is, from explications of the Intension of any Concepts which we see fit to frame. Of course, such Judgments are purely analytic, and if they contain no unfounded assumption, that the signification thus assigned to the Names of the Concepts is that which is usually affixed to them in the common use of language, or that the Marks enumerated are all the original and essential qualities of the real things which these Names denote, the Conclusions at which we arrive must be demonstratively certain.

4. The laws, or positive precepts, which emanate from any sufficient authority, whether human or divine. These are not Judgments, but commands, and, as they are to be obeyed at all hazards, and on all occasions, the only question which can arise respecting them concerns their interpretation. Of this nature are the injunctions of conscience, the laws of the land, and the commands of God, as made known in his revealed word. Apart from any doubt which may arise concerning the signification of the terms in which they are expressed, any Conclusion legitimately deduced from such commands must be absolutely valid, since universality is of the very nature of law.

5. Universal propositions previously demonstrated.

6. Truths of generalization, based upon observation and Induction or Analogy. These are true only to the extent of our experience, which, as we have seen, never extends to all or none. Consequently, these propositions rest only upon probable evidence; and though such evidence be sufficient for moral certainty, they are not available for Demonstration strictly so called. We may assume them to be universally true, and upon such assumptions may rest perfectly valid syllogisms; but the Conclusion in such cases will have no other or higher certainty than belongs to the Major Premise.

It should be observed, however, that, when we thus speak of merely probable evidence, the epithet is used only

in its technical sense, and it is not meant that we have necessarily less confidence in it than in mathematical Demonstration. "The word probable, when thus used," says Dugald Stewart, "does not imply any deficiency in the proof, but only marks the peculiar nature of that proof as contradistinguished from another species of evidence. It is opposed, not to what is certain, but to what admits of being demonstrated after the manner of mathematicians. This differs widely from the meaning annexed to the same word in popular discourse; according to which, whatever event is said to be probable is understood to be expected with some degree of doubt." Perhaps the clearest distinction between Demonstrative and Probable evidence consists in the fact, that the former does not admit of degrees, as a proposition is either demonstrated absolutely, or not at all; while the latter may exist in any degree, from the faintest shade of probability up to moral certainty.

This seems the proper place for the explanation of the technical terms, or Second Intentions of Judgments; that are used in the construction of Science. Most of these, however, are of infrequent occurrence, except in the mathematical sciences. All propositions are either Theoretical or Practical;- the former are purely speculative, the truths which they enounce being merely objects of contemplation by the mind, as having no reference to action or conduct; the latter have regard to something which is to be done or omitted, to some performance or mode of procedure. Propositions are also said to be demonstrable, if they require or admit of proof; they are indemonstrable, if they are self-evident, or intuitively known.

An indemonstrable judgment, if theoretical, is called an Axiom; if practical, it is styled a Postulate. A demonstrable judgment, or one which is announced as needing proof, if theoretical, is called a Theorem; if practical, it is a Problem. A Thesis coincides very nearly with a Theo

rem; it is a judgment proposed for discussion and proof. A Corollary is a truth announced as an immediate consequence or collateral result of another judgment that has just been proved, and therefore as not needing any separate proof for itself. A Judgment which does not properly belong to the science in which it appears, but is borrowed from some other, is called a Lemma; one which merely illustrates the science, but is not an integral part of it, is a Scholion. An Hypothesis is a judgment not known to be true, but accepted for the time as a provisional explanation. of some phenomena, and as liable to be modified or rejected altogether on the production of further evidence. A Theory, sometimes incorrectly used as a synonyme for Hypothesis, is a comprehensive and methodical arrangement of some large group of phenomena under their supposed Causes and Laws, offered as at least a provisional account of them and mode of reducing them to system. "Theoriarum vires," says Bacon, "arctâ et quasi se mutuo sustinente partium adaptatione, qua quasi in orbem cohærent, firmantur."

CHAPTER XII.

INDUCTION AND ANALOGY.

ANY act of Reasoning strictly so called presupposes the

universality of its Sumption or Major Premise. If I am not absolutely certain that all A are B, then, though the Subsumption that C is A be undoubtedly true, I cannot be sure that C is B.

Now it has been repeatedly proved, that universal Judgments cannot be derived from mere experience, which is competent to pronounce upon some, or many, but never upon all, or none. But as we cannot have any knowledge of real things, or actual existences, except by means of experience, it follows that such things are not objects of Reasoning in the proper sense of the term, — that is, of Demonstrative Reasoning, in which the Conclusion is accepted with absolute certainty. From the enumeration which has just been made, it appears that, with the unimportant exceptions of legal precepts and a few truths known a priori, all Major Premises must be either mere analytic judgments obtained by explicating our own abstract conceptions, or general rules that are true only to the extent of our experience. We may assume such rules to be universally true, and the Reasoning will then become perfect or Demonstrative in Form; but as the Conclusion can never be purged from the shade of uncertainty thrown upon it by the imperfect evidence of the universality of its Major Premise, such Reasoning is rightly considered as merely probable or contingent. We may suppose, also, that

the real existences perfectly correspond to the abstract conceptions that we have formed of them, and, in this way, may seem to obtain absolute Conclusions about matters of fact. This is commonly said to be reasoning from hypotheses; but just so far as such reasoning is Demonstrative, it concerns only the Concept, which cannot be more than an imperfect representation of the reality.

For illustration, I borrow from Mr. Bailey's "Theory of Reasoning," page 2, the following examples of Probable or contingent Reasoning.

1. "I am walking, I will suppose, on the sea-shore, and, perceiving a quantity of sea-weed lying on the beach, while the water is at the moment a quarter of a mile from it, I conclude that the tide has ebbed, and left the weed where I perceive it lying."

2. "I notice the print of a small foot on the sand, and I feel pretty sure that it was made by a child."

Each of these instances may be resolved into the Form of perfect or Demonstrative Reasoning, and it will then be seen that the uncertainty which attaches to the Conclusion arises solely from the doubt, which experience, however often repeated, is incompetent to remove, as to the absolute universality of the Major Premise.

1. All sea-weed found within the space usually covered by the sea at high water must have been left there by the ebbing of the tide;

This bunch of sea-weed was so found; therefore, &c.

2. No small foot-shaped imprint on the sand can have been left by anything else than the foot of a child;

This is a small foot-shaped imprint on the sand; therefore, &c. "In these several cases," says Mr. Bailey, "my mind is determined by the sight of present phenomena, conjoined with knowledge previously acquired, to believe something which I do not actually perceive through the organs of