Part One of the Encyclopedia of Philosophical Sciences: The Logic
The Development of the Syllogism
[a] Qualitative Syllogism – [b] Syllogism of Reflection – [c] Syllogism of Necessity
§ 181
The Syllogism brings the notion and the judgment into one. It is notion, being the simple identity into which the distinctions of form in the judgment have retired. It is judgment, because it is at the same time set in reality, that is, put in the distinction of its terms. The Syllogism is the reasonable, and everything reasonable.
Even the ordinary theories represent the Syllogism to be the form of reasonableness, but only a subjective form; and no interconnection whatever is shown to exist between it and any other reasonable content, such as a reasonable principle, a reasonable action, idea, etc. The name of reason is much and often heard, and appealed to: but no one thinks of explaining its specific character, or saying what it is, least of all that it has any connection with Syllogism. But formal Syllogism really presents what is reasonable in such a reasonless way that it has nothing to do with any reasonable matter. But as the matter in question can only be rational in virtue of the same quality by which thought is reason, it can be made so by the form only: and that form is Syllogism. And what is a Syllogism but an explicit putting, i.e. realising of the notion, at first in form only, as stated above? Accordingly the Syllogism is the essential ground of whatever is true: and at the present stage the definition of the Absolute is that it is the Syllogism, or stating the principle in a proposition: Everything is a Syllogism. Everything is a notion, the existence of which is the differentiation of its members or functions, so that the universal nature of the Notion gives itself external reality by means of particularity, and thereby, and as a negative reflection-into-self, makes itself an individual. Or, conversely: the actual thing is an individual, which by means of particularity rises to universality and makes itself identical with itself. The actual is one: but it is also the divergence from each other of the constituent elements of the notion; and the Syllogism represents the orbit of intermediation of its elements, by which it realises its unity.
The Syllogism, like the notion and the judgment, is usually described as a form merely of our subjective thinking. The Syllogism, it is said, is the process of proving the judgment. And certainly the judgment does in every case refer us to the syllogism. The step from the one to the other however is not brought about by our subjective action, but by the judgment itself which puts itself as Syllogism, and in the conclusion returns to the unity of the notion. The precise point by which we pass to the Syllogism is found in the Apodeictic judgment. In it we have an individual which by means of its qualities connects itself with its universal or notion. Here we see the particular becoming the mediating mean between the individual and the universal. This gives the fundamental form of the Syllogism, the gradual specification of which, formally considered, consists in the fact that universal and individual also occupy this place of mean. This again paves the way for the passage from subjectivity to objectivity.
§ 182
In the ‘immediate’ Syllogism the several aspects of the notion confront one another abstractly, and stand in an external relation only. We have first the two extremes, which are Individuality and Universality; and then the notion, as the mean for locking the two together, is in like manner only abstract Particularity. In this way the extremes are put as independent and without affinity either towards one another or towards their mean. Such a Syllogism contains reason, but in utter notionlessness — the formal Syllogism of Understanding. In it the subject is coupled with an other character; or the universal by this mediation subsumes a subject external to it. In the rational Syllogism, on the contrary, the subject is by means of the mediation coupled with itself. In this manner it first comes to be a subject: or, in the subject we have the first germ of the rational Syllogism.
In the following examination, the Syllogism of Understanding, according to the interpretation usually put upon it, is expressed in its subjective shape; the shape which it has when we are said to make such Syllogisms. And it really is only a subjective syllogising. Such Syllogism however has also an objective meaning; it expresses only the finitude of things, but does so in the specific mode which the form has here reached. In the case of finite things their subjectivity, being only thinghood, is separable from their properties or their particularity, but also separable from their universality: not only when the universality is the bare quality of the thing and its external interconnection with other things, but also when it is its genus and notion.
On the above mentioned theory of syllogism, as the rational form par excellence, reason has been defined as the faculty of syllogising, while understanding is defined as the faculty of forming notions. We might object to the conception on which this depends, and according to which the mind is merely a sum of forces or faculties existing side by side. But apart from that objection, we may observe in regard to the parallelism of understanding with the notion, as well as of reason with syllogism, that the notion is as little a mere category of the understanding as the syllogism is without qualification definable as rational. For, in the first place, what the formal logic usually examines in its theory of syllogism, is really nothing but the mere syllogism of understanding, which has no claim to the honour of being made a form of rationality, still less to be held as the embodiment of all reason. The notion, in the second place, so far from being a form of understanding, owed its degradation to such a place entirely to the influence of that abstract mode of thought. And it is not unusual to draw such a distinction between a notion of understanding and a notion of reason. The distinction however does not mean that notions are of two kinds. It means that our own action often stops short at the mere negative and abstract form of the notion, when we might also have proceeded to apprehend the notion in its true nature, as at once positive and concrete. It is for example the mere understanding which thinks freedom to be the abstract contrary of necessity, whereas the adequate rational notion of freedom requires the element of necessity to be merged in it.
