thing of indefinite stability and duration; as, e.g., a collision between two sidereal bodies may be due to the past existence during an unimaginable time of two such bodies proceeding along paths which ultimately coincide. After this preliminary inquiry in quest of some selfevident, fundamental truths, we may proceed to address. ourselves to the consideration of the self-evident force of some arguments. CHAPTER V. REASONING. Ratiocination can make things known to us which were before un- Some reasoning must be valid-Inference denied to the syllogism— Shown to exist by examples-The syllogism makes implicit truth explicit-Difference between implicit knowledge and actual knowledge-A general principle may be more evident than a concrete example-Force of the word "therefore"-Logic-Inference implies imperfection of the intellect. valid. As we remarked towards the end of the first chapter,* no one who himself argues, or who listens to or reads, with any serious intention, the arguments of other men, can, without stultifying himself, profess to think that no process of reasoning is valid. If the truth of no mode of Some reasoning is certainly true, if we can make no valid reasoning inference, then all arguments must be useless, and to proffer or to consider them, alike vain. A forced abstinence from reasoning, due to such doubt, would, however, carry with it yet more disastrous consequences; for if we doubt about one self-evident truth, we may doubt about all, and we should thus be landed once more in that absolute scepticism we have seen to be so self-destructive and irrational. But the truth of the "inference" that any given man will die, provided it be true that mortality is the lot of all men, is a statement the truth of which is self-evident. No one can possibly deny its truth, though some persons will * See above, p. 12. Inference denied to the syllogism. Shown to exist by deny that it contains any process of "inference." In order to see whether this is the case, let us draw out formally, for examination, the old stock example of the syllogismwith its major and minor premisses, and its conclusionthus: "All men are mortal. Socrates is a man, therefore Socrates is mortal." Those who object to such reasoning say, "Whoever has said that 'all men are mortal,' has already said that 'Socrates is mortal' also. The socalled 'conclusion,' is therefore but a repetition of part of the major premiss, all men are mortal.' Here, then, we really have no inference at all, but merely a restateWe do not in truth conclude' that Socrates is mortal, but we only say over again, with the mention of his name, what was said before without the mention of his name." To test the force of this objection, let us see, by an examples. example, what our meaning is when we declare that any one object belongs to a certain class of objects. Persons ignorant of zoology may fancy that a whale is a fish, but a knowledge of these matters is now so general that few will be surprised to read the statement that "a whale is a beast." Now, when we make this statement, what do we mean? We mean that a whale, in spite of its shape and exclusively marine mode of life, is nevertheless more closely allied in its nature to such creatures as cattle, beasts of prey, etc., than it is to any fishes. Even if we are zoological experts, we do not, in saying "A whale is a beast," distinctly advert in our minds to all those various anatomical conditions which characterize the class of beasts, but only to the fact of the predominance in its organization of the marks which distinguish that class of animals. We can if we choose, however, turn back our mind, and mentally, or verbally, refer to any one of such marks, or characters, and recognize the fact that the whale, inasmuch as it belongs to the class of beasts, must have that particular character so referred to, out of those various marks which are common to the whole class. Thus we may say to ourselves, or others, "The whale, being a beast, must have warm blood." In this manner we bring forward into explicit recognition a character, the existence of which gism makes truths, in the whale was implied in saying it was a beast, but which, nevertheless, was not distinctly present to the mind, may never have been even thought of before, and therefore never actually known-for we cannot be said to know what is not and never has been present to the mind. In The syllo saying, then, "All beasts have warm blood. The whale is a implicit beast, therefore the whale has warm blood," a new fact is explicit. brought distinctly and explicitly before consciousness which previously was but latent, and so the conclusion of the syllogism does impart knowledge. Thus the syllogism affords fresh knowledge to the mind by bringing about the explicit recognition of a truth which before was implicitly contained in an assertion to the effect that a certain object belongs to a class which has certain attributes. This process of bringing out into clear recognition a matter which before was latent, is a process of "inference" the whole force of which resides in, and is expressed by, the word "therefore," as we shall shortly more clearly see. Let us suppose a person to be looking at some very flexible and soft kind of fish. He may perhaps say to himself, "This creature cannot have any spinal column in it." Then it may strike him that naturalists have classed fishes, together with various other animals, in a great group, one character of which is the possession of a spinal column. He will then further say to himself, "Since it is a fish, it must, however soft and flexible it may be, have a spinal column." Thus he will really obtain by inference the knowledge of a new truth. It may, however, be further objected that by our explanation we have admitted the major premiss to implicitly contain the conclusion. But this further objection, to have any force, must be understood as saying in effect that implicit and explicit knowledge are, at least practically, the same thing. For if Difference "implicit knowledge" is not "actual knowledge," a fact plicit know "implicitly contained" in a major premiss is none the more actual "actually known" on account of its being so contained therein; and manifestly anything which makes "actually known" what before was not actually known, must convey fresh knowledge. There is, indeed, so great a difference between explicit and implicit knowledge that the between im ledge and knowledge. mind latter may not really deserve to be called "knowledge" at all. A little consideration will, we think, make this clear beyond all dispute. No one will venture to affirm that a student merely learning the axioms and definitions of Euclid, will, by having done so, have become at once. acquainted with all the geometrical truths the work contains, so that he will have no need to study its various propositions and theorems, all of which he will thus know. without having once read them. Yet all the propositions about circles, triangles, etc., in his "Euclid" are implicitly contained in the definitions and axioms. Although, then, he knows that mass of geometric truths implicitly, in knowing the definitions and axioms, he does not, for all that, really and actually know them at all. In order that he may come actually to know them he must go. through those various processes of "inference" by which the different truths implicitly contained in Euclid's definitions and axioms are brought to the student's knowledge explicitly. There would be much more weight in the assertion that the conclusion of a syllogism is contained in the major premiss, if that premiss were a truth which had been arrived at by an examination of every single instance of the kind referred to in it. For example, if every tree in a certain garden had been examined, and found to be a conifer, then the assertion, "All the trees in that garden are conifers," would be a truth of that kind. It would have been the result of an examination of every fact referred to— or, in other words, it would have been arrived at by what is called "a complete induction." In a syllogism with a proposition of this kind for its major premiss-e. g. "All the trees in the garden are conifers. This tree is a tree in the garden, therefore this tree is a conifer "-the conclusion is not contained in that premiss in a merely implicit manner. It is, however, very rarely the case that the major premiss expresses a truth arrived at by a complete induction, and in some sciences, and these chiefly the exact sciences, it is never so. In most cases we arrive at the general principle of our argument-the major premissfrom a consideration of but a few, sometimes but one or two, instances. Thus no one can pretend we know that |