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May 8, 2024 · Publishes research on the history of logic, referring to ancient times and the present century, and broad and general philosophical questions related to logic.
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history of logic, the history of the discipline from its origins among the ancient Greeks to the present time.
There was a medieval tradition according to which the Greek philosopher Parmenides (5th century bce) invented logic while living on a rock in Egypt. The story is pure legend, but it does reflect the fact that Parmenides was the first philosopher to use an extended argument for his views rather than merely proposing a vision of reality. But using arguments is not the same as studying them, and Parmenides never systematically formulated or studied principles of argumentation in their own right. Indeed, there is no evidence that he was even aware of the implicit rules of inference used in presenting his doctrine.
Perhaps Parmenides’ use of argument was inspired by the practice of early Greek mathematics among the Pythagoreans. Thus, it is significant that Parmenides is reported to have had a Pythagorean teacher. But the history of Pythagoreanism in this early period is shrouded in mystery, and it is hard to separate fact from legend.
If Parmenides was not aware of general rules underlying his arguments, the same perhaps is not true for his disciple Zeno of Elea (5th century bce). Zeno was the author of many arguments, known collectively as “Zeno’s Paradoxes,” purporting to infer impossible consequences from a non-Parmenidean view of things and so to refute such a view and indirectly to establish Parmenides’ monist position. The logical strategy of establishing a claim by showing that its opposite leads to absurd consequences is known as reductio ad absurdum. The fact that Zeno’s arguments were all of this form suggests that he recognized and reflected on the general pattern.
Other authors too contributed to a growing Greek interest in inference and proof. Early rhetoricians and Sophists—e.g., Gorgias, Hippias, Prodicus, and Protagoras (all 5th century bce)—cultivated the art of defending or attacking a thesis by means of argument. This concern for the techniques of argument on occasion merely led to verbal displays of debating skills, what Plato called “eristic.” But it is also true that the Sophists were instrumental in bringing argumentation to the central position it came uniquely to hold in Greek thought. The Sophists were, for example, among the first people anywhere to demand that moral claims be justified by reasons.
Certain particular teachings of the Sophists and rhetoricians are significant for the early history of logic. For example, Protagoras is reported to have been the first to distinguish different kinds of sentences: questions, answers, prayers, and injunctions. Prodicus appears to have maintained that no two words can mean exactly the same thing. Accordingly, he devoted much attention to carefully distinguishing and defining the meanings of apparent synonyms, including many ethical terms.
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The history of logic deals with the study of the development of the science of valid inference ( logic ). Formal logics developed in ancient times in India, China, and Greece.
Dec 13, 2006 · Logic as a discipline starts with the transition from the more or less unreflective use of logical methods and argument patterns to the reflection on and inquiry into these methods and patterns and their elements, including the syntax and semantics of sentences. In Greek and Roman antiquity, discussions of some elements of logic and a focus on ...
Philosophy of logic, the study, from a philosophical perspective, of the nature and types of logic, including problems in the field and the relation of logic to mathematics, computer science, the empirical sciences, and human disciplines such as linguistics, psychology, law, and education.
Sep 16, 2000 · The following sections provide the basics of a typical logic, sometimes called “classical elementary logic” or “classical first-order logic”. Section 2 develops a formal language, with a rigorous syntax and grammar. The formal language is a recursively defined collection of strings on a fixed alphabet.
