Surely this list does not represent the order of composition, but attempts to ascertain this through the varying complexity of doctrine are somewhat uncertain, since a thinker's development may not be continuous and homogeneous. The logical works of aristotle, known as the Organon, have been handed down in a systematic order: Categories, dealing with the term On Interpretation, the proposition Prior Analytics, the syllogism in general Posterior Analytics, Topics, and Sophistical Refutations, apodictic, dialectical, and sophistical syllogisms, respectively. Plato was surely influential in that he developed the notion of universal law, already in evidence among the pre-Socratics, but it was left for Aristotle to achieve the first conscious, general, explicit system of formal logic, so that Leibniz could say of him that he was the first to write mathematically outside of mathematics.Īristotelian Logic. Roughly speaking, Athens gave birth to the former, Megara to the latter. Both in the school founded by Euclid of Megara, who was a pupil of socrates, and in the Platonic Academy descended from the same source, as also in the tradition of the 5th-century sophists, discussion was so strongly cultivated that it is not surprising that people should have begun to reflect on the processes of argument, to notice patterns of recurrence, and to generalize in a reflective way about conclusive and inconclusive methods.Īlready in plato one can see intimations of what would become, in the hands of Aristotle, the syllogism, and, in the hands of the Megarians and Stoics, propositional logic. One can, of course, find a climate of intense discussion that favored such a development. Greco-Roman PeriodĪristotle claimed to be the founder of logic, saying that he could find nothing like what he had done among his philosophic predecessors. One thus has four periods to consider: (1) the Greco-Roman, (2) the medieval, (3) the post-Renaissance, and (4) the modern. Their work brought new understanding of the past and a huge increase in doctrine, presented with an altogether new completeness, strictness, and critical control. Boole and with renewed authority through the immense analytical acumen of G. In mid-19th century the modern period began with G. Only occasionally was the monotonous desert interrupted by something of interest, notably, by the great genius of G. About mid-15th century the impetus failed and within 100 years had died completely, giving place to a centuries-long crop of incompetent handbooks, often infected with rhetoric, entirely lacking in originality or serious investigation. It borrowed rather little from rhetoric but was a good deal influenced by grammar. While borrowing much from Aristotle and a little from Roman hints about Stoicism, it developed original methods in propositional and quantificational logic and in regard to logical antinomies. After the Dark Ages logic began to revive in the 12th century, and by the middle of the 13th century scholastic logic was well developed. It also began a long sequence of sketchy textbooks. The Greeks of the Hellenistic age and the Romans did nothing to advance these beginnings, but injected a stream of rhetoric that was to plague the subject until quite recent times. Western formal logic began among the Greeks of the 5th and 4th centuries b.c., who developed syllogistic and prepositional systems.
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