An excerpt from chapter 1:
Section 3. The two logics (P)
(This section can be omitted without losing anything you will need later on in the book. It’s here both to satisfy the advanced student’s curiosity and to sell the approach of this book to prospective teachers who may question its emphasis on Aristotelian rather than symbolic logic, by justifying this choice philosophically.)
Almost four hundred years before Christ, Aristotle wrote the world’s first logic textbook. Actually it was six short books, which collectively came to be known as the Organon, or “instrument.” From then until 1913, when Bertrand Russell and Alfred North Whitehead published Principia Mathematica, the first classic of mathematical or symbolic logic, all students learned Aristotelian logic, the logic taught in this book.
The only other “new logic” for twenty-four centuries was an improvement on the principles of inductive logic by Francis Bacon’s Novum Organum (“New Or-ganon”), in the 17th century, and another by John Stuart Mill, in the 19th century.
(Inductive reasoning could be very roughly and inadequately defined as reasoning from concrete particular instances, known by experience, while deduction reasons from general principles. Induction yields only probability, while deduction yields certainty. “Socrates, Plato and Aristotle are mortal, therefore probably all men are mortal” is an example of inductive reasoning; “All men are mortal, and Socrates is a man, therefore Socrates is mortal” is an example of deductive reasoning.)
Today nearly all logic textbooks use the new mathematical, or symbolic, logic as a kind of new language system for deductive logic. (It is not a new logic; logical principles are unchangeable, like the principles of algebra. It is more like changing from Roman numerals to Arabic numerals.) There are at least three reasons for this change:
(1) The first and most important one is that the new logic really is superior to the old in efficiency for expressing many long and complex arguments, as Arabic numerals are to Roman numerals, or a digital computer to an analog computer, or writing in shorthand to writing in longhand.
However, longhand is superior to shorthand in other ways: e.g. it has more beauty and elegance, it is intelligible to more people, and it gives a more personal touch. That is why most people prefer longhand most of the time – as most beginners prefer simpler computers (or even pens). It is somewhat similar in logic: most people “argue in longhand,” i.e. ordinary language; and Aristotelian logic stays close to ordinary language. That is why Aristotelian logic is more practical for beginners.
Even though symbolic language is superior in sophistication, it depends on commonsense logic as its foundation and root. Thus you will have a firmer foundation for all advanced logics if you first master this most basic logic. Strong roots are the key to healthy branches and leaves for any tree. Any farmer knows that the way to get better fruit is to tend the roots, not the fruits. (This is only an analogy. Analogies do not prove anything – that is a common fallacy – they only illuminate and illustrate. But it is an illuminating analogy.)
Modern symbolic logic is mathematical logic. “Modern symbolic logic has been developed primarily by mathematicians with mathematical applications in mind.” This from one of its defenders, not one of its critics (Henry C. Bayerly, in A Primer of Logic. N.Y.: Harper & Row, 1973, p.4).
Mathematics is a wonderful invention for saving time and empowering science, but it is not very useful in most ordinary conversations, especially philosophical conversations. The more important the subject matter, the less relevant mathematics seems. Its forte is quantity, not quality. Mathematics is the only totally clear, utterly unambiguous language in the world; yet it cannot say anything very interesting about anything very important. Compare the exercises in a symbolic logic text with those in this text. How many are taken from the Great Books? How many are from conversations you could have had in real life?
(2) A second reason for the popularity of symbolic logic is probably its more scientific and exact form. The very artificiality of its language is a plus for its defenders. But it is a minus for ordinary people. In fact, Ludwig Wittgenstein, probably the most influential philosophical logician of the 20th century, admitted, in Philosophical Investigations, that “because of the basic differences between natural and artificial languages, often such translations [between natural-language sentences and artificial symbolic language] are not even possible in principle.” “Many logicians now agree that the methods of symbolic logic are of little practical usefulness in dealing with much reasoning encountered in real-life situations” (Stephen N. Thomas, Practical Reasoning in Natural Language, Prentice-Hall, 1973).
– And in philosophy! “However helpful symbolic logic may be as a tool of the . . . sciences, it is [relatively] useless as a tool of philosophy. Philosophy aims at insight into principles and into the relationship of conclusions to the principles from which they are derived. Symbolic logic, however, does not aim at giving such insight” (Andrew Bachhuber, Introduction to Logic (New York: Appleton-Century Crofts, 1957), p. 318).
(3) But there is a third reason for the popularity of symbolic logic among philosophers, which is more substantial, for it involves a very important difference in philosophical belief. The old, Aristotelian logic was often scorned by 20th century philosophers because it rests on two commonsensical but unfashionable philosophical presuppositions. The technical names for them are “epistemological realism” and “metaphysical realism.” These two positions were held by the vast majority of all philosophers for over 2000 years (roughly, from Socrates to the 18th century) and are still held by most ordinary people today, since they seem so commonsensical, but they were not held by many of the influential philosophers of the past three centuries.
(The following summary should not scare off beginners; it is much more abstract and theoretical than most of the rest of this book.)
The first of these two presuppositions, “epistemological realism,” is the belief that the object of human reason, when reason is working naturally and rightly, is objective reality as it really is; that human reason can know objective reality, and can sometimes know it with certainty; that when we say “two apples plus two apples must always be four apples,” or that “apples grow on trees,” we are saying something true about the universe, not just about how we think or about how we choose to use symbols and words. Today many philosophers are skeptical of this belief, and call it naïve, largely because of two 18th century “Enlightenment” philosophers, Hume and Kant.
Hume inherited from his predecessor Locke the fatal assumption that the immediate object of human knowledge is our own ideas rather than objective reality. Locke naïvely assumed that we could know that these ideas “corresponded” to objective reality, somewhat like photographs; but it is difficult to see how we can be sure any photograph accurately corresponds to the real object of which it is a photograph if the only things we can ever know directly are photographs and not real objects. Hume drew the logical conclusion of skepticism from Locke’s premise.
Once he limited the objects of knowledge to our own ideas, Hume then distinguished two kinds of propositions expressing these ideas: what he called “matters of fact” and “relations of ideas.”
What Hume called “relations of ideas” are essentially what Kant later called “analytic propositions” and what logicians now call “tautologies”: propositions that are true by definition, true only because their predicate merely repeats all or part of their subject (e.g. “Trees are trees” or “Unicorns are not non-unicorns” or “Unmarried men are men”).
What Hume called “matters of fact” are essentially what Kant called “synthetic propositions,” propositions whose predicate adds some new information to the subject (like “No Englishman is 25 feet tall” or “Some trees never shed their leaves”); and these “matters of fact,” according to Hume, could be known only by sense observation. Thus they were always particular (e.g. “These two men are bald”) rather than universal (e.g. “All men are mortal”), for we do not sense universals (like “all men”), only particulars (like “these two men”).
Common sense says that we can be certain of some universal truths, e.g., that all men are mortal, and therefore that Socrates is mortal because he is a man. But according to Hume we cannot be certain of universal truths like “all men are mortal” because the only way we can come to know them is by generalizing from particular sense experiences (this man is mortal, and that man is mortal, etc.); and we cannot sense all men, only some, so our generalization can only be probable. Hume argued that particular facts deduced from these only-probable general principles could never be known or predicted with certainty. If it is only pr...