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 proposition relates to a class of (predacious animals in this case) objects which include the middle term, the necessity of invention is consequently dispensed with. we need only look well to what we have there. simplicity will be promoted by returning to our previous remark, viz.—that reasoning is asserting a proposition, and then showing why it is true—in other words, adducing the fact or facts, on which the assertion rests.
in the logic given in 'chambers' information,' it is said—' in choosing your middle terms, or arguments to prove any question, always take such topics as are purest and least fallible, and which carry the greatest evidence and strength with them,' but it rather appears that we have not to invent a middle term, but only to look to the major premises, and find it included there.
by methodical questioning any argument may be tested. thus, on any assertion being made, ask—why is the assertion true? in this manner, if an argument has truth in it, it may be elicited. in this manner you dig through assertions down to premises, and discover whether any ore of truth lies there.
the value of the argument depends upon the final answer which reveals the premises or data of facts, upon which the conclusion rests. forms of speech, classification of propositions, figures of syllogisms, are of minor importance when you have once elicited the rough truth. the best test of an argument is the soundness of its data, and the simplest formula for drawing out and exhibiting such data, is of the greatest service in enabling us to judge of the validity thereof.
tyranny, says cobbett, has no enemy so formidable as the pen, why? 'because the pen pursues tyranny both in life and beyond the grave.' how is this proved to be the most formidable enemy of tyranny? 'from the fact that tyranny has no enemy so formidable as that which assails not only its existence, but its reputation, which pursues it in life and beyond the grave.' such interrogatories and replies generate the expository syllogism.
1. tyranny has no enemy so formidable as that which assails not only its existence, but its reputation, which pursues it in life and beyond the grave.
2. the pen pursues tyranny in life and beyond the grave.
3. therefore, tyranny has no enemy so formidable as the pen. a syllogism is made up of collective and single facts. it is the process of reasoning, whereby we show that a single truth is proved by a collective one which contains it, or a less quantity is proved by a greater, or that an assertion is proved by an induction from a class of facts. from the class of the enemies of tyranny the pen is selected, and is proved, by passing in inductive review the whole class, to be the most formidable.
the usual manner in which an argument is presented is called the entihymeme. thus:—
he is an industrious man,
therefore
he will acquire wealth.
the first or major proposition is in this form suppressed. the syllogistic form would be this:—
every industrious man acquires wealth,
he is an industrious man,
therefore
he will acquire wealth.
but if we ask for the proof that every industrious man acquires wealth, we find the facts wanting—for the idle are often rich, and the diligent poor. the industrious may acquire wealth, the chances are in their favour.
again.
we must cherish self-respect,
because self-respect is the stay of virtue.
the suppressed proposition is—'we must cherish whatever is the stay of virtue.'
the whole syllogism then stands thus:—
we must cherish whatever is the stay of virtue,
self-respect is the stay of virtue,
therefore
we must cherish self-respect.
dilemma is derived from a greek word, and signifies twice an argument. it is an argument divided into several members, and infers of each part what is to be inferred of the whole. thus: either we shall live or die. if we live, we can only live happily by being virtuous; and if we die, we can only die happy by being virtuous; therefore, we ought always to be virtuous. in the dilemma, question one argument at a time, as in preceding cases.
the sorites uses several middle terms by which the predicate of the last proposition is connected with the first subject. of this argument the well-known speech of themistocles is a specimen. 'my son,' said that eminent person, 'governs his mother, his mother governs me, i govern the athenians, the athenians govern greece, greece governs europe, and europe governs the world; therefore, my son governs the world.' in these instances, question each assertion, as there are as many acts of reasoning as intermediate propositions.
the onus probandi, or burden of proof, is said to rest with him who would dispute any point in favour of a presumptive, or generally allowed truth. but manly logic holds no quibbling about who shall prove. whatever he asserts, the honest reasoner should be prompt to prove.
chalmers, it is said, made morell known—but morell has written a synopsis of metaphysical philosophy that only needed to be known to be appreciated. if chalmers gave morell distinction, morell had previously earned it. from his work i extract the following passage, which passes in review the steps taken, marks the analytic point reached, and outlines the ground before us:—'different as were the minds of those two great men [bacon and descartes] in themselves, different as were their respective labours, and opposite as were, in many respects, the results at which they arrived, yet the writings of both were marked by one and the same great characteristic, namely, by the spirit of method. the most important works of bacon, it will be remembered, were the "instanratio magna," and the "novum organum;" those of descartes were his "dissertatio de methodo," and his "meditationes de prima philosophia," the fruitlessness of the ancient logic, as an instrument of discovery, had been abundantly proved by past experience, and the watchword which these two great thinkers of their age both uttered, and which has been ever since the guiding principle of all philosophy, was—analysis. bacon, who gave his attention chiefly to the direction and improvement of physical science, taught to analyse nature, while descartes, who aimed rather at grounding all human knowledge upon its ultimate principles, instructed how to analyse thought. all modern philosophy, therefore, whether it arise from the baconian or the cartesian point of view, bears upon it the broad outline of the analytic method. it matters not whether it be the outer or the inner world to which its investigations apply, in each case it teaches us to observe and analyse facts to induce instances, and upon such observation and induction to ground our knowledge of laws and principles. in this alone consists the unity of modern science, and from this arises its broad distinction from that of the ancient world. every natural philosopher since bacon has grounded his success upon an induction of the facts of the outward world, and every metaphysician, since descartes, has progressed onwards in his department of knowledge by analysing the facts of our inward consciousness.'*
* morell: modern philosophy, pp. 76-8.