particular the fallacy of undistributed middle would be committed, because one of the middle terms would be the predicate of one affirmative premise and the subject of another particular premise. If any premise but the last were negative there would be a fallacy of illicit process of the major term. It is not to be supposed that the forms of the syllogism hitherto described are all the kinds of reasoning actually employed in science or common life. In addition to the hypothetical and disjunctive syllogisms and some other forms to be described in succeeding lessons, there are really many modes of reasoning of which logicians have not taken much notice as yet. This was clearly pointed out more than two hundred years ago by the writers of the Port Royal Logic, a work first printed in the year 1662, but which has been since reprinted very often and translated into a great many languages. The book is named from a place near Paris where a small religious community lived, of which the authors of the book, namely Arnauld and Nicole, and a contributor to it the great philosopher and mathematician Pascal, were the most celebrated members. The Port Royal Logic was to a considerable extent the basis of the well-known Watts' Logic, but the reader can now be referred to an admirable translation of the original work made by Professor Spencer Baynes, of St Andrew's. Many improvements of Logic may be found in this work, such as the doctrine of Extension and Intension explained in Lesson v. In the 9th Chapter of the 3rd Part moreover it is wisely pointed out that “little pains are taken in applying the rules of the syllogism to reasonings of which the propositions are complex, though this is often very difficult, and there are many arguments of this nature which appear bad, but which are nevertheless very good; and besides, the use of such reasonings is much more frequent than that of syllogisms which are quite simple." Some examples are given of the complex syllogisms here referred to; thus: The sun is a thing insensible, The Persians worship the sun; Therefore the Persians worship a thing insensible. This is an argument which cannot be proved by the rules of the syllogism, and yet it is not only evidently true, but is an exceedingly common kind of argument. example is as follows: Another The Divine Law commands us to honour kings; Therefore the Divine Law commands us to honour The reader will also find that arguments which are really quite valid and syllogistic are expressed in language so that they appear to have four distinct terms and thus to break one of the rules of the syllogism. Thus if I say "Diamonds are combustible, for they are composed of carbon and carbon is combustible,” there are four terms employed, namely, diamonds, combustible, composed of carbon, and carbon. But it is easy to alter the construction of the propositions so as to get a simple syllogism without really altering the sense, and we then have : What is composed of carbon is combustible; Therefore diamonds are combustible. Examples are given at the end of the book of concise arguments, taken from Bacon's Essays and other writings, which the student can reduce to the syllogistic form by easy alterations; but it should be clearly understood that these changes are of an extra-logical character, and belong more properly to the science of language. I may here explain that the syllogism and the sorites can be expressed either in the order of extension or that of intension. In regard to the number of individual things the noble metals are part of the metals, and the metals are part of the elements; but in regard to intension, that is to say the qualities implied in the names, element is part of metal, and metal is part of noble metal. So again in extension the genus of plants Anemone is part of the order Ranunculaceæ, and this is part of the great class Exogens; but in intension the character of Exogen is part of the character of Ranunculaceæ, and this is part of the character of Anemone. Syllogistic reasoning is equally valid and evident in either case, and we might represent the two modes in ordinary language as follows: Extensive Syllogism. All Ranunculaceæ are Exogens; The Anemone is one of the Ranunculaceæ ; Intensive Syllogism. All the qualities of Ranunculaceæ are qualities of All the qualities of Exogen are qualities of Ranun- Therefore all the qualities of Exogen are qualities of Any sorites can be similarly represented either in extension or intension. Concerning the Aristotelian doctrine of the Enthymeme, see Mansel's Aldrich, App. Note F, and Hamilton's Lectures on Logic, Lecture XX. Port Royal Logic, translated by T. Spencer Baynes, 5th ed. Edinburgh, 1861. LESSON XIX. OF CONDITIONAL ARGUMENTS. It will be remembered that when treating of propositions we divided them into two distinct kinds, Categorical Propositions, and Conditional Propositions. The former kind alone has hitherto been considered, and we must now proceed to describe Conditional propositions and the arguments which may be composed of them. Logicians have commonly described Conditional propositions as composed of two or more Categorical propositions united by a conjunction. This union may happen in two ways, giving rise to two very different species of conditionals, which we shall call Hypothetical Propositions and Disjunctive Propositions. The way in which the several kinds of propositions are related will be seen in the following diagram : Categorical. Propositions are Conditional Hypothetical. A conditional proposition may be further described as one which makes a statement under a certain condition or qualification restricting its application. In the hypothetical form this condition is introduced by the conjunction if, or some other word equivalent to it. Thus "If iron is impure, it is brittle" is a hypothetical proposition consisting of two distinct categorical propositions, the first of which, "Iron is impure," is called the Antecedent; the second, "It is brittle," the Consequent. In this case "impurity" is the condition or qualification which limits the application of the predicate brittle to iron. It was asserted by Horne Tooke in his celebrated work The Diversions of Purley, that all conjunctions are the remains or corrupted forms of verbs. This is certainly true in the case of the hypothetical conjunction; for the word if in old English is written gif, or gyf, and is undoubtedly derived from the verb to give. We may actually substitute at present any verb of similar meaning, as for instance-grant, allow, suppose. Thus we may say “ Grant that iron is impure, and it is brittle.” 66 Supposing that iron is impure, it is brittle." The hypothetical proposition might be employed in arguments of various form, but only two of these are of sufficient importance to receive special names. The hypothetical syllogism consists of two premises, called the major and minor, as in the case of the ordinary syllogism. The major premise is hypothetical in form; the minor premise is categorical, and according as it is affirmative or negative the argument is said to be a Constructive or a Destructive hypothetical syllogism. Thus the form, If A is B, C is D; But A is B; Therefore C is D, is a constructive hypothetical syllogism. It must be carefully observed that the minor premise affirms the antecedent of the major premise, whence the argument is said to be of the modus ponens, or mood which posits or affirms. It is probably one of the most familiar and common kinds of argument. The form, If A is B, C is D; But C is not D; Therefore A is not B, |