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die is necessary, because it contains the fact as a part of the meaning.

This form of deductive argument is a prevailing type of argumentative reasoning. The mode of expressing it is a kind of inverted exposition; instead of a general doctrine taking the lead of the particular examples or applications, a particular case is given first, and the principle is then adduced as the proof of it. To show that the Laplanders are not so miserable as we should expect from their climate, we bring forward the general principle that the mind of man shapes itself to his condition.

Another well-known type of deductive reasoning, consists in following out a conditional assertion. "If the moon has no atmosphere, animals constituted like those on the earth cannot exist there (major); now the moon has no atmosphere (minor); therefore animals constituted like those on the earth do not exist in the moon."

97. (2.) Inductive, sometimes called Contingent: as when from particulars observed, known, or admitted, we prove, through the medium of nature's uniformity, other particulars unobserved, unknown, or unadmitted.

The argument for the gravitation of the stars is inductive. The proof that quinine will cure ague is of the same class.

Although a knowledge of the various modes of inductive proof, as they are exhibited in Mill's Logic of Induction, would serve the purposes of exposition and persuasion, as well as of science, I cannot transfer a complete enumeration of these to the present work. A few select points may, nevertheless, be indicated.

The first species of Inductive proof is called the Method of Agreement. It is grounded on the uniform companionship of two facts through a great variety of circumstances, which leads to their being considered as cause and effect. We should prove by this method that extreme heat is a cause of deterioration of the human system; for, under all varieties of race and of individual character, a residence in the tropics is accompanied with enfeeblement of body, or of mind, or of both.

It is only a scientific man, or a logician, that is fully aware of the limits of this argument; the popular tendency is to accept it too easily: it has a rhetorical plausibility beyond its real worth.

Many common modes of reasoning are fallacious examples of this canon. A particular mode of life is called healthy, because it has been the habit of a healthy man; a certain institution is lauded, because a nation has prospered under it. The logician in such instances would say that the conditions of a true induction have not been complied with. The easiest mode of disabusing an ordinary mind, is to produce instances where the same thing has been present without the same effect.

It adds greatly to the force of conviction by this method, as well as to its genuine cogency, to combine cases of agreement in absence with agreement in presence. Thus the effects of political liberty are more fully certified by comparing a number of countries where it exists with others where it does not exist.

The other leading mode of establishing cause and effect is called the Method of Difference. When a man, in the fulness of life, is shot and falls lifeless, we know that the shot killed him, because that agency made the whole difference between his living and his dying. When a red-hot wire is immersed in oxygen gas, it bursts into a flame and is rapidly consumed. The contact with pure oxygen is the only difference that we have made in the circumstances of the wire, and that contact is thereby proved to be the cause of the combustion. When a nation suddenly rises to prosperity on the accession of a new minister, like the British people under Chatham, no other important change having occurred, we infer that he is the cause of the improvement.

The Method of Difference furnishes a more decided proof of causation than the Method of Agreement. It is hence often resorted to in argument, and not unfrequently abused; being put forward in cases where the difference is not reduced to the one single circumstance alleged.

A third mode of Inductive proof is a variety of the foregoing, called the Method of Eesidues. We take away from a

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phenomenon the effects of all known agents, and ascribe the remaining effect to the remaining cause. Knowing the sentiments and views of three men in a co-partnership of four, we can allow for the actions that would result from them; and, if there be anything left unexplained, we attribute that to the fourth. This method, so far as it can be carried, has the force of proof, and can accordingly be used in Argument.

Another important variety of the Method of Difference is that called the Method of Concomitant Variations; whereby we infer cause and effect from the proportionate rise or fall of two accompanying facts. By the circumstance that an increase of temperature in any substance is followed by a proportionate increase of bulk, we prove that heat expands bodies.

Whately, in his Rhetoric, has illustrated this kind of Argument under the name of Progressive Approach. It is a strong presumption in favor of increased toleration and liberty, that their increase has been a concomitant of the general improvement of nations. So any mode of reasoning that falls into discredit as accurate knowledge is extended, must be looked upon as in all probability fallacious.

