In this note we reproduce the book reviews that De Morgan wrote on Boole's and Jevons's first logical works. The most notable property of these documents is the mere fact of their existence and the absence of any reference to them in the specialized literature.

It is a commonplace that in the development of modern logic towards its actual shape at least two directions or traditions have to be distinguished. These traditions may be called, following the mo...

The history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole's The Mathematical Analysis of Logic of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical development of logic, although logic is (...) evidently one of the basic disciplines of philosophy. One needs only to recall some of the standard 19th century definitions of logic as, e.g., the art and science of reasoning (Whateley) or as giving the normative rules of correct reasoning (Herbart). In the paper the relationship between the philosophical and the mathematical development of logic will be discussed. Answers to the following questions will be provided: 1. What were the reasons for the philosophers' lack of interest in formal logic? 2. What were the reasons for the mathematicians' interest in logic? 3. What did "logic reform" mean in the 19th century? Were the systems of mathematical logic initially regarded as contributions to a reform of logic? 4. Was mathematical logic regarded as art, as science or as both? (shrink)

(1993). Thomas solly (1816–1875):an unknown pioneer of the mathematization of logic in england, 1839. History and Philosophy of Logic: Vol. 14, No. 2, pp. 133-169.

Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.

One way to determine the quality and pace of change in a science as it undergoes a major transition is to follow some feature of it which remains relatively stable throughout the process. Following the chosen item as it goes through reinterpretation permits conclusions to be drawn about the nature and scope of the broader change in question. In what follows, this device is applied to the change which took place in logic in the mid-nineteenth century. The feature chosen as (...) the focal point is the categorical syllogism. (shrink)

The present paper expounds the logic notation proposed by Augustus De Morgan in 1850 from within the original context of De Morgan’s account of syllogistic logic and his approach to quantification. The notational system of 1850 is shown to be a flexible tool to state inferences, to prove their validity and to derive formulæ of the respective system by ‘blind’ application of transformation rules. These pertain to the swapping of operator signs, which are of inverse ‘character’ in a two-fold sense: (...) The signs both represent inverse operations and exemplify oppositeness due to their very shapes. Thus, while De Morgan’s initial choice of symbol shapes is due to certain diagrammatic features, his notational system of 1850 leads to an account of logical operations as effected by manipulation of symbol tokens. It is concluded that as an instantiation of what De Morgan terms a ‘calculus of opposite relations’, his notation of 1850 may also be conceived of as a ‘graphicism’ affording for the working of a ‘symbolic machine’ on ‘de-semantification’. (shrink)

Contact relations have been studied in the context of qualitative geometry and physics since the early 1920s, and have recently received attention in qualitative spatial reasoning. In this paper, we present a sound and complete proof system in the style of Rasiowa and Sikorski (1963) for relation algebras generated by a contact relation.

Is it possible to distinguish communities of arguers by tracking the argumentation schemes they employ? There are many ways of relating schemes to communities, but not all are productive. Attention must be paid not only to the admissibility of schemes within a community of argumentational practice, but also to their comparative frequency. Two examples are discussed: informal mathematics, a convenient source of well-documented argumentational practice, and anthropological evidence of nonstandard reasoning.