Identity connective and modality

This paper is intended to present a detailed syst?matisation of the open part, i.e. without bound variables, of what is called in [3] the ontology of L. Wittgenstein. This is the content of sections 4?15 where a particular open theory of kind W is described and developed. It contains an extensional theory of modality. The three initial sections 1?3 serve as an introduction and involve a discussion of the Fregean axiom, basic logical notions and the general description of open theories of kind W. The second part of this paper, sections 16?26, contains certain metatheoretical investigations of some restricted theories of kind W. The author is indebted to his collaborators at Stevens Institute of Technology, S. L. Bloom, D. J. Brown, J. D. Kagan, R. W. Quackenbush for comments on an earlier version of this paper.