Division of logic

Boehner divides logic as follows:

By Aristotelian logic we understand the doctrines of Aristotle himself which are contained in the collection of his logical works known as the Organon. In this sense, Aristotelian logic is something quite different from scholastic, neo-scholastic or even Greek logic. Important as Aristotle's logic may be, it cannot simply be identified with Greek logic as such. For the logic of the Stoics, which is at least of equal importance as that of Aristotle, differs in this, that the Stoics developed the hypothetical syllogism with a clear insight into the material implication and its theorems and were well aware of the basic role played by the propositional calculus. Indeed, of all the systems of ancient times the Stoic logic appears to have the clearest right to be called the forerunner of modern logic. Because elements of this logic seem to have been incorporated in the works of the Aristotelian commentators, it seems best to confine the term "Aristotelian logic" precisely to the logic of the Organon.

By scholastic logic we refer to the logic taught during the 13th, 14th and 15th centuries in the Latin Occident, which has come down to us in various compendia, commentaries and other writings.

By neo-scholastic logic we mean that presentation of logic found in current textbooks written by neo-scholastics for the use of ecclesiastical seminaries and similar institutions. As types, we mention the textbooks of Hickey, Esser, Maritain and Gredt. In addition, we include under this term all presentations of logic similar to these works.

By modern logic we mean that tremendous development which has found its most outstanding expression in the Principia Mathematica of Whitehead and Russell … Such, for instance, is the Boolean Algebra, the works of Frege and Peano. Similarly, the term embraces all subsequent developments such as the poly-valued logics of Lukasiewicz and Post, or the logic of strict implication and modalities as advanced by Lewis-Langford and expanded by Carnap. This modern system is sometimes called "symbolic logic', "logistics" or "mathematical logic". It would seem preferable, however;' to avoid the term "symbolic logic", since the use of symbols is not confined to modern logic. It has been in vogue since ancient times. Similarly, it would seem advisable to avoid the name "mathematical logic", at least if we understand by logic precisely that more basic science which underlies mathematics, and for that very reason stops short of mathematics.

To this we can add traditional logic, namely the textbook tradition of logic lasting from the 16th century to the mid-19th century, of which examples are Arnauld's Port Royal Logic, and John Stuart Mill's System of Logic, which is almost the last work of the tradition.

See also

• Scholastic logic
• Syllogism