in the premise, being the predicate of an affirmative. From this it is manifest that the minor premise in the first and third figures must be affirmative. KHARSHEDJI MANECJI. 9. Q. Describe the various kinds of conversion. A. When we change the subject for the predicate and the predicate for the subject in a proposition, this process is called conversion. There are four kinds of propositions, viz. universal affirmative (or called A); universal negative (or E); particular affirmative (or I); particular negative (O). (E) a universal negative in which the subject and predicate are both distributed, and (I) a particular affirmative in which the subject and the predicate are both undistributed, can be converted illatively; as for example, " no carnivorous animal is ruminant," is the same thing as to say no ruminant is a carnivorous animal"; and some x is y means some y is x. Illative conversion is that in which no term is distributed in the converse which was undistributed in the exposita, (the original proposition.) The conversion of the universal affirmative, as, every x is y into every y is x, is fallacious, because y, being the predicate of an universal affirmative, is undistributed, according to a rule* in logic. But "every x is y" can be converted into " some y is x," because that is implied in the proposition. Then universal affirmative can be converted by limitation; similarly (E) can be converted by limitation if wished, as "6 no carnivorous animal is ruminant" into " some ruminant animals are not carnivorous;" but this is implying less than we are authorized to do. (O) a particular negative, can be converted by negation or contraposition, that is, by applying the negation to the predicate, as for instance, " some x is not y" can be taken as "some x is not y," where "some x" is the subject, "is" the copula, and "not y" is the predicate. This can be converted illatively into some not y is x, or "something that is not y is x;" or "some men are not negroes" can be converted into "some who are not negroes are men." (A) also can be changed by limitation, as “every x is y” is the same thing as no x is not y." 66 EDALJI NANABHAI. All negative propositions distribute their predicates; and in all affirmative propositions the predicate is undistributed. CLARE (OR FIRST YEAR'S) SCHOLARS. LOGIC. (Paper by the Student who obtained the Prize in the subject.) Q. What is the characteristic of all valid reasoning? A. The characteristic of all valid reasoning is that the argument may be reduced to a syllogism. Q. Define abstraction, and show the relation between it and generalization. A. When we attend to certain properties of an object, disregarding others, we are then said to be abstracting; and when we compare two or more substances, and take into consideration only the points wherein they resemble each other, or the circumstances which are common to them, and designate them by a common name, then we are said to generalize. The relation that exists between the two processes of abstraction and generalization is that though we may abstract without generalizing we can never generalize without abstracting first, or that generalization wholly depends on abs traction. Q. What is meant by the opposition of propositions? A. Propositions are divided, according to their "quantity," into universal and particular; and according to their "quality" into affirmative and negative. Thus we have, considering both quantity and quality, four kinds of propositions, namely,-universal affirmative, universal negative, particular affirmative, and particular negative; any two of these are said to be opposed to one another, thus there are four kinds of opposition. To say this in a few words is to say that propositions differing either in quantity or quality are said to be opposed to each other. Q. State and prove the six rules of syllogism. A. 1st, that there should be three and only three terms in a syllogism; 2nd, that there should be three propositions, viz. the two premises and a conclusion; 3rd, that there should be one and only one middle term with which the major and minor are compared in the premises, that is to say, it should not be double, but must be used in the same sense in the premises, and that it should be distributed in one at least of the premises; 4th, that there should be no term distributed in the conclusion that was undistributed in the premises, or that there should be no illicit process; 5th, that one premise at least must be affirmative; 6th, if one premise be negative, the conclusion must be negative. These six rules are thus proved : 1st. There should be only three terms, two of which are compared with a third, and they are thence compared with each other in the conclusion. If there are four terms, the two shall not be compared with the same, and thence they shall not be compared with each other in the conclusion. 2nd. There should be three propositions,-two premises and a conclusion; for no conclusion can be derived from one premise only. 3rd. That there should be only one middle term; for if it be used in different senses in the two premises, it would be introducing a fourth term; and it should be distributed in one at least of the premises, for if it be undistributed in both, or if the major and minor be compared in the premises with part only of the middle, that part may not happen to be the same, and hence we cannot compare the major and the minor in the conclusion. 4th. There should be no illicit process; for taking a term distributed in the conclusion that was-not distributed in the premises, would be introducing a new term. 5th. That one premise at least must be affirmative, for if both were negative, the middle would not have pronounced to agree with the one and disagree with the other, but to disagree with both, whence nothing can be inferred. 6th. If one premise be negative, the conclusion will be negative; for the middle is pronounced to agree with one term and disagree with the other, whence we can only pronounce the disagreement between the two terms. Q. How many moods are possible? Show that only eleven satisfy the rules of syllogism. A. There are sixty-four moods possible, of which eleven only satisfy the rules of syllogism. The sixty-four possible moods are as * Those moods that are marked are the only moods that satisfy the rules of syllogism; all others violate one or other of the rules given; as for instance, take any as A A E, it is not a mood, for a negative conclusion cannot follow from affirmative premises, and it is the same with others. Q. Given O to be the major, what is the mood and figure? Q. O cannot be a premise in the first figure? A. O cannot be a premise in the first figure, for then the dictum would not be followed, which says that something must be affirmed of a class, or denied of it universally, and something else must be referred to that class, and then the same thing in the conclusion be affirmed or denied, as the case may be, of that thing which is so referred. Q. What are the rules of definition? A. The definition of a thing is the genus to which that thing belongs, plus the differentia. It must give all the connotation; it must have nothing superfluous in it, or nothing wanting. Q. Point out the error, if any, in the following definitions :— 1.—Parallel lines are lines perpendicular to the same line. 2.-Triangles whose angles are equal, and the sides about the equal angles proportional, are similar. A. The first is not a correct definition, for those perpendicular lines may not be in the same plane, and may thus make an angle with each other: therefore there is something wanting, which is "lines in the same plane perpendicular to the same line," which, if added, would make it a correct definition. The second is not a correct definition also: it has another defect in it, it has something superfluous in it, which is "the sides about equal angles proportional," for it has been proved by Euclid that those triangles whose angles are equal have their sides proportional: therefore taking it out, which is a consequence of the other condition, would make the definition correct. NANABHAI HARIDASS. CLARE (OR FIRST YEAR'S) SCHOLARS. (Specimens of Answers by the remainder of the Class.) 1. Q. What is the characteristic of all valid reasoning? A. Valid reasoning is such, that the truth of it is made evident by looking to the mere form of expression, without any regard to the meaning of the terms themselves, and which if stated in the same form of expression, substituting unmeaning symbols, such as X, Y, and Z, instead of the terms which have a meaning, will equally hold good in enabling us to draw the same conclusion. BABA WITHOBA. 2. Q. Define abstraction, and show the relation between it and generalization? A. Abstraction is defined to be taking into consideration all the properties that are common to a number of things, and n glecting those in which they differ; while generalization is the act of giving a common name to those things that have the common properties; therefore, the relation between abstraction and generalization is that the former may be formed without the existence of the latter, but we cannot form generalization without abstraction. JAHANGIRJI RUSTOMJI. 3. Q. What is meant by the opposition of propositions? A. Propositions are said to oppose each other when, having the same subject and predicate, they differ either in quantity or quality. |