Ignacio Angelelli

Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new standard also in other fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively.

The author distinguishes a "term logic," where terms are the fundamental units, and a "sentential logic," where sentences are the fundamental units. Although this technical distinction is presented by Englebretsen as a war-like opposition throughout the entire history of logic, he reassures us that "no blood has been spilled". In recent times, the term-logic party has been eclipsed by the sentential-logic band; term logic is nowadays "almost mute". Only F. Sommers appears to proclaim the truth of term logic in the twentieth century. The author's main goal is to "recount the history" of term logic through an examination of its three champions: Aristotle, Leibniz, and Sommers. The chronological sequence of these three logicians is a sequence towards perfection as well. The shortcomings of Aristotle's achievement are partially corrected by Leibniz and then fully repaired by Sommers, who finally extends the Aristotelian syllogistic into a "universal logic". Englebretsen himself has added "certain emendations and extensions in a modest way".