Quantum-mechanical event descriptions are context-dependent descriptions. The role of quantum (nondistributive) logic is in the partial ordering of contexts rather than in the ordering of quantum-mechanical events. Moreover, the kind of quantum logic displayed by quantum mechanics can be easily inferred from the general notion of contextuality used in ordinary language. The formalizable core of Bohr's notion of complementarity is the type of context dependence discussed in this paper.

In numerous essays over the years, and most recently in his Meaning, Paul Horwich has worked to articulate and defend a version of the use theory of meaning. At the heart of his project is the idea that the meaning of a word is constituted by a regularity in speakers’ use of it — i.e., by a regularity in speakers’ dispositions to accept as true, to reject as false, or neither to accept nor to reject sentences containing it. A ‘use (...) regularity,’ thus construed, is a dispositional acceptance property distinctive of a particular word and, derivatively, of sentences containing the word. For example, the use regularity constituting the meaning of ‘red’ can be very roughly characterized as speakers’ disposition to accept the application of ‘red’ to observed surfaces if and only if they are clearly red. Of course, the use regularity constituting the meaning of a word can be described in different ways; in particular, in describing a use regularity we might merely mention, and not use, the corresponding word. Furthermore, not every regularity in the use of a word is meaning-constituting. The use regularity that constitutes the meaning of the word ‘tall,’ for example, does so in virtue of the fact that, taken together with general psychological laws and the use regularities governing other words, it is basic to the explanation of speakers’ overall pattern of use of ‘tall.’ Hence, a central claim of Horwich’s use theory is that linguistic use is in general to be ‘unified and explained in terms of a relatively small and simple body of factors and principles including, for each word, a basic use regularity’. (shrink)

It is well known that Niklas Luhmann’s theory of social systems is grounded in Spencer-Brown’s seminal Laws of Form (LoF) or ‘calculus of indications’. It is also known that the reception of the latter has been rather problematic. This article attempts to describe the construction of LoF, and confront it with Niklas Luhmann’s ontological and epistemological premises. I show how LoF must be considered a protologic, or research into the fundamentals of logical systems. The clue to its understanding is to (...) be found in its profoundly topological conception of common mathematics and (Boolean) algebra. Both are explained as direct offspring of their planar orientation. Self-reference is a justified instance of an extended, more intricate topological arrangement. Its consequences for ontology (non-identity) and epistemology (autology), I argue, have been adopted correctly by Niklas Luhmann. Separate sections are devoted to how Spencer-Brown’s notion of re-entry relates to Luhmann’s definition of system/environment, and to a comparison between Luhmann’s and Parsons’ functionalism. (shrink)

SummaryIt is not the inconsistency in the sense of classical logic that we have to tolerate. The dialectical reasoning, described by N. Rescher, is outside the domain where CI is defined. The apparent contradiction between CI and paraconsistent logic can be removed by realizing that PL is a widening of the conceptual framework of classical logic. In this new framework the meaning of some words was changed similarly as, according to N. Bohr, in quantum mechanics the words “particle” and “wave” (...) have changed their meaning. (shrink)