sees (2) the faculty of vision—(3) an exercise of this faculty-(4) the thing seen, or the colors-(5) a knowledge that we think and see these colors-and, (6) the cause of our seeing them, which is, the action of rays of light on the retina.

Various errors have arisen from confounding several of those things with each other, which happens the more readily because they are designated by the same term. A common instance is, confounding apprehensions with those qualities of substances which cause them, as when it is said "I feel the heat of the fire." The confusion becomes evident from the difficulty which is generally experienced in distinguishing the perception of color from the objective reality which causes it. We do not readily believe that there can be nothing either in or on the colored substance which in the least resembles its color, any more than there can be anything in a bell resembling its sounds. A similar, but much less common, error is, confounding thought with the thinker. The former is only an act of the latter, and totally different from its essence or substance, of which it cannot possibly form a part.

§ 3. OF PROPOSITIONS.-Definition of Propositions.-Subject and Predicate.-Expression of a Proposition.-Converse, contrary, and contradictory of a Proposition.-Identical Propositions.-Important property of these. Simple, Alternative or Disjunctive, and Complex or Compound Propositions.-Absolute and Conditional or Hypothetical Propositions.-Affirmative and Negative Propositions.-Universal, General, Particular or Indefinite, and Individual or Singular Propositions.-Frequent ambiguities.-Various forms of Propositions.-Caution.-Combinations.

Everything affirmed or denied is expressed by a proposition, which is, an assertion of a truth, assumption, supposition, belief or opinion: and it is either expressed in words or simply declared by the mind. It may refer to the past, the present, or the future, or to any two of them, or to all time.

Every proposition necessarily consists of at least two parts, the one relating to the thing of which something is said, or the subject, and the other, to what is said of it, which is termed the predicate. Thus, in the proposition "just men abhor deception" the first two words are the subject, and the latter, the predicate. These are essential parts of every proposition, since, in every assertion,

there must be something of which we assert, and something which is asserted regarding it. The subject and predicate may each consist of a single term, as "John sleeps," or of a long clause, as "every one who desires the welfare of his country, will cheerfully submit to privations, for the public good, during times of general distress;" or each part may consist of several connected clauses, as "the true patriot, and the wise and upright statesman, will not be turned from the path of duty, either by the threats of the powerful or the clamor of the multitude."(2)

The proper expression of a proposition requires at least two words, one denoting the thing spoken of, and the other, what is said of it. The common idiom of a language may, indeed, require only one word, as in the Latin expression pluit, (which is equivalent to "it rains:") but, in all such cases, some second word is understood. Thus the preceding verb has some nominative_understood, such as Jupiter, or Deus (God). So the English expressions yes and no are only abbreviations for a responsive repetition of the terms of the question.

The converse of a proposition is one in which the subject is asserted of the thing predicated, so that subject and predicate change places. Thus-"those who abhor deception are just men," is the converse of the first example given above. The contrary of a proposition is one which predicates the contrary attribute of the same subject. Thus-"John is weak" is the contrary of "John is strong." By contrary attributes are meant those which are most unlike, of the same class, as good and bad, wise and foolish, hard and soft, high and low, black and white, light and heavy. The contradictory of a proposition is one which denies of the subject the attribute which the former asserted. Thus-"John is not strong" is the contradictory of " John is strong."

An identical proposition is one which predicates the subject of itself, or whose subject and predicate are identical, as a man is a man”- "azote is another name for nitrogen"-"Philip was the father of Alexander" "London is the capital of the British Empire." To this class. of propositions belong all verbal definitions, or those which explain the signification of terms, provided that they are accurate and it is an evident property of the whole class that, if the original proposition is true, so is

the converse.

A simple proposition is one which attributes a single property to a single thing, as "John died." One which attributes one or other of several properties to a subject, is termed alternative or disjunctive, as "John is either in London or in Paris or in New York." A complex or compound proposition attributes various properties to the same or to different things, as “man is mortal, and yet frequently forgets his mortality"-" John died yesterday, and James died to-day." Propositions of this kind consist of several simple propositions united, into which they may be resolved. On the other hand, where the different things contained in a compound proposition form one whole, and the same thing is attributed to every one of them, the compound proposition may be expressed simply. Thus, the compound proposition "John is a descendant of Adam; Mary is a descendant of Adam, etc." is tantamount to "All mankind are descendants of Adam."

An absolute or unconditional proposition affirms the predicate absolutely, without any condition, as "All men are mortal." A conditional or hypothetical proposition predicates only upon some condition or supposition, as "If report be true, all men are mortal”—“ Although he should do that, he would gain nothing by it.”

