_Pure, and Modal._--The proposition, moreover, may be either pure or modal, the former asserting or denying without qualification,--as, Man is liable to err; the latter qualifying the statement,--as, Man is extremely or unquestionably liable to err.
_Proposition the Link, Syllogism the Chain._--All reasoning admits of being reduced to the form of a syllogism. Having discussed the proposition which forms the material or groundwork of every connected chain of argument, we are prepared now to examine the syllogism, or chain itself, into which the several propositions, as so many links, are wrought.
_Syllogism defined._--A syllogism is an argument so expressed that the conclusiveness of it is manifest from the mere form of expression. When, for example, I affirm that all A is B, that all B is C, and that, consequently, all A is C, it is impossible that any one who is able to reason at all, and who comprehends the force of these several propositions taken singly, should fail to perceive that the conclusion follows inevitably from the premises. That which is affirmed, may or may not be _true_, but it is _conclusive_. If the premises are true, so is the conclusion; but whether they are true or not, the argument, as such, is conclusive; nay, even if they are false, the conclusion may possibly be true. For example, Every tyrant is a good man; Washington was a tyrant; therefore, Washington was a good man, Both the premises are false, but the argument, as regards the form, is valid, and the conclusion is not only correctly drawn, but is, moreover, a true proposition. In a word, the syllogism concerns itself not at all with the truth or falsity of the thing stated, but only with the form of stating, and that form must be such, that the premises being conceded, the conclusion shall be obvious and inevitable. All valid reasoning admits of such statement.
_Composition of a Syllogism._--Every syllogism contains three propositions, of which two state the grounds or reasons, and are called the premises, the other states the inference from those positions, and is called the conclusion. These three propositions contain three, and only three, distinct terms, of which one is common to both premises, and is called the _middle_ term; the others are the extremes, one of which is the subject of the conclusion, and is called the _minor_ term; the other the predicate of the conclusion, and is called the _major_ term, from the fact that it denotes the class to which the subject or minor term belongs. In the syllogism,--Every man is mortal; Socrates is a man; therefore, Socrates is mortal,--the three terms are, man, mortal, and Socrates: of these, Socrates, or the subject of the conclusion, is the minor; mortal, or the predicate of the conclusion, is the major; and man, with which both the others are compared, is the middle term.