Syllogism

“ Neither do they reckon better a syllogism that ends in syllogism. For they have a supreme eye to facts, and theirs is a logic that brings salt to soup, hammer to nail, oar to boat, the logic of cooks, carpenters, and chemists, following the sequence of nature, and one on which words make no impression. Their mind is not dazzled by its own means, but locked and bolted to results. They love men, who, like Samuel Johnson, a doctor in the schools, would jump out of his syllogism the instant his major proposition was in danger, to save that, at all hazards. ”

“ Logicians have been remarkably unanimous in their mode of answering this question. It is universally allowed that a syllogism is vicious if there be any thing more in the conclusion than was assumed in the premises. But this is, in fact, to say, that nothing ever was, or can be, proved by syllogism, which was not known, or assumed to be known, before. Is ratiocination, then, not a process of inference? And is the syllogism, to which the word reasoning has so often been represented to be exclusively appropriate, not really entitled to be called reasoning at all? ”

“ For in common logic, almost our whole labour is spent upon the syllogism. Logicians hitherto appear scarcely to have noticed induction, passing it over with some slight comment. But we reject the syllogistic method as being too confused, and allowing nature to escape out of our hands. For though nobody can doubt that those things which agree with the middle term agree with each other, nevertheless, there is this source of error, that a syllogism consists of propositions, propositions of words, and words are but the token and signs of things. ”

“ But is the syllogism, it has been asked, this veritable type of our reasoning? Has the analysis which would explain it to be such, been accurately conducted?
Several of our northern metaphysicians, it is well known—as, for example, Dr Campbell and Dugald Stewart—have laid rude hands upon the syllogism. They have pronounced it to be a vain invention. ”

“ To a legitimate syllogism it is essential that there should be three, and no more than three, propositions, namely, the conclusion, or proposition to be proved, and two other propositions which together prove it, and which are called the premises. It is essential that there should be three, and no more than three, terms, namely, the subject and predicate of the conclusion, and another called the middle term, which must be found in both premises, since it is by means of it that the other two terms are to be connected together. ”

“ It hence appears, that if we throw the whole course of any inductive argument into a series of syllogisms, we shall arrive by more or fewer steps at an ultimate syllogism, which will have for its major premise the principle, or axiom, of the uniformity of the course of nature. ”

“ For when the syllogism is in the first figure, the truth will be in the middle, or in the last, the negative indeed in the middle, but the affirmative in the last. When however the syllogism is in the middle figure, the truth will be in the first in all the problems, but when the syllogism is in the last, the truth will be in the first and in the middle, affirmatives in the first, but negatives in the middle. ”

“ Whether the Principles of Demonstration are finite or infinite Syllogisms being either affirmative or negative, are the attributes of a subject and the subjects of an attribute limited or unlimited in number? Further, can an infinity of middle terms exist between two given extremes? Every syllogism proceeds by means of three terms. The aim of one, the affirmative, class is to shew that C is A, because B is A and C is B; the negative syllogism has as one of its premises the proposition stating that one term is true of another, as its second that one term is not true of another. ”

“ But it is also manifest that we may infer a true conclusion from false premises, as we have observed before, but from opposites we cannot, for a syllogism always arises contrary to the fact, as if a thing is good, (the conclusion will be,) that it is not good, or if it is an animal, that it is not an animal, because the syllogism is from contradiction, and the subject terms are either the same, or the one is a whole, but the other a part. ”

“ Yet if the universal be joined to the less extreme, but particular to the greater, whether negative or affirmative, contingent or pure, there will by no means be a syllogism, nor if particular or indefinite propositions be assumed, whether they take the contingent, or simply the being present with, or vice versâ, will there thus be a syllogism, and the demonstration is the same as before ”

“ Wherefore in all syllogism we must have an universal; universal is also shown from all universal terms, but the particular in this or that way, so that if the conclusion be universal, the terms must of necessity be universal, but if the terms be universal, the conclusion may happen not to be universal. It appears also that in every syllogism either both premises or one of them must be similar to the conclusion, I mean not only in its being affirmative or negative, but in that it is either necessary, or absolute, or contingent ”

“ The Disjunctive Syllogism may be exactly defined as follows—
A complex syllogism, which has for its major premiss a disjunctive proposition, either the antecedent or consequent of which is in the minor premiss simply affirmed or denied.
§ 762. Thus there are four types of disjunctive syllogism possible.
Constructive Moods.
(1) Either A is B or C is D. (2) Either A is B or C is D.
A is not B. C is not D.
.'. C is D. .'. A is B.
Either death is annihilation or we are immortal. ”

“ For the rest, we must also remember that the syllogism consists in the process of thought itself, and the words and propositions through which it is expressed only indicate the traces it has left behind it they are related to it as the sound-figures of sand are related to the notes whose vibrations they express. When we reflect upon something, we collect our data, reduce them to judgments, which are all quickly brought together and compared, and thereby the conclusions which it is possible to draw from them are instantly arrived at by means of the use of all the three syllogistic figures. ”

“ Chapter 4 Let then so far these things be matters of doubt, but as to what a thing is whether is there, or is there not, a syllogism and a demonstration of it, as the present discussion supposed? for a syllogism shows something in respect of somewhat through a medium, but the (definition) what a thing is, is both peculiar and is predicated in respect of what it is. ”

