a route can be retraced from Oskar Becker’s original “Cartesian” approach to intersubjectivity, which facilitates a new reading of Brouwer’s own way of conceptualizing “mutual understanding”. In doing so, our general purpose is therefore to promote an insertion of dialogical constructivism into Mark van Atten’s take on the intuitionist Creating Subject.