operation be accurate, the result of a problem requiring a million of figures is as certain as that of one requiring

but two.

Such are the most distinguishing characteristics of mathematical reasoning. It leaves little room for the exercise of judgment, except in planning the work. It proceeds, mainly, by direct positive intuitions. Admirable as a mental exercise to train the intellect to severe and exact habits, yet, prosecuted exclusively, it may tend to disqualify the mind for those processes of reasoning in which large demands are made upon the judgment, in weighing probabilities and estimating evidences which fall below positive certainty. Exclusive mathematicians would be likely to prove very indifferent moral reasoners.

But it may be well to add, that most pupils are in little danger of injuring their reasoning powers by too much study of mathematics; the danger is, rather, that they will suffer for the want of that severe discipline which these studies afford.

QUESTIONS ON CHAPTER V.

Opening remark? The Kantian philosophers? Remark? Definition of reason? Illustrations? What have modern writers of the empirical school adopted? Stewart's observations? How do we proceed in reasoning? How are propositions divided? Illustrations of simple? Complex ? Modal? Of what are propositions the materials? Hypothetical and declarative propositions? How may propositions be false and the reasoning from them be sound? Must all propositions be formally stated? Remark and illustration? What is said of propositions involving intuitive truths? What is said respecting order of propositions? Object in reasoning? nto how many kinds is reasoning divided? What is said of Leibnitz? On what is mathematical reasoning founded? Explain. Second peculiarity of mathematical reasoning? Explain. Third? Remark? Fourth? Explain. Fifth? Sixth? Remarks. What is said of mathematical reasoning In conclusion?

CHAPTER VI.

MORAL REASONING.

LET us now briefly notice the distinguishing characteristics of moral reasoning.

1. Moral reasoning has, like mathematical, its axioms and definitions, but they cannot ordinarily be so exactly stated. Instead of shutting us up to an absolute necessity, they leave some play for the exercise of our moral nature. Let the reader refer to any of the moral axioms laid down under the head of Intuition, and he will readily see the truth of this remark.

2. Moral reasoning is not concerned with abstractions, but with things in the concrete. Its proof has respect to matters and events as they actually are or have been, instead of those abstract ideas and relations assumed in mathematics. Hence the subjects of moral reasoning are, in their nature, variable and contingent.

3. In moral reasoning, we are compelled to place more or less reliance on testimony and authority. The due consideration of these makes large demands on our judgment and our moral dispositions. For the proof respecting the life and work of Jesus Christ, for example, we must depend on testimony - testimony which a perverse judg ment and an evil disposition may reject.

4. Moral reasoning admits of degrees. Evidence in proof may rise through every stage, from the lowest probability to the highest certainty. Any person may find ample illustration of this in our courts of justice. As this kind of reasoning admits of degrees, it becomes expedient, and often necessary, to examine both sides, in

order to obtain a satisfactory result. This principle is recognized in all courts of justice.

5. Moral reasoning does not proceed in a single chain, but is made up of many arguments combined. These arguments may sustain some mutual relation, or they may be entirely independent of each other. "Each possesses

some weight, and bestows on the conclusion a certain degree of probability; of all which, accumulated, the credibility of the fact is compounded. Thus the proof that the Romans once possessed Great Britain is made up of a variety of independent arguments; as, immemorial tradition; the testimony of historians; the ruins of Roman buildings, camps, and walls; Roman coins, inscriptions, and the like. These are independent arguments, but they all conspire to establish the fact."

6. The difficulties attending a course of moral reasoning are entirely different from those attending a mathematical demonstration. "Those which impede our progress in demonstration arise from the large number of intermediate steps and the difficulty of finding suitable media of proof. In moral reasoning, the processes are usually short, and the chief obstacles by which we are retarded arise from the want of exact definitions to our words, the difficulty of keeping steadily in view the various circumstances on which our judgment should be formed, and from the prejudices arising from early impressions and associations." † Other difficulties still more serious, connected with the investigation of moral and religious subjects, result from aversion to truth which conflicts with perverse inclinations. Mathematical reasoning encounters no difficulties here; moral reasoning often encounters them at every step.

RESULTS OF MORAL REASONING MAY BE CERTAIN.

Logicians have frequently applied the epithet demonstrative to mathematical reasoning; and probable, to moral reasoning. The distinction is not happy. A

and thus, finally, in the light of those great lavs of se quence by which the steady course of nature moves on.

―

Let the child begin with the simplest thing. He sees the green grass shooting up in the spring. What, under God, are the causes? As he observes, he perceives three things the soil, the warmth, the moisture. Remove either of these, and the grass does not grow. Combine these, as in the spring, and the seed or root always shoots upward into the green blade. He observes the same next year, the year following, and thus arrives at the knowledge of a general law a law running through all time. He is now a chronicler of the past; he can tell what has been going on, in this particular, in ages past; he is also a prophet of the future he can tell what will be going on in ages coming. Thousands of years hence, as spring sends its warmth and its showers upon the earth, grass will clothe hills and valleys with its living green. From this simple illustration, the student of nature may easily extend his observations and inductions to things more complicated.

Thirdly, early care should be taken to distinguish real causes, or permanent antecedents, from mere accidental circumstances. This marks the distinction between sound and false induction. Some minds are slow to make the distinction; others make it readily.

The following is a good illustration of false induction: "Let us suppose that a savage, who in a particular instance had found himself relieved of some bodily indisposition by a draught of cold water, is a second time afflicted with a similar disorder, and is desirous to repeat the same remedy. With the limited degree of experi ence which we have here supposed him to possess, it would be impossible for the acutest philosopher, in his situation, to determine whether the cure was owing to the water which was drank, to the cup in which it was contained, to the fountain from which it was taken, to the particular day of the month, or to the particular age of the moon. In order, therefore, to insure the success of the remedy, he will very naturally and very wisely copy, so far as he can recollect, every circumstance which accompanied the first application of it. He will make

use of the same cup, draw the water from the same fountain, hold his body in the same posture, and turn his face in the same direction; and thus all the accidental circumstances in which the first experiment was made will come to be associated equally in his mind with the effect produced.” *

The remedy for such false inductions is to be found in careful and repeated observation; in separating, one after another, those antecedents whose loss does not prevent the effect; and in bringing a general and gradually enlarging experience to bear upon the subject.

QUESTIONS ON CHAPTER IV.

For what are we indebted to the power of induction? What do we mean by law? Illustrate. How far can science go? On what is science founded? Stewart's classification, and remarks upon it? What is said of our faith in the constancy of nature's course? The two opinions of its origin? What seems to be the real truth? How illustrated? How is induction shown to be a distinguishing attribute? Illustration? Some of the various uses of induction? Illustrate its relation to religion. The distinction between wisdom and fanaticism? How shown? Moses? What is said of duty and happiness? Of the relative value of induction as distinguishing the philosopher? Brown's remarks? First direction for improving the inductive faculty? Remarks? Second? Remarks? The training of the child? Third? Remark? Case supposed? The remedy for false inductions?

* Stewart's Philosophy, vol. i. p. 199.