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Similarly the definition of God, given by what is called Deism, is merely the mode in which the understanding thinks God: whereas Christianity, to which he is known as the Trinity, contains the rational notion of God.
§ 183
The first syllogism is a syllogism of definite being — a Qualitative Syllogism, as stated in the last paragraph. Its form (1) is I-P-U: i.e. a subject as Individual is coupled (concluded) with a Universal character by means of a (Particular) quality.
Of course the subject (terminus minor) has other characteristics besides individuality, just as the other extreme (the predicate of the conclusion, or terminus major) has other characteristics than mere universality. But here the interest turns only on the characteristics through which these terms make a syllogism.
The syllogism of existence is a syllogism of understanding merely, at least in so far as it leaves the individual, the particular, and the universal to confront each other quite abstractly. In this syllogism the notion is at the very height of self-estrangement. We have in it an immediately individual thing as subject: next some one particular aspect or property attaching to this subject is selected, and by means of this property the individual turns out to be a universal. Thus we may say, This rose is red: Red is. a colour: Therefore, this rose is a coloured object. It is this aspect of the syllogism which the common logics mainly treat of. There was a time when the syllogism was regarded as an absolute rule for all cognition, and when a scientific statement was not held to be valid until it had been shown to follow from a process of syllogism. At present, on the contrary, the different forms of the syllogism are met nowhere save in the manuals of Logic; and an acquaintance with them is considered a piece of mere pedantry, of no further use either in practical life or in science. It would indeed be both useless and pedantic to parade the whole machinery of the formal syllogism on every occasion. And yet the several forms of syllogism make themselves constantly felt in our cognition. If any one, when awaking on a winter morning, hears the creaking of the carriages on the street, and is thus led to conclude that it has frozen hard in the night, he has gone through a syllogistic operation — an operation which is every day repeated under the greatest variety of conditions. The interest, therefore, ought at least not to be less in becoming expressly conscious of this daily action of our thinking selves, than confessedly belongs to the study of the functions of organic life, such as the processes of digestion, assimilation, respiration, or even the processes and structures of the nature around us. We do not, however, for a moment deny that a study of Logic is no more necessary to teach us how to draw correct conclusions, than a previous study of anatomy and physiology is required in order to digest or breathe.
Aristotle was the first to observe and describe the different forms, or, as they are called, figures of syllogism, in their subjective meaning: and he performed this work so exactly and surely, that no essential addition has ever been required. But while sensible of the value of what he has thus done, we must not forget that the forms of the syllogism of understanding, and of finite thought altogether, are not what Aristotle has made use of in his properly philosophical investigations. (See § 187.) ®
§ 184
This syllogism is completely contingent (i) in the matter of its terms. The Middle Term, being an abstract particularity, is nothing but any quality whatever of the subject: but the subject being immediate and thus empirically concrete, has several others, and could therefore be coupled with exactly as many other universalities as it possesses single qualities. Similarly a single particularity may have various characters in itself, so that the same medius terminus would serve to connect the subject with several different universals.
It is more a caprice of fashion, than a sense of its incorrectness, which has led to the disuse of ceremonious syllogising. This and the following section indicate the uselessness of such syllogising for the ends of truth.
The point of view indicated in the paragraph shows how this style of syllogism can ‘demonstrate’ (as the phrase goes) the most diverse conclusions. All that is requisite is to find a medius terminus from which the transition can be made to the proposition sought. Another medius terminus would enable us to demonstrate something else, and even the contrary of the last. And the more concrete an object is, the more aspects it has, which may become such middle terms. To determine which of these aspects is more essential than another, again, requires a further syllogism of this kind, which fixing on the single quality can with equal ease discover in it some aspect or consideration by which it can make good its claims to be considered necessary and important.
Little as we usually think on the Syllogism of Understanding in the daily business of life, it never ceases to play its part there. In a civil suit, for instance, it is the duty of the advocate to give due force to the legal titles which make in favour of his client. In logical language, such a legal title is nothing but a middle term. Diplomatic transactions afford another illustration of the same, when, for instance, different powers lay claim to one and the same territory. In such a case the laws of inheritance, the geographical position of the country, the descent and the language of its inhabitants, or any other ground, may be emphasised as a medius terminus.
