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In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, the Peripatetics. It was revived after the third century CE by Porphyry's Isagoge.
But Aristotelian logic requires that, necessarily, one of these statements (more generally 'some particular A is B ' and 'some particular A is not B ') is true, i.e., they cannot both be false. Therefore, since both statements imply the presence of at least one thing that is a man, the presence of a man or men is followed.
Organon Roman copy in marble of a Greek bronze bust of Aristotle by Lysippos, c. 330 BC, with modern alabaster mantle. The Organon (Ancient Greek: Ὄργανον, meaning "instrument, tool, organ") is the standard collection of Aristotle's six works on logical analysis and dialectic.
Aristotelianism (/ ˌ ær ɪ s t ə ˈ t iː l i ə n ɪ z əm / ARR-i-stə-TEE-lee-ə-niz-əm) is a philosophical tradition inspired by the work of Aristotle, usually characterized by deductive logic and an analytic inductive method in the study of natural philosophy and metaphysics.
The history of logic deals with the study of the development of the science of valid inference ().Formal logics developed in ancient times in India, China, and Greece.Greek methods, particularly Aristotelian logic (or term logic) as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. [1]
In Aristotelian logic, dictum de omni et nullo (Latin: "the maxim of all and none") is the principle that whatever is affirmed or denied of a whole kind K may be affirmed or denied (respectively) of any subkind of K.
Early approaches include Aristotelian logic, Stoic logic, Nyaya, and Mohism. Aristotelian logic focuses on reasoning in the form of syllogisms. It was considered the main system of logic in the Western world until it was replaced by modern formal logic, which has its roots in the work of late 19th-century mathematicians such as Gottlob Frege.
The modern view is more complex, since a single judgement of Aristotle's system involves two or more logical connectives. For example, the sentence "All men are mortal" involves, in term logic, two non-logical terms "is a man" (here M) and "is mortal" (here D): the sentence is given by the judgement A(M,D).