within the generalizations of experience, reasoning from the general; and (2) reasoning from particular facts accumulated for the purpose to a conclusion general enough to cover all facts of the same class, the attempt to conclude a case by the evidence of investigation into that case, reasoning from the particular. The first kind, argument before or without investigation, as when we conclude that a man will go to Mass on Sunday because he is a Catholic, is called a priori;1 a posteriori, on the other hand, is sometimes used of the second class, as when we conclude from investigation that an epidemic of typhoid is due to contaminated milk. These two terms correspond roughly to the more definite terms deduction and induction. Deduction, or a priori reasoning, then, is reasoning from general principles, from one's store of previous generalizations; induction, or a posteriori reasoning, is reasoning from particular facts collected and interpreted for the purpose.

95. The terms general and particular being relative, it should be observed that sometimes the same conclusion may be reached both deductively and inductively. In the one process the premises would be more general than the conclusion; in the other, less general. What is of more consequence, the generalizations reached by induction may be the basis for subsequent deduction; the conclusions of either process may be tested by the other; and finally, the two processes are habitually used by turns. One may be called the method of reflection; the other, the method of research.

1A priori is sometimes still defined to mean reasoning from cause to effect (a posteriori, reasoning from effect to cause); but this definition is not commensurate with current use.

I. DEDUCTION

(a) Argument from Antecedent Probability

96. That form of deductive reasoning which is perhaps most obviously a priori is the argument from antecedent probability. My friend A is accused of forgery. Before hearing any of the evidence I argue that the charge is false because it is not in A to commit forgery. We all recognize this as a fair way of rejecting some propositions. If a newspaper should announce the invention of an air-ship capable of carrying one hundred passengers across the Atlantic at a speed of three hundred miles an hour, most of us would doubt, and some of us would utterly deny, the statement without investigation. In approaching an investigation, moreover, antecedent probability is most useful (§ 129). We say to ourselves, "No use in spending time on such testimony"; or, "There should be traces here"; or, more generally, "It will not be hard to make a great array of supporting evidence"; or, "This cannot be settled by evidence; it must be fought out on general considerations." In fact, this is the chief use of antecedent probability — to clear the way, to forecast. It is preliminary, not final. Though I rightly refuse to tolerate a charge of forgery against my friend, yet I must admit that even his well-known uprightness does not, as against positive evidence of his having signed such and such cheques, prove his innocence. The argument from antecedent probability shows which way the probabilities lean before the case is investigated; it establishes a presumption. In some cases we are content to accept it as sufficient; in other cases,

as sometimes in astronomy and philology, we have nothing better; in most cases we go on to the evidence.

(b) Syllogism

97. The typical form of deductive reasoning is the syllogism:

Major Premise. Marriage with a divorced person is contrary to Catholic law.

Minor Premise. A's marriage was with a divorced person. Conclusion.

A's marriage was contrary to Catholic law.

The major premise is ideally a univeral, indisputable truth; the minor premise indicates the course of the argument, which is to prove that a particular instance falls within that universal, indisputable truth; the conclusion follows of necessity. The conclusion, being necessary, being demonstrated as a universal, indisputable truth, becomes in turn the major premise for succeeding syllogisms, and so on. Thus geometry is a chain, or rather a web, of syllogisms; and, conversely, all syllogistic argument may be carried back and back until it

rests on some axiom.

(c) Enthymeme

98. In common speech we express the syllogistic argument less formally. We say: "He must go the way of all men"; "Nothing else could come of that vice in the blood," — implying those links of reasoning with which every one is familiar. And we use it less absolutely; else (except as a formal test) we could never use it at all; for persuasion, as Aristotle says, is not absolute and abstract, but relative and concrete. Our

arguments concern "things which appear to admit the possibility of conclusion either way

for no one

ever deliberated about things which offer no alternative, which can exist or issue only in one way."

An informal syllogism, or a syllogism whose major premise is not the ideal "universal," but simply an accepted generalization, is called an enthymeme. Persuasion, then, according to Aristotle, deals with enthymemes, with incomplete syllogisms.

2. INDUCTION

(a) Mill's Canons

99. Inductive argument, or reasoning from evidence, is ultimately the investigation of causes. Inductive logic, therefore, sets forth the conditions of a valid inference of cause. These were formulated by John Stuart Mill in the five "canons" that are known by his name.

"I. The Canon of Agreement.

"If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon."

In an epidemic of typhoid the only circumstance in which all the cases are found to agree is the use of milk from a particular herd of cows. Therefore it is argued that the immediate cause of the typhoid is that milk. The "characteristic imperfection" of this method is "the impossibility of assuring ourselves that we know all the antecedents in our instances."1 It is hard enough in a country village to be

1Killick, Handbook to Mill, page 118.

sure that milk from a particular source is the only thing in which all the cases agree (one of the patients was out of town a part of every day before his illness; another has a contaminated well, which may have been used by disobedient children; etc.); in a great city, it may easily be impossible. Hence there is further

"II. The Canon of Difference.

"If an instance in which the phenomenon under investigation occurs and an instance in which it does not occur have every circumstance save one in common, that one occurring only in the former, the circumstance in which alone the two instances differ is the effect, or cause, or a necessary part of the cause, of the phenom

enon.

"

"The principle is that of comparing an instance of the occurrence of a phenomenon with a similar instance in which it does not occur, to discover in what they differ."1 This is typically the method of experiment. If after pressure upon a certain point of a monkey's brain certain muscles of the monkey's right leg are immediately paralyzed, no other change having occurred in the animal's physical conditions, it is inferred that the nerve-centre thus injured is the motor-centre for those leg-muscles. And, in fact, experiments of this sort have enabled physicians, from certain symptoms, to locate the exact spot of a human brain at which an operation is necessary to relieve pressure.

"III. The Canon of the Joint Method of Agreement and Difference.

"If two or more instances in which the phenomenon occurs have only one circumstance in common, while

1 Killick, Handbook to Mill, page 120.