# History of logic

Logic has been studied as part of the philosophy since ancient times. Since the middle of XIX century, math has found the interest in logic as well, giving rise to the new math branch called mathematical logic. In more recent times, logic became a subject of study in computer science, linguistics, and other cognitive sciences.

The word comes from the Ancient Greek `λογική` \[logikḗ] logic.

## Quick timeline

BCE

* Formal logics developed in ancient times in India, China, Greece.
* Aristotle, father of logic, developed the first formalized logic method, syllogistic logic, that has found wide acceptance in the next millennias.
* The Stoics with Chrysippus initiated the development of predicate logic.

Middle Ages

* Christian and Islamic philosophers further developed Aristotle's logic,
* which peaked in the mid-XIV with Jean Buridan.
* from XIV to the beginning of XIX century, the study of logic halted.
* The Middle Ages have excluded logic, for which classical logic later retaliated by excluding the middle.

XIX

* Logic was revived in the mid-XIX century
* From then on it was developing into a formal discipline based on rigorous argumentation that was used in mathematics, dating back to Euclid.
* The development of the modern logic with Boole, Frege, Russell, Peano et al., was the most flourishing period of not only logic but of human intellectual endeavour in general.

XX

* ML progressed at the start of XX century due to work of Gödel and Tarski.
* ML had a significant impact on analytic philosophy and philosophical logic.
* new logics: modal, temporal, deontic, relevance, etc.

## Western logic

Valid reasoning has been employed in all periods of human history. However, logic studies the principles of valid reasoning, inference and demonstration.

While the ancient Egyptians empirically discovered some truths of geometry, the great achievement of the ancient Greeks was to replace empirical methods by demonstrative proof.

Fragments of early proofs are preserved in the works of Plato and Aristotle, and the idea of a deductive system was probably known in the Pythagorean school and the Platonic Academy. The proofs of **Euclid of Alexandria** are a paradigm of Greek geometry.

Further evidence that early Greek thinkers were concerned with the principles of reasoning is found in the fragment called *δισσοὶ λόγοι* (dissoi logoi, "contrasting arguments"), a part of a debate about truth and falsity, probably from the IV century BCE.

**Thales** measured the height of the pyramids by their shadows at the moment when his own shadow was equal to his height. Thereby, Thales is the first known individual to use deductive reasoning, by deriving four corollaries to his theorem, and the first known individual to whom a mathematical discovery has been attributed.

The systematic study of proof seems to have begun with the school of **Pythagoras** in the late VI century BCE. The Pythagoreans, believing everything was a number, are the first philosophers to emphasize form rather than matter.

**Heraclitus** held that πάντα ῥεῖ ("everything flows") and all was fire and conflicting opposites, seemingly unified only by the logos (reason). In contrast to Heraclitus, **Parmenides** held that all is one and nothing changes. Instead of sense perceptions, which is in grievous error, Parmenides advocated logos as the means to Truth. He has been called the discoverer of logic.

**Zeno of Elea**, a pupil of Parmenides, had the idea of a standard argument pattern found in the method of proof known as **reductio ad absurdum** - a method of drawing a false conclusion from an assumption, thus demonstrating that the assumption is false. Therefore, Zeno and his teacher are seen as the first to apply the art of logic.

None of the surviving works of the great fourth-century philosopher **Plato** (428–347 BCE) include any formal logic, but they include important contributions to the field of philosophical logic. Plato raises questions about the the nature of the connection between the assumptions of a valid argument and its conclusion, about the nature of definition, and about the state of truth and falsity.

**Aristotle** (384–322 BCE) was the first to attempt a systematic analysis of logical syntax. He was the first formal logician, in that he demonstrated the principles of reasoning by employing variables to show the underlying logical form of an argument. He sought relations of dependence which characterize necessary inference, and distinguished the validity of these relations, from the truth of the premises (soundness). He was the first to deal with the principles of contradiction and excluded middle in a systematic way. He also developed a theory of non-formal logic i.e. the theory of fallacies. Aristotle gave a comprehensive treatment of the notions of opposition and conversion, introducing the idea for the square of opposition, as well as modal logic.

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