§ 185
(ii) This syllogism, if it is contingent in point of its terms, is no less contingent in virtue of the form of relation which is found in it. In the syllogism, according to its notion, truth lies in connecting two distinct things by a Middle Term in which they are one. But connections of the extremes with the Middle Term (the so-called premises, the major and the minor premise) are in the case of this syllogism much more decidedly immediate connections. In other words, they have not a proper Middle Term.
This contradiction in the syllogism exhibits a new case of the infinite progression. Each of the premises evidently calls for a fresh syllogism to demonstrate it: and as the new syllogism has two immediate premises, like its predecessor, the demand for proof is doubled at every step, and repeated without end.
§ 186
On account of its importance for experience, there has been here noted a defect in the syllogism, to which in this form absolute correctness had been ascribed. This defect however must lose itself in the further specification of the syllogism. For we are now within the sphere of the notion; and here therefore, as well as in the judgment, the opposite character is not merely present potentially, but is explicit. To work out the gradual specification of the syllogism, therefore, there need only be admitted and accepted what is at each step realised by the syllogism itself.
Through the immediate syllogism I-P-U, the Individual is mediated (through a Particular) with the Universal, and in this conclusion put as a universal. It follows that the individual subject, becoming itself a universal, serves to unite the two extremes, and to form their ground of intermediation. This gives the second figure of the syllogism, (2) U-I-P. It expresses the truth of the first; it shows in other words that the intermediation has taken place in the individual, and is thus something contingent.
§ 187
The universal, which in the first conclusion was specified through individuality, passes over into the second figure and there now occupies the place that belonged to the immediate subject. In the second figure it is concluded with the particular. By this conclusion therefore the universal is explicitly put as particular — and is now made to mediate between the two extremes, the places of which are occupied by the two others (the particular and the individual). This is the third figure of the syllogism: (3) P-U-I.
What are called the Figures of the syllogism (being three in number, for the fourth is a superfluous and even absurd addition of the Moderns to the three known to Aristotle) are in the usual mode of treatment put side by side, without the slightest thought of showing their necessity, and still less of pointing out their import and value. No wonder then that the figures have been in later times treated as an empty piece of formalism. They have however a very real significance, derived from the necessity for every function or characteristic element of the Notion to become the whole itself, and to stand as mediating ground.
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But to find out what ‘moods’ of the propositions (such as whether they may be universals, or negatives) are needed to enable us to draw a correct conclusion in the different figures, is a mechanical inquiry, which its purely mechanical nature and its intrinsic meaninglessness have very properly consigned to oblivion. And Aristotle would have been the last person to give any countenance to those who wish to attach importance to such inquiries or to the syllogism of understanding in general. It is true that he described these, as well as numerous other forms of mind and nature, and that he examined and expounded their specialities. But in his metaphysical theories, as well as his theories of nature and mind, he was very far from taking as basis, or criterion, the syllogistic forms of the ‘understanding’. Indeed it might be maintained that not one of these theories would ever have come into existence, or been allowed to exist, if it had been compelled to submit to the laws of understanding. With all the descriptiveness and analytic faculty which Aristotle after his fashion is substantially strong in, his ruling principle is always the speculative notion; and that syllogistic of ‘understanding’ to which he first gave such a definite expression is never allowed to intrude in the higher domain of philosophy.
In their objective sense, the three figures of the syllogism declare that everything rational is manifested as a triple syllogism; that is to say, each one of the members takes in turn the place of the extremes, as well as of the mean which reconciles them. Such, for example, is the case with the three branches of philosophy: the Logical Idea, Nature, and Mind. As we first see them, Nature is the middle term which links the others together. Nature, the totality immediately before us, unfolds itself into the two extremes of the Logical Idea and Mind. But Mind is Mind only when it is mediated through nature. Then, in the second place, Mind, which we know as the principle of individuality, or as the actualising principle, is the mean; and Nature and the Logical Idea are the extremes. It is Mind which cognises the Logical Idea in Nature and which thus raises Nature to its essence. In the third place again the Logical Idea itself becomes the mean: it is the absolute substance both of mind and of nature, the universal and all-pervading principle. These are the members of the Absolute Syllogism.
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§ 188
In the round by which each constituent function assumes successively the place of mean and of the two extremes, their specific difference from each other has been superseded. In this form, where there is no distinction between its constituent elements, the syllogism at first has for its connective link equality, or the external identity of understanding. This is the Quantitative or Mathematical Syllogism: if two things are equal to a third, they are equal to one another.
