Propositions being assertions—as soon as sufficient reasons are adduced to make the proposition credible, it becomes a truth probable or certain, as the case may be. Reasoning is a simple business. To reason is to state facts in support of a proposition. A conclusive fact so advanced is called a reason. All the reasons offered in proof of a proposition are called premises. The Pythagorean, who lays down the proposition that fruits and grain are the proper food of man, and cites facts to prove his assertion—reasons. A proposition and its reasons are called an argument.
Reason is the faculty of perceiving coherences. Effective reasoning is stating them so that others cannot but see them too. 'Reasoning on the abstrusest questions is nothing more than arriving at a remote truth by discovering its coherence with the preceding facts in the same chain.'*
     * Uses and Beauties of Euclid, p. 52.
A syllogism is a peculiar form of expression, in which every argument may be stated. It consists of three propositions.
1. Whoever have their heads cut off ought to be allowed to ask the reason why.
2. Women have their heads cut off.
3. Therefore women ought to be allowed to ask (politically) the reason why.
This is an argument of Mad. de Stael, in allusion to the beheading of women in France, without allowing them any voice in making the laws which determine the offences for which they suffered.
A syllogism is constructed upon the principle (known as the Dictum of Aristotle) that whatever is affirmed or denied universally of a whole class of things, may be affirmed or denied of anything comprehended in that class. Thus the first proposition introduces the class of persons who have their heads cut off. Of this class it is affirmed that they ought to be allowed to ask the reason why. But women are included in the class of persons who have their heads cut off, and consequently that may be affirmed of them which is affirmed of the whole class—that they should be allowed to ask the reason why.
'To prove an affirmative,' says Mr. Mill, 'the argument must admit of being stated in this form:—
All animals are mortal;
  All men        |
  Some men       }    are animals;
  Socrates       |
 
  therefore
 
  All men        |
  Some men       }    are mortal.
  Socrates       |
'To prove a negative, the argument must be capable of being expressed in this form:—
'No one who is capable of self-control is necessarily vicious;
  All negroes        |
  Some negroes       }   are capable of self-control;
  Mr. A.'s negro     |
 
  therefore
 
  No negroes are           |
  Some negroes are not     }   necessarily vicious.
  Mr. A.'s negro is not    |
'Although all ratiocination admits of being thrown into one or the other of these forms, and sometimes gains considerably by the transformation, both in clearness and in the obviousness of its consequence; there are, no doubt, cases in which the argument falls more naturally into one of the other three figures, and in which its conclusiveness is more apparent at the first glance in those figures, than when reduced into the first. Thus, if the proposition were that pagans may be virtuous, and the evidence to prove it were the example of Aristides; a syllogism in the third figure,
  Aristides was virtuous,
  Aristides was a pagan,
therefore
  Some pagan was virtuous,
Would be a more natural mode of stating the argument, and would carry conviction more instantly home, than the same ratiocination strained into the first figure, thus—
 Aristides was virtuous,
 Some pagan was Aristides,
therefore
  Some pagan was virtuous.'
The best thing that can be said in favour of the syllogism, as an instrument of reasoning, is that it is a regular form to which every valid argument can be reduced; and may be accompanied by a rule, showing the validity of every argument in that form, and consequently the unsoundness of any apparent argument which cannot be reduced to it. This would be high praise if every 'valid argument' was a trusty one. But unfortunately 'the question respecting the validity of an argument is not whether the conclusion be true, but whether it follows from the premises adduced.'* Even this small advantage is purchased at a greater expense of tedium and trouble than the bulk of mankind are willing to pay, or able to pay if they were willing.
     * Logic, vol. 1, pp. 232-3.
There is some reason to believe that the syllogistic form, as a test of valid arguments, may be entirely dispensed with, if we can secure accuracy of data, and intelligibility in terms.
It is not contended now that we discover new truths by the syllogism. The syllogism is allowed to be only a form of stating a truth. Example:—
  No predacious animals are ruminant,
  The lion is predacious,
therefore
  The lion is not ruminant.
 
     * Whately's Logic, Anal. Out. chap. 1, sec. 3.
Of course, if we know that no animal that lives by prey chews the cud, and know, also, that the lion lives by prey, we know that the lion does not chew the cud. This conclusion, as Lord Kames contends, and Dr. Whately admits, is not a truth inferred from the fundamental premises, but included in it. Smart, whom Mr. J. S. Mill calls acute and often profound, remarks—'Every one, as to the mere act of reasoning, reasons rightly: we may reason from wrong premises, or mistake right ones; we may be unable to infer from proper ones; but from such premises as we do reason from, we reason correctly: for all premises contain their conclusion; and in knowing the premises, we therefore know the conclusion. The art wanted is one that will enable us to use language perspicuously in expressing our premises:' and he might have added—direct us in selecting proper materials of which to make premises.
The strength and weakness of the syllogism as an instrument of reasoning will now be understood. Whately remarks, that 'since all reasoning may be resolved into syllogisms, and since in a syllogism the premises do virtually assert the conclusion, it follows at once that no new truth can be elicited by any process of reasoning.'* We therefore no longer look to the syllogism to discover truth, its value is in stating it. In this sense it is worthy of all attention. It is the form of nature.
     * Logic, p. 223.
Of such a syllogism as the one quoted—
  No predacious animals are ruminant,
  The lion is predacious,
therefore
  The lion is not ruminant.
It has been insisted by some logicians that the genius required for its construction was invention. Having made a general proposition like the first, we then have to invent or find out a middle term as the second—but if we bear in mind that the general affirmation of the first propositi............