This chapter discusses paraconsistent logic, in which contradictions do not entail everything. However, the roots of paraconsistency lie deep in the history of logic, its modern developments date to just before the middle of the 20th century. Since then, the paraconsistent logic have been proposed and constructed for many and for different reasons. The most philosophically challenging of these reasons is dialetheism, the view that some contradictions are true. The chapter discusses the history of paraconsistency and the history of dialetheism. The chapter also discusses the modern developments of paraconsistency and dialetheism, those since about 1950. Some important issues that bear on paraconsistency, or on which paraconsistency bears the foundations of mathematics, the notion of negation, and rationality are discussed in the chapter.

To be and not to be – That is the Answer. On Aristotle on the Law of Non-Contradiction.

Paraconsistency and dialetheism

The present work is the first volume of A Practical Logic of Cognitive Systems. We here concentrate on the analysis of a notion which lies at the very heart of cognitive competence. The notion is relevance, and its centrality is attested to by the considerable facility with which beings like us ignore irrelevancies and 'stay on point' in the performance of our cognitive tasks. In so saying, we have a particular conception of what it is to be a cognitive agent, and accordingly, of how we should think of a logic of cognitive agency. Offering a rudimentary description of this logic, PLCS, is the principal business of the present chapter. We wish to lay some emphasis on the fact that we are here attempting to run on two tracks concurrently. We want, of course, to get relevance right. But we also wish to develop PLCS, indeed, to embed the theory of relevance in it. For various reasons, both expository and tactical, we do not wade right in with the account of relevance, but rather we devote some time to describing and motivating PLCS. Relevance takes over in Chapter 5, and holds centre-stage for the remainder of the book. Readers who are impatient to be getting on with relevance can skip the preamble on PLCS and move directly to page 69.

Chapter 2 - The Practical Logic of Cognitive Systems

ing from the temporal effects. a snapshot of the world can be described by the formula which Goodchild called 'geographic reality ' (Goodchild 1992) .

Rationality and Irrationality

(2000). Could everything be true? Australasian Journal of Philosophy: Vol. 78, No. 2, pp. 189-195.

background

Could everything be true

In Metaphysics Gamma 3 Aristotle declares that the philosopher investigates things that are qua things that are and that he therefore should be able to state the firmest principles of everything. The firmest principle of all is identified as the principle of non-contradiction (PNC). The main focus of Gamma 3 is Aristotle's proof for this identification. This paper begins with remarks about Aristotle's notion of the firmness of a principle and then offers an analysis of the firmness proof for PNC. It focuses on some key assumptions of the proof and on the range and force of the proof. Aristotle closes Gamma 3 with the claim that PNC is ultimate in the sense that all other principles somehow rest on it. This, rather controversial, claim is given a defensible reading and shown to be central to the chapter's effort to establish PNC as the firmest principle of all. As such it completes the firmness proof and is not simply an appended remark.

To be and not to be – That is the Answer. On Aristotle on the Law of Non-Contradiction.

Citations

Paraconsistency and dialetheism

Chapter 2 - The Practical Logic of Cognitive Systems

Rationality and Irrationality

Could everything be true

Aristotle on the Firmness of the Principle of Non-Contradiction

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