Everybody knows that this Quantitative syllogism appears as a mathematical axiom, which like other axioms is said to be a principle that does not admit of proof, and which indeed being self-evident does not require such proof. These mathematical axioms however are really nothing but logical propositions, which, so far as they enunciate definite and particular thoughts, are deducible from the universal and self-characterising thought. To deduce them is to give their proof. That is true of the Quantitative syllogism, to which mathematics gives the rank of an axiom. It is really the proximate result of the qualitative or immediate syllogism. Finally, the Quantitative syllogism is the syllogism in utter formlessness. The difference between the terms which is required by the notion is suspended. Extraneous circumstances alone can decide what propositions are to be premises here: and therefore in applying this syllogism we make a presupposition of what has been elsewhere proved and established.
§ 189
Two results follow as to the form. In the first place, each constituent element has taken the place and performed the function of the mean and therefore of the whole, thus implicitly losing its partial and abstract character (§ 182 and § 184); secondly, the mediation has been completed (§ 185), though the completion too is only implicit, that is, only as a circle of mediations which in turn presuppose each other. In the first figure I-P-U the two premises I is P and P is U are yet without a mediation. The former premise is mediated in the third, the latter in the second figure. But each of these two figures, again, for the mediation of its premises presupposes the two others.
In consequence of this, the mediating unity of the notion must be put no longer as an abstract particularity, but as a developed unity of the individual and universal — and in the first place a reflected unity of these elements. That is to say, the individuality gets at the same time the character of universality. A mean of this kind gives the Syllogism of Reflection.
§ 190
If the mean, in the first place, be not only an abstract particular character of the subject, but at the same time all the individual concrete subjects which possess that character, but possess it only along with others, (1) we have the Syllogism of Allness. The major premise, however, which has for its subject the particular character, the terminus medius, as allness, presupposes the very conclusion which ought rather to have presupposed it. It rests therefore (2) on an Induction, in which the mean is given by the complete list of individuals as such, A, B, C, D, etc. On account of the disparity, however, between universality and an immediate and empirical individuality, the list can never be complete. Induction therefore rests upon (3) Analogy. The middle term of Analogy is an individual, which however is understood as equivalent to its essential universality, its genus, or essential character. The first syllogism for its intermediation turns us over to the second, and the second turns us over to the third. But the third no less demands an intrinsically determinate Universality, or an individuality as type of the genus, after the round of the forms of external connection between individuality and universality has been run through in the figures of the Reflective Syllogism.
By the Syllogism of Allness the defect in the first form of the Syllogism of Understanding, noted in § 184, is remedied, but only to give rise to a new defect. This defect is that the major premise itself presupposes what really ought to be the conclusion, and presupposes it as what is thus an ‘immediate’ proposition. All men are mortal, therefore Caius is mortal: All metals conduct electricity, therefore, e.g. copper does so. In order to enunciate these major premises, which when they say ‘all’ mean the ‘immediate’ individuals and are properly intended to be empirical propositions, it is requisite that the propositions about the individual man Caius, or the individual metal copper, should previously have been ascertained to be correct. Everybody feels not merely the pedantry, but the unmeaning formalism of such syllogisms as: All men are mortal, Caius is a man, therefore Caius is mortal.
The syllogism of Allness hands us over to the syllogism of Induction, in which the individuals form the coupling mean. ‘All metals conduct electricity’ is an empirical proposition derived from experiments made with each of the individual metals. We thus get the syllogism of Induction in the following shape:
I
P – I – U
I
Gold is a metal: silver is a metal: so is copper, lead, etc. This is the major premise. Then comes the minor premise: All these bodies conduct electricity; and hence results the conclusion, that all metals conduct electricity. The point which brings about a combination here is individuality in the shape of allness. But this syllogism once more hands us over to another syllogism. Its mean is constituted by the complete list of the individuals. That presupposes that over a certain region observation and experience are completed. But the things in question here are individuals; and as again we are landed in the progression ad infinitum (I, I, I, etc.). In other words, in no Induction can we ever exhaust the individuals. The ‘all metals’, ‘all plants’, of our statements, mean only all the metals, all the plants, which we have hitherto become acquainted with. Every Induction is consequently imperfect. One and the other observation, many it may be, have been made: but all the cases, all the individuals, have not been observed. By this defect of Induction we are led on to Analogy. In the syllogism of Analogy we conclude from the fact that some things of a certain kind possess a certain quality, that the same quality is possessed by other things of the same kind. It would be a syllogism of Analogy, for example, if we said: In all planets hitherto discovered this has been found to be the law of motion, consequently a newly discovered planet will probably move according to the same law. In the experiential sciences Analogy deservedly occupies a high place, and has led to results of the highest importance. Analogy is the instinct or reason, creating an anticipation that this or that characteristic, which experience has discovered, has its root in the inner nature or kind of an object, and arguing on the faith of that anticipation.