“ 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. ”

“ If we regard syllogism as employing a universal premise, it presupposes the axiom of induction, under which a universal truth is asserted and applied on the round of a particular observation. Taking next deduction to be the combination of several universals in a chain of reasoning, we here assert a relation between two universals on the ground of the relation of each to one or more intermediate universals, i.e. ”

“ They never doubted the certainty of their method. To them words had fixed values, like numbers, and syllogisms were hewn stones that needed only to be set in place, in order to reach any height or support any weight. Every sentence was made to take the form of a syllogism. One must have been educated in a Jesuit or Dominican school in order to frame these syllogisms correctly, but merely by way of illustration one may timidly suggest how the phrases sounded in their simplest form. ”

“ When any process of mediate inference appears to have more than two premisses, it will always be found that there is more than one syllogism. If there are less than three propositions, as in the fallacy of 'begging the question,' in which the conclusion simply reiterates one of the premisses, there is no syllogism at all. ”

“ Now in particular syllogisms we cannot demonstrate universal proposition through others, but we can the particular, and that we cannot demonstrate universal is evident, for the universal is shown by universals, but the conclusion is not universal, and we must demonstrate from the conclusion, and from the other proposition. Besides, there is no syllogism produced at all when the proposition is converted, since both premises become particular. ”

“ Notwithstanding, since we must believe in and know a thing from possessing such a syllogism as we call demonstration, and this is, because these are so, of which syllogism consists—it is necessary not only to have a previous knowledge of the first, or all, or some things, but that they should be more known, for that on account of which any thing exists, always exists itself in a greater degree; for example, that on account of which we love is itself more beloved. ”

“ As it was showed before, that in necessary propositions a categorical and hypothetical proposition are equipollent; so likewise it is manifest that a categorical and hypothetical syllogism are equivalent. For every categorical syllogism, as this,
Every man is a living creature,
Every living creature is a body,
Therefore, Every man is a body, is of equal force with this hypothetical syllogism:
If any thing be a man, the same is also a living creature,
If any thing be a living creature, the same is a body,
Therefore, If any thing be a man, the same is a body. ”

“ Has one not however really used the same term, the notion of formal cause, twice over? for one must effect the proof by means of the middle term which ought itself to be proved. Further, just as in a syllogism there is no assumption as to the nature of inference, for the premises on which the syllogism is based always bear the relation of whole or of part to each other, so the essential form of syllogism ought not to be included in the syllogism, but to remain outside the particular premises. ”

“ To give the name of syllogism to inferences which infringe the general rules against undistributed middle, illicit process, two negative premises, non-sequitur from negative to affirmative, and the introduction of what is not in the premises into the conclusion, and which consequently infringe the special rules against affirmative conclusions in the second figure, and against universal conclusions in the third figure, is to open the door to fallacy, and at best to confuse the syllogism with other kinds of inference, without enabling us to understand any one kind. ”

“ Many philosophers still worship the syllogism, because it seems to them an incomparable exemplar of absolute security firmly fixed in the sphere of immutable necessity far above the flux of phenomena, which it illumines with its steady radiance. ”

“ Some prosperous men are not happy.
§ 567. In the mood we have selected, owing to the peculiar nature of the premisses, both of which admit of simple conversion, it happens that the resulting syllogisms are all valid. But in the great majority of moods no syllogism would be valid at all, and in many moods a syllogism would be valid in one figure and invalid in another. ”

“ The impossibility of reasoning from four terms may be shown by circles.
All men are mortal.
All trees grow.
FIG. 8.
These circles show that no connection can be established between either group. Using four terms in any syllogism is known as the fallacy of four terms.
(2) A syllogism must have three and only three propositions. The proposition containing the major term is called the major premise, while the one containing the minor term is called the minor premise. In a strictly logical syllogism the major premise is written first, the minor premise second and the conclusion third. ”

“ As the syllogism, which is the founding of one judgment upon another by means of a third, never has to do with anything but judgments; and as judgments are only combinations of conceptions, and conceptions again are the exclusive object of our Reason: syllogizing has been rightly called Reason's special function. The whole syllogistic science, in fact, is nothing but the sum-total of the rules for applying the principle of sufficient reason to the mutual relations of judgments ”

“ If a syllogistic question be the same as one of the members of an alternative, and if there be premises in each science from which the syllogism belonging specially to each science may be deduced, there must be some scientific question from which the special syllogism corresponding to each science is derived. ”

“ The tacit assumption, indeed (if there were any such understood assertion) , of the existence of an object with properties corresponding to the definition, would, in the present instance, be false. Out of this definition we may carve the premises of the following syllogism:
A dragon is a thing which breathes flame:
A dragon is a serpent: From which the conclusion is,
Therefore some serpent or serpents breathe flame: an unexceptionable syllogism in the first mode of the third figure, in which both premises are true and yet the conclusion false; which every logician knows to be an absurdity. ”

“ That other modes of speculation also, as regards selection, are useless for the construction of syllogism is apparent; for instance, if the consequents to each are identical, or if those which A (the predicate) follows, and which cannot be with E (the subject) , or again those which cannot concur to be with either, for no syllogism arises through these. ”