Term logic

Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by Jan Lukasiewicz of a revolutionary paradigm.

[1] Lukasiewicz's approach was reinvigorated in the early 1970s by John Corcoran and Timothy Smiley – which informs modern translations of Prior Analytics by Robin Smith in 1989 and Gisela Striker in 2009.

[3] In the Prior Analytics, Aristotle identifies valid and invalid forms of arguments called syllogisms.

Although Aristotle does not call them "categorical sentences", tradition does; he deals with them briefly in the Analytics and more extensively in On Interpretation.

A method of symbolization that originated and was used in the Middle Ages greatly simplifies the study of the Prior Analytics.

For early modern logicians like Arnauld (whose Port-Royal Logic was the best-known text of his day), it is a psychological entity like an "idea" or "concept".

In term logic, a "proposition" is simply a form of language: a particular kind of sentence, in which the subject and predicate are combined, so as to assert something true or false.

Aristotle uses the word premise (protasis) as a sentence affirming or denying one thing or another (Posterior Analytics 1.

As a further confusion the word "sentence" derives from the Latin, meaning an opinion or judgment, and so is equivalent to "proposition".

However, in a popular 17th-century version of the syllogism, Port-Royal Logic, singular terms were treated as universals:[12] This is clearly awkward, a weakness exploited by Frege in his devastating attack on the system.

[17]In the Prior Analytics translated by A. J. Jenkins as it appears in volume 8 of the Great Books of the Western World, Aristotle says of the First Figure: "...

"[23] The above statement can be simplified by using the symbolical method used in the Middle Ages: When the four syllogistic propositions, a, e, i, o are placed in the second figure, Aristotle comes up with the following valid forms of deduction for the second figure: In the Middle Ages, for mnemonic reasons they were called respectively "Camestres", "Cesare", "Festino" and "Baroco".

Referring to universal terms, "... then when both P and R belongs to every S, it results of necessity that P will belong to some R."[25] Simplifying: When the four syllogistic propositions, a, e, i, o are placed in the third figure, Aristotle develops six more valid forms of deduction: In the Middle Ages, for mnemonic reasons, these six forms were called respectively: "Darapti", "Felapton", "Disamis", "Datisi", "Bocardo" and "Ferison".

19th-century attempts to algebraize logic, such as the work of Boole (1815–1864) and Venn (1834–1923), typically yielded systems highly influenced by the term-logic tradition.

Modern predicate logic as we know it began in the 1880s with the writings of Charles Sanders Peirce, who influenced Peano (1858–1932) and even more, Ernst Schröder (1841–1902).

It reached fruition in the hands of Bertrand Russell and A. N. Whitehead, whose Principia Mathematica (1910–13) made use of a variant of Peano's predicate logic.

For example, Joyce's Principles of Logic (1908; 3rd edition 1949), written for use in Catholic seminaries, made no mention of Frege or of Bertrand Russell.

[28][page needed][need quotation to verify] Some philosophers have complained that predicate logic: Even academic philosophers entirely in the mainstream, such as Gareth Evans, have written as follows: George Boole's unwavering acceptance of Aristotle's logic is emphasized by the historian of logic John Corcoran in an accessible introduction to Laws of Thought[29] Corcoran also wrote a point-by-point comparison of Prior Analytics and Laws of Thought.