[Source & Text: Jevons, "Elementary Lessons in Logic"]
One name which has been given to Logic, namely the Science of Sciences, very aptly describes the all extensive power of logical principles. The cultivators of special branches of knowledge appear to have been fully aware of the allegiance they owe to the highest of the sciences, for they have usually given names implying this allegiance. The very name of logic occurs as part of nearly all the names recently adopted for the sciences, which are often vulgarly called the "ologies," but are really the "logics," the "o" being only a connecting vowel or part of the previous word. Thus geology is logic applied to explain the formation of the earth's crust; biology is logic applied to the phenomena of life; psychology is logic applied to the nature of the mind; &c. Each science is thus distinctly confessed to be a special logic. The whole of logic and the whole of any science consists in so arranging the individual things we meet in general notions or classes, and in giving them appropriate general names or terms, that our knowledge of them may be made as simple and general as possible. Every general notion that is properly formed admits of the statement of general laws or truth. The study of logic not only explains the principles on which everyone has often reasoned correctly before, but points out the dangers which exist of erroneous argument. The reasoner thus becomes consciously a correct reasoner and learns consciously to avoid the snares of fallacy.
The most convenient and usual mode of studying logic is to consider first the component parts of which any argument must be made up. If we examine a simple argument such as -
Iron is a metal,
Every metal is an element,
Therefore Iron is an element,-
we see that it is made up of three statements or assertions, and that each of these contains, besides minor words, two nouns substantive or names of things, and the verb "is." In short, two names, or terms, when connected by a verb, make up an assertion or proposition; and three such propositions make up an argument, called in this case a syllogism.
If, when reduced to language, there be three parts of logic, terms, propositions, and syllogisms, there must be as many different kinds of thought or operations of mind. These are usually called-
- Simple apprehension.
- Reasoning or discourse.
The first of these, Simple Apprehension, is the act of mind by which we merely become aware of something, or have a notion, idea, or impression of it brought into the mind. The adjective simple means apart from other things, and apprehension the taking hold by the mind.
Judgment is a different action of mind, and consists in comparing together two notions or ideas of objects derived from simple apprehension, so as to ascertain whether they agree or differ. It is evident, therefore, that we cannot judge or compare unless we are conscious of two things or have the notions of two things in the miud at the same time.
Reasoning or Discourse, then, may be defined as the progress of the mind from one or more given propositions to a proposition different from those given. Those propositions from which we argue are called Premises, and that which is drawn from them is called the Conclusion. The latter is said to follow, to be concluded, inferred or collected from them; and the premises are so called because they are put forward or at the beginning. The essence of the process consists in gathering the truth that is contained in the premises when joined together, and carrying it with us into the conclusion, where it is embodied in a new proposition or assertion. We extract out of the premises all the information which is useful for the purpose in view - and this is the whole which reasoning accomplishes.
The Reader should give a careful attention to the very simple laws of thought on which all reasoning must ultimately depend. These laws describe the very simplest truths, in which all people must agree, and which at the same time apply to all notions which we can conceive. It is impossible to think correctly and avoid evident self-contradiction unless we observe what are called the Three Primary Laws of thought, which may be stated as follows:
- The Law of Identity. Whatever is, is.
- The Law of Contradiction. Nothing can both be and not be.
- The Law of Excluded Middle. Everything must either be or not be.
These three laws then being universally and necessarily true to whatever things they are applied, become the foundation of reasoning. All acts of reasoning proceed from certain judgments, and the act of judgment consists in comparing two things or ideas together and discovering whether they agree or differ, toot is to say whether they are identical in any qualities. The laws of thought inform us of the very nature of this identity with which all thought is concerned. But in the operation of discourse or reasoning we need certain additional laws, or axioms, or self-evident truths, which may be thus stated:
- Two terms agreeing with one and the same third term agree with each other.
- Two terms on which one agrees and the other does not agree with one and the same third term, do not agree with each other.
- Two terms both disagreeing with, one and the same third term, may or may not agree with each other.
These self-evident truths are commonly called the Canons or Fundamental Principles of Syllogism, and they are true whatever may be the kind of agreement in question. Self-evident rules, of an exactly similar nature to these three Canons, are the basis of all mathematical reasoning, and are usually called axioms.
I have so freely used the word axiom that it is desirable to clear up its meaning as far as possible. Philosophers do not perfectly agree about its derivation or exact meaning, but it certainly comes from the verb ἀξίωμα, which is rendered, to think worthy. It generally denotes a self-evident truth of so simple a character that it must be assumed to be true, and, as it cannot be proved by any simpler proposition, It must itself be taken as the basis of reasoning. In mathematics it is clearly used in this sense.
To express the difference between knowledge derived deductively and that obtained inductively the Latin phrases a priori and a posteriori are often used. By a priori reasoning we mean argument based on truths previously known; a posteriori reasoning, on the contrary, proceeds to infer from the consequences of a general truth what that general truth is. Many philosophers consider that the mind is naturally in possession of certain laws or truths which it must recognise in every act of thought; as such, if they exist, would be a priori truths.It is probably the greatest merit in Mr. Mill's logical writings that he points out the entire insufficiency of what is called the Baconian method to detect the more obscure and difficult laws of nature. Bacon advised that we should always begin by collecting facts, classifying them according to their agreement and difference, and gradually gathering from them laws of greater and greater generality. He protested altogether against "anticipating nature," that is, forming our own hypotheses and theories as to what the laws of nature probably are, and he seemed to think that systematic arrangement of facts would take the place of all other methods. When a law of nature is ascertained purely by induction from certain observations or experiments, and has no other guarantee for its truth, it is said to be an empirical law. The reader will soon see that the progress of Science has not confirmed his opinions.
The history of science would show conclusively that deduction was the clue to all the greatest discoveries. Newton, after Galileo the chief founder of experimental philosophy, possessed beyond all question the greatest power of deductive thought which has ever been enjoyed by man. It is striking indeed to compare his results in optics with those in chemistry or alchemy. It is not generally known that Newton was really an alchemist, and spent days and nights in constant experiments in his laboratory, trying to discover the secret by which metals could be transmuted into gold. But in these researches all was purely empirical, and he had no clue to guide him to successful experiments. A few happy guesses given in his celebrated Queries are all the result of this labour. But in the science of Optics it was quite otherwise; here he grasped general laws, and every experiment only led him to devise and anticipate the results of several others, each more beautiful than the last. Thus he was enabled to establish beyond all doubt the foundations of the science of the Spectrum, now bearing such wonderful results. Some persons may suppose that Newton, living shortly after Bacon, adopted the Baconian method, but I believe that there is no reference to Bacon in Newton's works; and it is certain that he did not employ the method of Bacon. The Principia, though containing constant appeals to experiment and observation, is nevertheless the result of a constant and sustained effort of deductive mathematical reasoning.
It will now be apparent, I think, that though observation and induction must ever be the ground of all certain knowledge of nature, their unaided employment could never have led to the results of modern science. He who merely collects and digests facts will seldom acquire a comprehension of their laws. He who frames a theory and is content with his own deductions from it, like Descartes, will only surprise the world with his misused genius; but the best student of science is he who with a copious store of theories and fancies has the highest power of foreseeing their consequences, the greatest diligence in comparing them with undoubted facts, and the greatest candour in confessing the ninety-nine mistakes he has made in reaching the one true law of nature.
Logic is not only an exact science, but is the most simple and elementary of all sciences; it ought therefore undoubtedly to find some place in every course of education.