Logic is the science and art which so directs the mind in the process of reasoning and subsidiary processes as to enable it to attain clearness, consistency, and validity in those processes. The aim of logic is to secure clearness in the definition and arrangement of our ideas and other mental images, consistency in our judgments, and validity in our processes of inference.
The Greek word logos, meaning “reason”, is the origin of the term logic–logike (techen, pragmateia, or episteme, understood).
It is a curious fact that, although logic is the science which treats of definition, logicians are not agreed as to how logic itself should be defined.
St. Thomas Aquinas
In his commentary on Aristotle’s logical treatises (separate commentaries, that is), we may render St. Thomas’s definition as follows:
“Logic is the science and art which directs the act of the reason, by which a man in the exercise of his reason is enabled to proceed without error, confusion, or unnecessary difficulty.”
Taking reason in its broadest sense, so as to include all the operations of the mind which are strictly cognitive, namely, the formation of mental images, judgment, and ratiocination, we may expand St. Thomas’ definition and define logic as “the science and art which so directs the mind in the process of reasoning and subsidiary processes as to enable it to attain clearness (or order), consistency, and validity in those processes”.
Is it even necessary to point out how much of this has been lost in our current education? It seems to me that today, math is taught in the place of logic, and while this is a good exercise for the mind in properly ordering things, it is not, to my knowledge, taught with this in mind. In fact, all of our education seems to be more a mass of unrelated facts than any kind of synthesis. For anyone willing to take the task, I recommend The Way Toward Wisdom by Fr. Benedict Ashley to see what has come of education and how we might remedy it. But I digress.
Division of logic
The traditional mode of dividing logic, into “formal” and “material”, is maintained in many modern treatises on the subject.
In formal logic the processes of thought are studied independently of, or without consideration of, their content.
An example from arithmetic will serve to illustrate the function of formal logic. When we add two and two, and pronounce the result to be four, we are dealing with a process of addition in its formal aspect, without paying attention to the content. The process is valid whatever the content may be, whether the “two and two “refer to books, horses, trees, or circles. This is precisely how we study judgments and arguments in logic. From the judgment “All A is B” we infer “Therefore some B is A”; and the process is valid whether the original proposition be “All circles are round” or “All lions are carnivorous”.
In material logic the chief question is the truth of the content of mental processes. In material logic we inquire into the content of the judgments or premises and endeavour to determine whether they are true or false. The principles of material logic, an important part of trivium language study, are now almost forgotten—a casualty of the almost exclusive modern secular emphasis on math and sciences, which I mentioned above. Formal logic was once termed minor (or lesser) logic, while material logic usually went by the name of major (or greater) logic—a measure of how important classical thinkers considered them.
Aristotle, the founder of logic
In the six treatises which he devoted to the subject, Aristotle examined and analysed the thinking processes for the purpose of formulating the laws of thought. These treatises are
- “The Categories”,
- “Prior Analytics”,
- “Posterior Analytics”,
- “Topics”, and
- “Sophisms”. These were afterwards given the title of “Organon”, or “Instrument of Knowledge”; this designation, however, did not come into common use until the fifteenth century.
The first four treatises contain, with occasional excursions into the domain of grammar and metaphysics, the science of formal logic essentially the same as it is taught at the present day.
The definite triumph of Aristotelean logic in the schools of the thirteenth century was influenced by the introduction into Christian Europe of the complete works of Aristotle in Greek. The occasion of this was the taking of Constantinople by the crusaders in 1204. The Crusades had also the effect of bringing Christian Europe into closer contact with the Arabian scholars who, ever since the ninth century, had cultivated Aristotelean logic as well as the neo-Platonic interpretation of Aristotle’s metaphysics.