When I say that my conception of metaphysics is Aristotelian, or neo-Aristotelian, this may have more to do with Aristotle’s philosophical methodology than his metaphysics, but, as I see it, the core of this Aristotelian conception of metaphysics is the idea that metaphysics is the first philosophy. In what follows I will attempt to clarify what this conception of metaphysics amounts to in the ...

Peterson’s Intermediate Syllogisms, generalizing Aristotelian syllogisms by intermediate quantifiers ‘Many’, ‘Most’ and ‘Almost all’, are studied. It is demonstrated that, by associating certain values V, W and U on standard Lukasiewicz MV–algebra with the first and second premise and the conclusion, respectively, the validity of a corresponding intermediate syllogism is determined by a simple ...

In Aristotelian logic, the predominant view has always been that there are only two kinds of quantities: universal and particular. For this reason, philosophers have struggled with singular propositions (e.g., “Socrates is running”). One modern approach to this problem, as first proposed in 1955 by Tadeusz Czeżowski, is to extend the traditional Square of Opposition to a Hexagon of Opposition. ...

In order to provide a consistent explanation for Aristotelian modal syllogistic, this paper reveals the reductions between syllogism ◇I□A◇I-3 and other valid syllogisms. Specifically, on basis of formalizing syllogisms, proves validity by means truth value definition (modal) categorical propositions. Then in line with classical propositional logic logic, generalized quantifier theory set theory...

I present an analytic tableau system for a small fragment of natural language called RC. RC is an extension of the classical Aristotelian syllogisms (“All computer-scientists are mathematicians”) to include relations in the form of transitive verbs (“All who hate all logic programmers know some who hate all proof theoreticians”) and to permit the negation of nouns (“Some non-linguists love all ...

This paper examines fundamental problems underlying difficulties encountered by pattern recognition algorithms, neural networks, and rule systems. These problems are manifested as combinatorial complexity of algorithms, of their computational or training requirements. The paper relates particular types of complexity problems to the roles of a priori knowledge and adaptive learning. Paradigms ba...

The paper examines the fortunes of Aristotelian metaphysics in science and the philosophy of science. It considers the Enlightenment claim that such a metaphysics is fundamentally unscientific, and that its abandonment was essential to the scientific revolution. The history of the scientific revolution and the metaphysical debates involved in it is examined, and it is argued that the eclipse of...

Predicate logic is a sub-discipline of logic that had its roots in the last quarter of the nineteenth century, though it had to wait until the second decade of the twentieth century for a solid foundation. Like any other logic, it is concerned with the validity of arguments, though not of any kind: its interest lies in reasoning about what is universally true. As such, predicate logic is especi...

Aristotle (384–322 BC), the founder of the discipline of logic, also founded the study of quantification. Normally, Aristotle begins a topic by reviewing the common opinions, including the opinions of his chief predecessors. In logic, however, he could not adopt the same strategy; before him, he reports, “there was nothing at all” (Sophistical Refutations 183b34–36). Aristotle’s theory dominate...