Intuitionist mathematics has claimed a philosophy deriving from Kant. This paper aims to draw attention to significant similarities with a much older source, Aristotle. At the same time, the connection should not be over-stretched, given two millennia between them.

Identification of distinct items is a basic technique in mathematics. However, identification suffers from a certain weakness of resolve in that it is (classically) accompanied by dropping the original disidentification, which causes a loss of information about the theory which sources the identity. This article proposes an alternative, namely keeping the disidentification along with the identification. This produces an inconsistent theory which is generally an extension of the source theory. The concept of a Dunn–Meyer extension is defined to study these (...) properties. It is seen that this technique is sensitive to the choice of background logic, particularly RM3 as opposed to closed-set logic. By employing the Routley functor, a best-choice logic is found for this construction. (shrink)

Chris Mortensen, Graham Nerlich, Garrett Cullity and Gerard O'Brien.

We apply linear algebra to the study of the inconsistent figure known as the Crazy Crate. Disambiguation by means of occlusions leads to a class of sixteen such figures: consistent, complete, both and neither. Necessary and sufficien conditions for inconsistency are obtained.

Parmenides has been widely regarded as someone whose main assertions are outrageously false, since he seems to have denied change, motion and diversity. In this note I will show that, while there is some justice in the received view, nonetheless there are important insights to be gained from taking his position seriously. Along the way, I will register agreement or disagreement, where appropriate, with the papers by ScottMann and Peter Woolcock in this volume. My final position is more in agreement (...) with Mann than Woolcock, though I have disagreements with both. (shrink)

We consider the question of whether paradoxes are essentially verbal. It is argued that paradoxes have an essentially verbal component, but that there is a special class of paradoxes, such as the “impossible triangle”, which are not wholly verbal, but partly perceptual as well. Along the way, attention is paid to explicating the idea of non-verbal content.

The general theory of variable binding term operators is an interesting recent development in logic. It opens up a rich class of semantic and model-theoretic problems. In this paper we survey the recent literature on the topic, and offer some remarks on its significances and on its connections with other branches of mathematical logic.

Three indexes have been compiled: authors of main articles (including our special departments such as ‘Projects in progress’ and ‘Notes and discussions’); essay reviews; and book reviews. Co-author...

Buddhist teachings and modern science are analogous both in their approach to the search for truth and in some of the discoveries of contemporary physics, biology, and psychology. However, despite these congruencies and the recognized benefits of science, Buddhism reminds us of the dangers of a tendency toward scientific reductionism and imperialism and of the sciences’ inability to deal with human moral and spiritual values and needs. Buddhism and science have human concerns and final goals that are different, but as (...) long as the boundaries between them are not trespassed, they can be mutually corrective and allied to benefit humankind. Buddhism must be open to the discoveries of science about the physical world as must all religions today, but no matter how much it may have to modify some of its ancient beliefs, its basic truths—the truths about human suffering and its release—will remain untouched. (shrink)

This paper is dedicated to Newton da Costa, who,among his many achievements, was the first toaim at dualising intuitionism in order to produce paraconsistent logics,the C-systems. This paper similarly dualises intuitionism to aparaconsistent logic, but the dual is a different logic, namely closed setlogic. We study the interaction between the properties of topologicalspaces, particularly separation properties, and logical theories on thosespaces. The paper begins with a brief survey of what is known about therelation between topology and modal logic, intuitionist logic (...) and paraconsistentlogic in respect of the incompleteness and inconsistency of theories.Necessary and sufficient conditions which relate the T1-property to theproperties of logical theories, are obtained. The result is then extendedto Hausdorff and Normal spaces. In the final section these methods areused to vary the modelling conditions for identity. (shrink)

This paper is dedicated to Newton da Costa, who,among his many achievements, was the first toaim at dualising intuitionism in order to produce paraconsistent logics,the C-systems. This paper similarly dualises intuitionism to aparaconsistent logic, but the dual is a different logic, namely closed setlogic. We study the interaction between the properties of topologicalspaces, particularly separation properties, and logical theories on thosespaces. The paper begins with a brief survey of what is known about therelation between topology and modal logic, intuitionist logic (...) and paraconsistentlogic in respect of the incompleteness and inconsistency of theories.Necessary and sufficient conditions which relate the T 1-property to theproperties of logical theories, are obtained. The result is then extendedto Hausdorff and Normal spaces. In the final section these methods areused to vary the modelling conditions for identity. (shrink)

Reviewed Works:Chris Mortensen, Inconsistent Mathematics.Chris Mortensen, Peter Lavers, Category Theory.William James, Closed Set Sheaves and Their Categories.Chris Mortensen, Joshua Cole, Foundations: Provability, Truth and Sets.

Ultralogic as Universal was drafted in 1976, appeared in 1977 as ‘Ultralogic as Universal?’ in The Relevance Logic Newsletter, 2 (1–2) and was reprinted as an appendix to Exploring Meinong’s Jungle...