Wednesday, December 12, 2012

The Difference between Traditional and Modern Logic and the Difference it Makes

This is the first two pages or so of a 20 page essay I wrote some years ago. I've gone back to it several times, realizing it needed more work. I am going to use the recent article by Peter Kreeft in Touchstone Magazine and the recent response at First Thoughts as an excuse to go ahead and start posting it in pieces here to give me an excuse to finish it. It is still in draft form and parts of it clearly need more work, but what I'll publish here is at least approaching some kind of finished form.

I am often asked why, as a logic teacher, I teach traditional logic rather than the modern system of logic, which is much more common today.  I would like to answer this question by explaining what traditional logic is and how it differs from modern logic.

In analyzing the differences between traditional and modern logic, we will discuss the assumptions behind the two systems, the structure of the systems and their competing purposes.  As we do this, we should be aware that, for the most part, the nature of these differences is not disputed by the chief proponents of either system.  In other words, both traditional and modern logicians agree that these are in fact the differences: their only disagreement has to do with the extent of the differences and the merit of the respective systems.

What is Traditional Logic?
Traditional logic is the system of logic originally formulated by Aristotle, the Greek philosopher, in the fourth century B. C.  It was taken up by the great Christian thinkers of the Middle Ages, who simplified its structure and formalized the methods of teaching it to students.

Traditional logic involves mostly the study of the classical syllogism.  Here is a classic example of a simple syllogism, which we will use shortly as a way to see how the two systems of traditional and modern logic are different:
All men are mortal
Socrates is a man
Therefore, Socrates is mortal
Traditional logic has also been called “term logic,” since it deals primarily (but not exclusively) with the relation of terms in an argument (in this case, the terms man, mortal, and Socrates). Whether the reasoning is valid depends on the proper arrangement of these terms in an argument.

It wasn’t until the 18th and 19th centuries that Aristotle’s system of traditional logic fell on hard times.  Beginning in the Enlightenment, the influence of scientific materialism grew tremendously.  Because of the incredible technological progress made possible by the sciences, the quantitative methods of science came eventually to be seen as an intellectual elixir, applicable to any and all intellectual disciplines.  The whole discipline of philosophy changed, beginning with William of Ockham, and continuing on into the radical rationalism of Descartes and the radical empiricism of Francis Bacon—the two intellectual traditions that still constitute the two basic impulses of the modern mind.

Traditional logic appealed to Medieval thinkers not only because it was based on Aristotelian metaphysical assumptions (not a big surprise since it was Aristotle who developed it in the first place), but also because of its uses in the determination of Christian truth. It was displaced by modern mathematical logic for two reasons: first, because of the rejection by modern philosophers of certain traditional assumptions about meaning and reality—assumptions that affect the entire system of logic; and second, because modern philosophers were looking for a way to make a science out of human reasoning—a way to completely capture the intricacies of human statements in a formal “scientific” system.

The chief actors in the drama that produced modern logic were Gottlob Frege, Bertrand Russell, Alfred North Whitehead, and Ludwig Wittgenstein. Frege, partly through his unsuccessful effort to show that mathematics was reducible to logic, developed a method of quantifying thoughts and inferences in a system of symbols. Russell and Whitehead took the basic conceptual framework of Frege’s symbolic system and used it to develop a full-fledged system of symbolic logic in their book, Principia Mathematica, the purpose of which, like Frege’s work, was to prove that mathematics was an extension of logic, but the most influential aspect of which was its system of logic. Wittgenstein both influenced and was influenced by Russell, and many of his ideas affected the Principia. Wittgenstein is reputed to have invented the truth tables that have become an essential fixture of modern logic.

The Differences Between Traditional and Modern Logic
The first thing to note about the differences between traditional and modern logic is that they are indeed different.  Although most modern logicians see the differences as differences in degree, they still consider these differences significant.  Irving Copi, the author of one widely used college logic text, does not reject the traditional system, but he does see the two systems as being very different:

Although the difference in this respect between modern and classical logic is not one of kind but of degree the difference in degree is tremendous.” [Introduction to Logic, 3rd Ed., 1968, Irving Copi, p. 212]

To the traditional logician, the difference goes even deeper:

“Aristotelian logic and symbolic logic,” says Edward Simmons, “are radically distinct disciplines.” [The Scientific Art of Logic: An Introduction to the Principles of Formal and Material Logic, 1961, Edward D. Simmons, p. 322]

Jacques Maritain, a traditional logician who referred to modern symbolic logic as “logistics,” put it this way:
Logistics differs essentially from Logic … Logistics and logic remain separate disciplines, entirely foreign to one another. (emphasis in the original)
Many traditional logicians, in fact, reject much of modern logic as mistaken.  Maritain, in fact, goes so far as to argue that modern logic is not logic at all.  This favor is returned by some modern logicians.  Traditional logic, says Bertrand Russell, one of the founders of the modern system, “is as definitely antiquated as Ptolemaic astronomy.” [Bertrand Russell, A History of Western Philosophy (New York: Simon and Schuster, 1945), p. 195].  Anyone wanting to know Russell’s view of Aristotelian logic will find it at the end of his chapter on Aristotle in this book:
I conclude that the Aristotelian doctrines with which we have been concerned in this chapter are wholly false, with the exception of the formal theory of the syllogism, which is unimportant.  Any person in the present day who wishes to learn logic will be wasting his time if he reads Aristotle or any of his disciples. [Russell, p. 202]
So there.

In short, some of the most important traditional and modern logicians agree that the systems are different, and some advocates of the respective systems reject, in whole or in part, the opposing system.

As we mentioned above, the two systems differ in three respects:  First, the assumptions behind the two systems are different.  Second, the format or structure of the two systems is different.  Third, the respective purposes of the two systems are different.  In all three cases—in the assumptions, structure, and the purpose—the traditional system reflects traditional views, and the modern system reflects modern views about reality. Each system is based on a different metaphysic.

To be continued ...

UPDATE: Although I am still in the process of finishing the line of thought started in this post, I have posted another related article on the issue of why traditional logic does not employ truth tables that should be of interest to those interested in this article: here
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