An argument of this kind is described by Cromwell as having decided the leaders of the Commonwealth to proceed to extremities against Charles. At a conference at Hampton Court, the officers in the Puritan army, on reviewing their experience, were agreed, that so long as they maintained uncompromising opposition to the king, their military operations prospered, but in proportion as they entered into diplomacy with a view to reconciliation, Providence was against them in the field.

98. (3.) Analogy is much resorted to as a means of proof.

When we argue from one man to another man, on any common property of men, as their birth, growth, &C., we reason Inductively, they being the same in kind; when we reason from men to animals far removed from them in structure, or to plants,

we reason Analogically; there is a sameness, but accompanied with a vast amount of difference. It is an argument from Analogy, when we compare nations to individuals in respect of vital constitution, and infer that every nation will pass through the successive stages of maturity, old age, and death. So, because there is a certain resemblance between the metropolis of a country and the heart, it has been argued that its expansion becomes at last a disease.

The existence of sensibility or consciousness in animals is proved by the analogy of their expression, their actions, and their organization.

Analogical arguments are not without rhetorical plausibility. They contain the foundation circumstances of all reasoning, a resemblance of particulars; but the accompanying disparity limits their application.

99. (4.) Argument or proof is frequently no more than Probable.

The nature of a probable assertion admits of being explained in a very simple form. Every certain inference respecting a particular case, implies that there is a law of nature absolutely uniform applying to that case. It is certain that every grown man now living will be dead within a hundred years. This inference reposes upon a natural law, authenticated by the universal experience of mankind. But it is not certain that A. B., born in 1830, will be dead in 1930, although highly probable. It is not a uniform law of nature that every man dies before attaining one hundred years of age, though it happens in a vast preponderance of instances, the exact number being known by the bills of mortality. Supposing, then, that of those attaining the age of thirty-six, 9,999 out of 10,000 die before a hundred, A. B.'s probability of living till that age is 1 to 9,999. Thus, whereas an inference that is certain rests on a universal truth, or an induction that knows no break, a probable inference rests on an induction of the form—most X's are Y's; and the degree of probability is expressed by the number of X's that are Y's. If, in a miscellaneous crowd of men, three out of every four will

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tell the truth when asked, without an oath, the probability of the testimony of any one of them is 3 to 1, or . If the addition of an oath has such an effect that, on an experience sufficiently large, it is found that 19 men out of 20 can be relied on, that ratio is the measure of the value of a single testimony on oath.

The rules for combining probable inferences to calculate their approach to certainty are not difficult of apprehension. If two independent witnesses, whose separate testimony is valued at , concur in the same statement, the combined probability is ; if one is valued at, and the other at f, the united value is §. The principle of computation may be roughly stated thus:—A probability of is the same as 2 to 1; now, two such probabilities are combined by multiplication into the product 4 to 1, which is the same as . Again, to combine and f, we must multiply 2 to 1 by 3 to 1, which yields 6 to 1, or . Hence, on the supposition that two witnesses on oath were separately valued at 18, we should have to multiply 19 to 1 by 19 to 1, and the product, 361 to 1, or 1, would be the value of their concurring testimony; a degree of probability that, however obtained, would be received as sufficient either in historical evidence or in a court of law.

Now, although, as already said, we cannot expect to put in exact numbers the probability of the proofs in historical, legal, and practical questions, yet we do always form some vague estimate of what we consider the force of an inference that is not certain; and there would be no harm in stating to ourselves ' the figure that would come nearest to that estimate. We use adjectives to express the degrees of our confidence,—as very slight, slight, tolerable, considerable, high, very high, almost certain; and we should not make our estimate less exact by representing it by a number, being all the time aware that this is but a rude approximation, although not more rude than the estimate without the number. And we might further revert to the ultimate criterion of probability, as above stated, namely, the number of cases out of the total happening in nature, where the supposed connection holds.

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