Logic was established as an academic discipline by Greek philosophers. Aristotle (384–322 BC) was the first to systematically describe logic, in particular the syllogistic method. He argued that knowledge could be divided into three parts: sense perception, memory, and reason. Reasoning logically from premises to conclusions was the hallmark of logic. Aristotle also introduced the notions of terms, propositions, and truth. His student Alexander of Aphrodisias (c. 200 AD) wrote On Interpretations – where he distinguished between direct and indirect discourse. Direct discourse states what something actually is, whereas indirect discourse describes what something seems to be. A proposition is a statement about a subject matter, expressed using predicates. For example, ‘Socrates is wise’ is a proposition. Propositions can be true or false, according to whether the subject matters match. Truth is correspondence, meaning that if the subject matter matches then the proposition must be true. Aristotle defined truth as the conformity of a proposition to reality.
In the 18th century, logicians worked out formal definitions of logical terms, including those for identity and contradiction. George Boole (1815–64) introduced mathematical proofs to demonstrate that all logical operations were equivalent to algebraic formulas. Boole’s ideas led to the development of symbolic logic, which became the standard tool for studying logic. Boole believed that logic should be grounded in mathematics and he presented his work in terms of Boolean algebras. Gottlob Frege (1848–1925) gave a thorough analysis of quantifiers. Rudolf Carnap (1891–1970) was the first to give a systematic treatment of modality, and Alfred Tarski (1903–83) laid down the foundations of semantics. These developments in the early 1900s led to the emergence of modern analytic philosophy.
