Definition and Inquiry in Archytas

In Archytas of Tarentum, Carl Huffman reconstructs Archytas’ theory of definition by linking definitions to the mathematical study of ratios and proportions. This paper considers whether and how Archytas used definitions and whether he possessed a theory of definition. Our evidence does not support the claim that Archytas has a theory of definition, and his approach to the science of harmonics suggests that he relied on analogies and proportions in the practice of inquiry. We understand sounds and other entities by placing them in a network of relations governed by mathematical proportions. Although he does not seem to have formulated definitions of sound, Archytas pursued inquiry into motion and rest by formulating definitions in such a way that they fit into a larger network of causal explanations.

Herbert Hart’s Theory of Definition in the Context of Analytical Legal Philosophy

The article presents Herbert Hart’s theory of definition in the context of modern analytical legal philosophy. Dissatisfaction with the applicability of the traditional method of definition by the genus and differentia to the elucidation of legal concepts led Hart to the development a new method of definition. It is shown that Hart not only modifies the paraphrase of Jeremy Bentham, but also tries to adapt to the analysis of legal concepts the definition in use borrowed from analytical philosophers and logicians. It has been established that the key point of Hart’s method is that instead of defining a separate term, it is necessary to consider a statement, where the utterance plays a characteristic role, and is explained by specifying the conditions under which the entire statement is true. Some difficulties that arise when one uses this definition in the framework of the truth-conditional semantics are considered. In particular, it is shown that Hart uses open sentences of the form “X has a right” in its definition, which differ from closed sentences, primarily because they contain free variables with indefinite range of values. This uncertainty does not allow us to attribute to them the truth-value. The concepts of truth and falsity apply only to statements that are expressed by closed sentences. Thus, Hart’s claim of a special semantic nature of legal concepts and a special epistemological task of definitions in jurisprudence is reflected in his theory of the truth-conditional definition - a kind of contextual definition.

A Brief History of Self-Reference Notion Implementation in Byzantium

The article presents an overview of implementation of self-referential notions in the logical and theological texts of Byzantine scholars up to the 12th century. The commentaries on Porphyry’s and Aristotle’s theory of definition by John of Damascus, John Italus, and Theodore Prodromos are discussed. It is argued that the Byzantine scholars performed different original implementations of basic logical notions and discovered their self-referential property. The attention is paid to the five predicabilia notions of Porphyry and Aristotelian categories applications in logical, philosophical, and theological Byzantine texts. The authors conclude that the Byzantine solutions resemble some of the modern logical ideas of 20th century.