means either that the qualities which belong to all exogens are the same as those which belong to all dicotyledons, or else that every individual falling under one name falls equally under the other. Hence it may be said that there are two distinct fields of logical thought. We may argue either by the qualitative meaning of names or by the quantitative, that is, the extensive meaning. Every argument involving concrete plural terms might be converted into one involving only abstract singular terms, and *vice versâ*. But there are reasons for believing that the intensive or qualitative form of reasoning is the primary and fundamental one. It is sufficient to point out that the extensive meaning of a name is a changeable and fleeting thing, while the intensive meaning may nevertheless remain fixed. Very numerous additions have been lately made to the extensive meanings both of planet and element. Every iron steam-ship which is made or destroyed adds to or subtracts from the extensive meaning of the name steam-ship, without necessarily affecting the intensive meaning. Stage coach means as much as ever in one way, but in extension the class is nearly extinct. Chinese railway, on the other hand, is a term represented only by a single instance; in twenty years it may be the name of a large class. CHAPTER IV. DEDUCTIVE REASONING. The general principle of inference having been explained in the previous chapters, and a suitable system of symbols provided, we have now before us the comparatively easy task of tracing out the most common and important forms of deductive reasoning. The general problem of deduction is as follows:--*From one or more propositions called premises to draw such other propositions as will necessarily be true when the premises are true.* By deduction we investigate and unfold the information contained in the premises; and this we can do by one single rule--*For any term occurring in any proposition substitute the term which is asserted in any premise to be identical with it.* To obtain certain deductions, especially those involving negative conclusions, we shall require to bring into use the second and third Laws of Thought, and the process of reasoning will then be called *Indirect Deduction*. In the present chapter, however, I shall confine my attention to those results which can be obtained by the process of *Direct Deduction*, that is, by applying to the premises themselves the rule of substitution. It will be found that we can combine into one harmonious system, not only the various moods of the ancient syllogism but a great number of equally important forms of reasoning, which had no recognised place in the old logic. We can at the same time dispense entirely with the elaborate apparatus of logical rules and mnemonic lines, which were requisite so long as the vital principle of reasoning was not clearly expressed. *Immediate Inference.*