Primary Laws of Thought.
In connection with this subject we herewith call the attention of the student to the well-known Primary Laws of Thought which have been recognized as valid from the time of the ancient Greek logicians. These laws are self-evident, and are uncontradictable. They are axiomatic. Jevons says of them: "Students are seldom able to see at first their full meaning and importance. All arguments may be explained when these self-evident laws are granted; and it is not too much to say that the whole of logic will be plain to those who will constantly use these laws as their key." Here are the Three Primary Laws of Thought:--
I. _Law of Identity._ "Whatever is, _is_."
II. _Law of Contradiction._ "Nothing can both be and not be."
III. _Law of Excluded Middle._ "Everything must either be or not be; there is no middle course."
I. The first of these laws, called "_The Law of Identity_," informs us that a thing is always itself, no matter under what guise or form it is perceived or may present itself. An animal is always a bird if it possesses the general characteristics of a "bird," no matter whether it exhibits the minor characteristics of an eagle, a wren, a stork, or a humming bird. In the same way a whale is a mammal because it possesses the general characteristics of a mammal notwithstanding that it swims in the water like a fish. Also, sweetness is always sweetness, whether manifested in sugar, honey, flowers, or products of coal tar. If a thing _is_ that thing, then it _is_, and it cannot be logically claimed that it _is not_.
II. The second of these laws, called "_The Law of Contradiction_," informs us that the same quality or class cannot be both affirmed and denied of a thing at the same time and place. A sparrow cannot be said to be both "bird" and "not bird" at the same time. Neither can sugar be said to be "sweet" and "not sweet" at the same time. A piece of iron may be "hot" at one end and "not hot" at another, but it cannot be both "hot" and "not hot" at the same place at the same time.
III. The third of these laws, called "_The Law of Excluded Middle_," informs us that a given quality or class _must_ be affirmed or denied to _everything_ at any given time and place. Everything either must be of a certain class or not, must possess a certain quality or not, at a given time or place. There is no other alternative or middle course. It is axiomatic that any statement _must_ either be or not be true of a certain other thing at any certain time and place; there is no escape from this. Anything _either_ must be "black" or "not black," a bird or not a bird, alive or not alive, at any certain time or place. There is nothing else that it can be; it cannot both be and not be at the same time and place, as we have seen; therefore, it must either be or not be that which is asserted of it. The judgment must decide which alternative; but it has only two possible choices.
But the student must not confuse opposite qualities or things with "not-ness." A thing may be "black" or "not black," but it need not be white to be "not black," for blue is likewise "not black" just as it is "not white." The neglect of this fact frequently causes error. We must always affirm either the existence or non-existence of a quality in a thing; but this is far different from affirming or denying the existence of the opposite quality. Thus a thing may be "not hard" and yet it does not follow that it is "soft"; it may be _neither_ hard nor soft.
FALLACIOUS APPLICATION.
There exists what are known as "fallacies" of application of these primary laws. A fallacy is an unsound argument or conclusion. For instance, because a particular man is found to be a liar, it is fallacious to assume that "_all_ men are liars," for lying is a particular quality of the individual man, and not a general quality of the family of men. In the same way because a stork has long legs and a long bill, it does not follow that all birds must have these characteristics simply because the stork is a bird. _It is fallacious to extend an individual quality to a class._ But it is sound judgment to assume that a class quality must be possessed by all individuals in that class. It is a far different proposition which asserts that "_some_ birds are black," from that which asserts that "_all_ birds are black." The same rule, of course, is true regarding negative propositions.
Another fallacy is that which assumes that because the affirmative or negative proposition has not been, or cannot be, proved, it follows that the opposite proposition must be true. The true judgment is simply "not proven."
Another fallacious judgment is that which is based on attributing absolute quality to that which is but relative or comparative. For instance, the terms "hot" and "cold" are relative and comparative, and simply denote one's relative opinion regarding a fixed and certain degree of temperature. The _certain_ thing is the degree of temperature, say 75 degrees Fahrenheit; of this we may logically claim that it _is_ or _is not_ true at a certain time or place. It either _is_ 75 degrees Fahrenheit or it _is not_. But to one man this may seem _warm_ and to another _cold_; both are right in their judgments, so far as their own relative feelings are concerned. But neither can claim absolutely that it is _warm_ or _cold_. Therefore, it is a fallacy to ascribe absolute quality to a relative one. The _absolute fact_ comes under the Law of Excluded Middle, but a personal opinion is not an absolute fact.
There are other fallacies which will be considered in other chapters of this book, under their appropriate heading.