Notable pre-Aristotelian philosophers who prepared the way for the formal study of Logic
include Zeno of Elea, the Sophists, Socrates, and Plato.
Ancient Period (650 B. C.-400 A.D.)
Considered by some as the founder of dialectic, Zeno of Elea (490-430 B. C.) provided early
examples of arguments and paradoxes. Socrates (470-399 B. C.) gave emphasis on definition,
deduction, and the use of dialectic to obtain non-relative truths. Plato, his student, was also
concern about truth in such a way that the correspondence theory of truth—that which attempts
to make the connection between the world and our descriptions of it—can be attributed to him.
Believing that truth is relative, the Sophists were paid teachers who taught skills in language and
communication. Among them were Protagoras (490-421 B. C.) who distinguished various types
of sentences, Prodicus (460-399) who showed interest in the correct use of words, and Gorgias
(480-399) who taught about rhetoric and persuasion.
Just when the Sophists were active in the West, the Nyaya philosophy developed in the East.
Nyaya is a philosophical system in Indiareputedly developed by Gotama. It takes its name from
the word nyaya, meaning logical argument, or syllogism. This Indian syllogism is relatively
more detailed as it consists of five propositions.
In the West, Plato’s student Aristotle (384-322 BC) was the first to comprehensively systematize
logic. In his collection of treatises in logic called the ‘Organon’ (“tool’), he introduced his
systems in reasoning, especially the theory of the categorical syllogism which comprises three
propositions.
On the other hand, Aristotle’s contemporaries, the Stoics, studied compound statements, thereby
organizing another division of logic called propositional logic. They also investigated various
logical antinomies and paradoxes.
Later in history, Roman philosophers would propagate the logic of the Greek. Following Greek’s
tradition in logic, Cicero (106-43 B.C.) introduced the term ‘proposition’, Galen the physician
(129-199 A.D.) wrote “Introduction to Dialectic”, and Alexander of Aphrodisias (3rd century
A.D.) used the term ‘logic’ in the modern sense of distinguishing correct from incorrect
reasoning.
Medieval period (400 A.D.-1600 A.D.)
Boethius (470 524) wrote commentaries on Aristotle’s works in Logic, exemplifying that
medieval philosophers were very mush influenced by Aristotelian logic.
In the early twelfth century, Peter Abelard (1079-1142) wrote extensive commentaries tackling
issues like opposition, conversion, opposition, quantity, and quality, and composed his treatise,
‘the Dialectica’.
William of Sherwood (1200-1271) developed mnemonic verses (e.g. Barbara for AAA
syllogism) as an aid in mastering the syllogisms. Later known for Ockham’s razor (which
emphasizes the importance of simplicity), William of Ockham (1280-1349) made important
contributions to the doctrine of supposition of terms. Jean Buridan elaborated a theory of
consequences which somewhat discussed the rules of inference.
Scholastic logician Raymond Lully (1234-1315) used logic to prove the Christian faith. He also
remarkably designed machines that would perform logical calculations, and is thus arguably
considered the father of computer programming.
Early Modern Period (1600-1850 A.D.):
In 1662, Antoine Arnauld and Pierre Nicole published the “Port Royal Logic” in which logic is
defined as the “art of managing one’s reason right in the knowledge of things, both for the
instruction of oneself and of others”.
Having invented calculus, Wilhelm Leibniz (1646-1716) concluded that the whole of logic
depends on mathematics and thus worked on reducing scientific and philosophical speculation to
computation. Immanuel Kant (1724-1804), on the other hand, distinguished between analytic
statements (whose truth can be determined through the meanings of the words in the
propositions) and synthetic statements (which are based on direct experience of things).
Modern and Contemporary Period (1850-present)
Logicians in the modern period ‘rediscovered’ the Stoic’s logic of proposition. Augustus De
Morgan (1806-1871), for instance, proposed some theorems in that logic which now bear his
name. Considered the founder of symbolic logic, George Boole (1815-1864) gave us Boolean
Logic which treats propositions as either true or false. His use of numbers to express the truth
values of compound statements influenced the development of computers. Programmers today
use his principle to test the truth of program results or user feedback.
John Venn (1834-1923) introduced circular diagrams as a tool to test the validity of syllogisms.
John Stuart Mill (1806-1873) made a thorough study about inductive reasoning and introduced
methods for checking such arguments now known as “Mill’s Methods”. In 1877, Charles
Sanders Peirce (1839-1914) introduced Pragmatism, at the core of which he argued that ideas
should be evaluated solely by their practical effects, and not by any intrinsic qualities of reason
or logic.
Gottlob Frege (1848-1925) pronounced that logic is the basis of mathematics and that arithmetic
and analysis are part of logic. By developing the predicate calculus (quantification theory), he
had remarkably combined Aristotelian and Stoic’s logics.
In 1903, Bertrand Russell (1872-1970) started his project ‘The Principles of Mathematics’ in
which he purposed to prove that “all pure mathematics deals exclusively with concepts definable
in terms of a very small number of logical principles.” With Alfred North Whitehead (1861-
1947), Russell continued (in their ‘Principia Mathematica’)the development of the predicate
calculus pioneered by Frege, though Russell had criticisms on some of Frege’s ideas.
The famous Ludwig Wittgenstein (1819-1951) entered the list of significant logician by being
one of the developers of the ‘truth tables’. Using many applications of the rules of logic (called a
proof), Kurt Godel (1916-1978) proved his “incompleteness theorem”, which proposes that some
parts of mathematics are based on ideas that cannot be proved within the system of mathematics.
Logical empiricist Rudolph Carnap (1891-1970) was associated with the famous verifiability
principle, according to which a synthetic statement is meaningful only if it is verifiable. Logical
positivist A.J. Ayer, on the other hand, wrote in 1936 his ‘Language, Truth, and Logic’ in which
he focused on the role of language as the medium through which knowledge is understood and
verified. In 1965, Lofti Zadeh developed ‘fuzzy logic’ which allows imprecise answers to
questions in addition to being either clear-cut true or false. This logic now serves as the basis of
computer programming designed to mimic human intelligence.
Ref: http://ourhappyschool.com/philosophy/short-history-logic
