Validity and quantification in intuitionism

We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logical notions considered we suggest that the most natural reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.This paper was partly written while the first author, H. C. M. de Swart, was a Visiting Fellow at Princeton University for the academic year 1976–1977. This opportunity was given to him by the Niels Stensen Stichting in Amsterdam, the department of philosophy of the Catholic University in Nijmegen and by Princeton University. He is happy to express his appreciation for that opportunity.