An affirmative proposition asserts the predicate of the subject, as "John is dead." A negative proposition denies it, as "John is not dead”—“No man is mortal."

A universal proposition predicates of all the individuals of a class or all the parts of a whole, as “All men are mortal”—“No matter is unextended." A general proposition predicates of most of a class or whole, as "Most men are rational"—"Carbonic acid is generally gaseous." A particular or indefinite proposition affirms or denies of a small or indefinite part, as "Some men are wise." A singular or individual proposition predicates of a single individual or part of a whole, as "John thinks” "This piece of wood is brittle."

The classes of propositions defined in the preceding paragraph are frequently expressed in such a manner as to render the extent of the subject ambiguous or doubtful. Thus, in the proposition "Man is mortal," the subject may mean either "every man" or only "Most men." So, "Men say so"-may mean "All" or "Most" or only "Some men." Such ambiguities have been a frequent occasion of error.

Propositions may frequently be varied in the form of expression, so as to bring them under a different class, without in the least changing their signification. Thus, the conditional proposition "If report be true, all men are rational," is equivalent to the absolute proposition "It is reported that all men are rational," or, "The rationality of all men is reported." So the affirmative proposition "All men are mortal" is tantamount to the negative proposition "No man is immortal;" and "John is not dead" is equivalent to "John is alive." As the negative of an attribute is tantamount to the affirmative of its contradictory, every negative proposition may be converted into an equivalent affirmative. Hence it appears that, in examining propositions, we should regard their real signification or import, rather than their form.

The several kinds of propositions may be combined with each other indefinitely. Thus, the proposition "If John did that, he is either a knave or a fool," combines the conditional and alternative forms. So we may combine the conditional with an affirmative or negative, simple or compound, universal or particular, and so forth.

§ 4. OF PROBABILITY.-Definition of Probability.—(1) Probabilities founded on previous experience regarding the concomitance of certain properties.-What these imply.-When they become certainties. Principle of Reasoning.-(2) Probabilities founded on what we know has happened in cases apparently similar.-Principle of Reasoning. Why we often err. Connection between Agencies and their Results. (3) Probabilities based solely on what must happen. Distinction between these and the preceding classes.Source of frequent error, and mode of avoiding it.—(4) Probabilitics founded on the known connection between Causes and Effects. -Use of Experience.-Common error.-(5) Probabilities based on actual investigation of proof.-Distinction between Probability and Certainty. Principles of Reasoning in all cases of Probability.Influence of individual Experience.-Uses of Probability.-Circumstances in which it exists, and to what generally proportional. -Resultant Probabilities.-Means of ascertaining their value.

A probability is, a proposition implying facts which tend to prove, but which do not absolutely prove, that it is a truth. Probabilities are of various kinds, the most common of which are included under one or other of the five following classes.

1. In comparing two things, we frequently observe that they possess many obvious properties in common; and although there is no proof that they possess unob

served properties in common, yet experience informs us that this has been found to hold true, in similar instances; and this we indicate by saying that such is probably the case. Here the probability implies, not only that a proposition may be true, but that it has actually been found true, in similar cases; and the probability is greater or less, according as the cases in which the unobserved attributes were afterwards found to be common, are more or less numerous, or as the resemblance is more or less extensive.

Of this kind is the probability that a certain effect will follow from an agency similar to one whose effects are known, that an effect has been produced by a cause known to have produced similar effects, and that two or more similar phenomena have similar causes, antecedents, concomitants or effects. Other cases are, that the testimony of a person of doubtful veracity or a stranger, regarding some unknown subject, is true, that a man will continue to act as he has hitherto done, in apparently similar circumstances, that a certain phenomenon has been preceded by its usual antecedent, or the reverse, and that a newly discovered species will be found similar, in unobserved attributes, to known species to which it bears a general resemblance.

This class of probabilities is based on the self evident principle that where the determining conditions or agencies are the same, the results will be the same. Whenever we ascertain that the conditions or agencies are actually the same, in two or more cases, the results must be the same, and probability gives place to certainty, as the former exists only where we know but of a partial similarity of the determining conditions.

2. Results are found to vary, in cases apparently similar, while the previous variations are known. Thus, if a person has succeeded in effecting a certain result, by the same apparent means, in seven cases out of ten, we say the probability, or chance of his succeeding, in the next attempt, is seven tenths, and of his failing, three tenths, the cases being all alike, so far as is known. We reason on the self-evident principle that results must follow as they have done, in the same circumstances. But there is frequently no means of ascertaining that the several cases are, in reality, perfectly alike; and hence the future results often turn out differently from what the probabil