It is widely known that Aristotle rules out the existence of actual infinities but allows for potential infinities. However, precisely why Aristotle should deny the existence of actual infinities remains somewhat obscure and has received relatively little attention in the secondary literature. In this paper I investigate the motivations of Aristotle’s finitism and offer a careful examination of...

Aristotelian, or non-Platonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity, or numerosity, or symmetry. Let us start with an example, as Ari...

I argue that a modern gloss on Aristotle’s notions of Form and Matter not only allows us to escape a dualism of the psychological and the physical, but also results in a plausible sort of materialism. This is because Aristotle held that the essential nature of any psychological state, including perception and human thought, is to be some physical property. I also show that Hilary Putnam and Mar...

Aristotle's theory of causation has multiple threads, and his texts invite multiple interpretations. The variation in interpretation is, in part, a result of different perspectives and questions that are brought to the text. For instance, Aristotle's theory of the four causes has invited scrutiny from contemporary philosophers of science, who are interested in theories of explanation (van Fraas...

The synthesis of polysyllogisms in Critical Logic is an important topic within the larger topic of Critical mathematics. My previous treatises (Wells, 2006; Wells, 2009) have touched upon the logical organization of the manifold of concepts and the manifold of rules in nous, but the levels and scopes of these works are too high and broad to have permitted a detailed exposition of the Logic of s...

This paper is a report on the results of intervention program designed for improving higher-order thinking skills (HOTS) Israeli Arab student teachers. The represents series webinars foundations Aristotelian logic, propositional and some contemporary models informal argumentation. Zoom application was used implementation webinars. research project as pre-/post-test quantitative study with quali...

Contemporary students of logic tend to think of the logic of the connectives as the most basic area of the subject, which can then be extended with a logic of quantifiers. Historically, however, the logic of the quantifiers, in the form of the Aristotelian theory of the syllogism, came first. Truth conditions for negation, conjunction, and disjunction were well understood in ancient times, thou...

1. Introduction No other philosopher had such a deep and long-standing impact on Western science as Aristotle. In the fourth century BC he developed a fully comprehensive worldview that would with only few modifications stand for about two thousand years. Rather than just collecting isolated facts, he posed fundamental questions about nature and about the methods to study nature. Physics in the...

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of (sub)contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for ...