To understand the goals of communist education and shaping of the human being we need deep study of human activity.

Johann Friedrich Ludwig Schröder (1774-1845 ) was born in Germany but moved to Holland at the age of 13. After studying at Halle he joined the Kantian movement in Amsterdam as an active member, cooperating with Paulus van Hemert and contributing articles to his Kantian magazine. During his professional career as a marine instructor (1803-11 ), however, he became increasingly critical of Kantianism. As professor of mathematics, physics and philosophy at the University of Utrecht (1816-44) he traded in his former (...) Kantianism for a variant of the common sense philosophy then in favour in the Netherlands. He now regarded Kantianism as a form of scepticism. Accordingly, in his major work, the Contnbution to a Critique of the Truth of Human Knowledge, he propounds an anti-sceptical doctrine of such ‘basic truths’ as are founded on the immediate relevation of our consciousness. Schröder also attempts to reduce the Kantian doctrine of the noumenon to an inconsistent set of propositions, by showing them to be antinomies in the Kantian sense of the term, even using Kant's own dialectical method in proving their contradictoriness ; these contradictory propositions he calls the 'antinomies of the Kantian philosophy'. In a minor work, The Sign Relation as the Basis of Human Knowledge (translated freely), we find reminiscences of Thomas Reid's Inquiry into the Human Mind: of the doctrine of sensations suggesting our conceptions of things, of causes being the signs of their effects, of 'the natural language of mankind'. Schröder, in developing these ideas in his own way, presents the sign relation as being fundamental to the construction of our knowledge of both nature and the human soul. Only by taking one thing as the ‘sign’ (signal, symbol, symptom, index, expression, picture, representation etc.) of another can we attain a conception of the world as a coherent whole. Our perception of this relation is partly a matter of innate capacities, partly the result of acquired skill. (shrink)

This paper described a formal theory of type judgments for propositional logic notations of PM; I felt the need of my own automated type checker to check their examples. The type checker I wrote did indeed serve to help me referee the paper, but also took a rather different approach to notation and typing for propositional functions of PM, which proved worth writing up independently in our own paper: Holmes, M. Randall, “Polymorphic type– checking for the ramified theory of types (...) of Principia Mathematica”, in Fairouz Kamareddine, ed., Thirty–five Years of Automating Mathematics, Kluwer, 2003, pp. 173-215. (shrink)

Let κ be a regular cardinal, and let B be a subalgebra of an interval algebra of size κ. The existence of a chain or an antichain of size κ in B is due to M. Rubin (see [7]). We show that if the density of B is countable, then the same conclusion holds without this assumption on κ. Next we also show that this is the best possible result by showing that it is consistent with 2 ℵ 0 = (...) ℵ ω 1 that there is a boolean algebra B of size ℵ ω 1 such that length(B) = ℵ ω 1 is not attained and the incomparability of B is less than ℵ ω 1 . Notice that B is a subalgebra of an interval algebra. For more on chains and antichains in boolean algebras see, e.g. [1] and [2]. (shrink)