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Analogy it should be added may be superficial or it may be thorough. It would certainly be a very bad analogy to argue that since the man Caius is a scholar, and Titus also is a man, Titus will probably be a scholar too: and it would be bad because a man’s learning is not an unconditional consequence of his manhood. Superficial analogies of this kind however are very frequently met with. It is often argued, for example:
The earth is a celestial body, so is the moon, and it is therefore in all probability inhabited as well as the earth. The analogy is not one whit better than that previously mentioned. That the earth is inhabited does not depend on its being a celestial body, but on other conditions, such as the presence of an atmosphere, and of water in connection with the atmosphere, etc.: and these are precisely the conditions which the moon, so far as we know, does not possess. What has in modern times been called the Philosophy of Nature consists principally in a frivolous play with empty and external analogies, which, however, claim to be considered profound results. The natural consequence has been to discredit the philosophical study of nature.
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§ 191
The Syllogism of Necessity, if we look to its purely abstract characteristics or terms, has for its mean the Universal in the same way as the Syllogism of Reflection has the Individual, the latter being in the second, and the former in the third figure (§ 187)The Universal is expressly put as in its very nature intrinsically determinate. In the first place (1) the Particular, meaning by the particular the specific genus or species, is the term for mediating the extremes — as is done in the Categorical syllogism. (2) The same office is performed by the Individual, taking the individual as immediate being, so that it is as much mediating as mediated as happens in the Hypothetical syllogism. (3) We have also the mediating Universal explicitly put as a totality of its particular members, and as a single particular, or exclusive individuality — which happens in the Disjunctive syllogism. It is one and the same universal which is in these terms of the Disjunctive syllogism; they are only different forms for expressing it.
§ 192
The syllogism has been taken conformably to the distinctions which it contains; and the general result of the course of their evolution has been to show that these differences work out their own abolition and destroy the notion’s outwardness to its own self. And, as we see, in the first place, (1) each of the dynamic elements has proved itself the systematic whole of these elements, in short, a whole syllogism — they are consequently implicitly identical. In the second place, (2) the negation of their distinctions and of the mediation of one through another constitutes independency; so that it is one and the same universal which is in these forms, and which is in this way also explicitly put as their identity. In this ideality of its dynamic elements, the syllogistic process may be described as essentially involving the negation of the characters through which its course runs, as being a mediative process through the suspension of mediation — as coupling the subject not with another, but with a suspended other, in one word, with itself.
In the common logic, the doctrine of syllogism is supposed to conclude the first part, or what is called the ‘elementary’ theory. It is followed by the second part, the doctrine of Method, which appears to show how a body of scientific knowledge is created by applying to existing objects the forms of thought discussed in the elementary part. Whence these objects originate, and what the thought of objectivity generally speaking implies, are questions to which the Logic of Understanding vouchsafes no further answer.
It believes thought to be a mere subjective and formal activity, and the objective fact, which confronts thought, to have a separate and permanent being. But this duality is a half-truth: and there is a want of intelligence in the procedure which at once accepts, without inquiring into their origin, the categories of subjectivity and objectivity. Both of them, subjectivity as well as objectivity, are certainly thoughts – even specific thoughts: which must show themselves founded on the universal and self-determining thought. This has here been done – at least for subjectivity. We have recognised it, or the notion subjective (which includes the notion proper, the judgment, and the syllogism) as the dialectical result of the first two main stages of the Logical Idea, Being and Essence.
To say that the notion is subjective and subjective only, is so far quite correct: for the notion certainly is subjectivity itself. Not less subjective than the notion are also the judgment and syllogism: and these forms, together with the so-called Laws of Thought (the Laws of Identity, Difference and Sufficient Ground), make up the contents of what is called the ‘Elements’ in the common logic. But we may go a step further. This subjectivity, with its functions of notion, judgment, and syllogism, is not like a set of empty compartments which has to get filled from without by separately existing objects. It would be truer to say that it is subjectivity itself, which, as dialectical, breaks through its own barriers and opens out into objectivity by means of the syllogism.
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Subjective Notion (Transition to the Object, Next Section)