This paper is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics. The paper has a survey character, too. The most frequently used algebras like cylindric-, relation-, polyadic-, and quasi-polyadic algebras are carefully introduced and intuitively explained for the nonspecialist. Their variants, connections with logic, abstract model theory, and further algebraic logics are also reviewed. Efforts were made to make the review part relatively comprehensive. In some (...) directions we tried to give an overview of the most recent results and research trends, too. (shrink)

Realism about the external, natural world is an overarching empirical hypothesis. The method of hypothetical realism rejects as an excessive concession to the skeptic these two assumptions of constructivist intuitionism: first, that everything real must be exhaustively inspectable; and second, that our beliefs are to be justified to the point of certainty. We prefer to say that nothing is ever known directly; that all of our contact with the world is mediated by thoughts, words, and percepts construed as signs having (...) referents distinct from themselves. We organize these signs into meaningful and possibly true hypotheses as we speculate--in practice, science and metaphysics--about a world we have not made. (shrink)