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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| History of logic | 3/13 | https://en.wikipedia.org/wiki/History_of_logic | reference | science, encyclopedia | 2026-05-05T06:40:54.611600+00:00 | kb-cron |
In contrast to Heraclitus, Parmenides held that all is one and nothing changes. He may have been a dissident Pythagorean, disagreeing that One (a number) produced the many. "X is not" must always be false or meaningless. What exists can in no way not exist. Our sense perceptions with its noticing of generation and destruction are in grievous error. Instead of sense perception, Parmenides advocated logos as the means to Truth. He has been called the discoverer of logic,
For this view, that That Which Is Not exists, can never predominate. You must debar your thought from this way of search, nor let ordinary experience in its variety force you along this way, (namely, that of allowing) the eye, sightless as it is, and the ear, full of sound, and the tongue, to rule; but (you must) judge by means of the Reason (Logos) the much-contested proof which is expounded by me. 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. This is the technique of drawing an obviously false (that is, "absurd") 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. Plato's dialogue Parmenides portrays Zeno as claiming to have written a book defending the monism of Parmenides by demonstrating the absurd consequence of assuming that there is plurality. Zeno famously used this method to develop his paradoxes in his arguments against motion. Such dialectic reasoning later became popular. The members of this school were called "dialecticians" (from a Greek word meaning "to discuss").
==== Plato ==== Let no one ignorant of geometry enter here.
None of the surviving works of the great fourth-century philosopher Plato (428–347 BC) include any formal logic, but they include important contributions to the field of philosophical logic. Plato raises three questions:
What is it that can properly be called true or false? What is the nature of the connection between the assumptions of a valid argument and its conclusion? What is the nature of definition? The first question arises in the dialogue Theaetetus, where Plato identifies thought or opinion with talk or discourse (logos). The second question is a result of Plato's theory of Forms. Forms are not things in the ordinary sense, nor strictly ideas in the mind, but they correspond to what philosophers later called universals, namely an abstract entity common to each set of things that have the same name. In both the Republic and the Sophist, Plato suggests that the necessary connection between the assumptions of a valid argument and its conclusion corresponds to a necessary connection between "forms". The third question is about definition. Many of Plato's dialogues concern the search for a definition of some important concept (justice, truth, the Good), and it is likely that Plato was impressed by the importance of definition in mathematics. What underlies every definition is a Platonic Form, the common nature present in different particular things. Thus, a definition reflects the ultimate object of understanding, and is the foundation of all valid inference. This had a great influence on Plato's student Aristotle, in particular Aristotle's notion of the essence of a thing.
=== Aristotle ===
The logic of Aristotle, and particularly his theory of the syllogism, has had an enormous influence on the history of logic and Western thought in general. Aristotle was the first logician to attempt a systematic analysis of logical syntax, of noun (or term), and of verb. 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. He was the first to explicitly discuss the principles of non-contradiction and excluded middle.
==== The Organon ==== His logical works, called the Organon, are the earliest formal study of logic that have come down to modern times. Though it is difficult to determine the dates, the probable order of writing of Aristotle's logical works is:
The Categories, a study of the ten kinds of primitive term. The Topics (with an appendix called On Sophistical Refutations), a discussion of dialectics. On Interpretation, an analysis of simple categorical propositions into simple terms, negation, and signs of quantity. The Prior Analytics, a formal analysis of what makes a syllogism (a valid argument, according to Aristotle). The Posterior Analytics, a study of scientific demonstration, containing Aristotle's mature views on logic.
The Categories influence his work the Metaphysics, which itself had a profound influence on Western thought; the namesake of the subject of metaphysics. Aristotle also developed a theory of non-formal logic (i.e., the theory of fallacies), which is presented in Topics and Sophistical Refutations. On Interpretation contains a comprehensive treatment of the notions of opposition and conversion; chapter 7 is at the origin of the square of opposition (or logical square); chapter 9 contains the beginning of modal logic and the famous sea battle argument. The Prior Analytics contains his exposition of the syllogism, wherein three important advances are made for the first time in history: the use of variables, a purely formal treatment, and the use of an axiomatic system.
=== Stoics ===
The other great school of Greek logic is that of the Stoics. Stoic logic traces its roots back to the late 5th century BC philosopher Euclid of Megara, a pupil of Socrates and slightly older contemporary of Plato, probably following in the tradition of Parmenides and Zeno. His pupils and successors were called "Megarians", or "Eristics", and later the "Dialecticians". The two most important dialecticians of the Megarian school were Diodorus Cronus and Philo, who were active in the late 4th century BC.