Hegel’s Logic: An Essay in Interpretation. John Grier Hibben 1902
The subjective notion, as we have seen, is the notion regarded merely in one of its aspects, as constituting the sum of the thought processes.
These processes taken together form a system in which all of the thought relations are determined by the fundamental nature of thought itself.
These relations divide naturally into three typical thought forms, and in this division Hegel follows the traditional logic. These forms are as follows –
(1) The Notion regarded simply as a formal Notion. (Der Begriff als solcher.)
(2) The Judgment. (Das Urteil.)
(3) The Syllogism. (Der Schluss.)
The primary type of thought which Hegel calls the notion, regarded simply as notion, corresponds in some of its main features to the ordinary concept of formal logic. It is treated in the Hegelian system without reference to its natural setting as one of the component parts of the judgment and syllogism. This view of the notion is of course only a provisional one which represents merely an abstract analysis of the thought processes, preliminary to a subsequent synthesis, which will represent their component parts as properly coordinated and unified.
The notion thus conceived as a separate thought element, is found to contain three essential factors, or as the Hegelian terminology goes, moments, – that of universality, of particularity, and of individuality (das Allgemeine, das Besondere, das Einzelne).
It should be noticed that Hegel does not divide notions into three kinds, the universal, the particular, and the individual, but he regards the one and the same notion as embracing in a unity these three coordinated aspects. Hegel at the outset in the discussion of the notion evidently wishes to emphasize the truth that while the categories of reflection, such as appearance and ground, cause and effect, and the like, may be separately apprehended each apart from its correlative, this however is not the case concerning the categories of the notion. These categories must be conceived as inseparable moments of the one notion, and if they do not all appear in a complete synthesis of thought, the very integrity of the simple notion itself is essentially impaired. A notion regarded as representing a universal merely, that is a class or group idea, must rank in our thoughts as an absolutely empty genus unless it contains some suggestion at least of the capacity to realize itself in different kinds of species which would then represent its particularity. And a particular notion, representing a species, not only implies a higher genus which is its necessary universal, but it in turn must suggest also the capacity of realizing itself in definite individuals. The relations of genus, species, and the individual, represent most clearly and adequately the three Hegelian moments of the simple notion, – universality, particularity, and individuality. Any one of them necessarily implies the other two.
Hegel’s criticism of the traditional logic is that its general term or class idea is a notion in only one of its aspects, that of its universality, and that the other two moments of particularity and of individuality are overlooked. Thus it follows that the purely formal logician, the literalist, often ignores particular instances which are not in accord with his general notions, or else wrests his individual facts so that they may conform to his preconceived theories. It is the moment of individuality in the notion which constitutes its actuality, which differentiates it from the mere fancy of the imagination. The individual object is always the most convincing proof as well as the clearest illustration of the universal.
Nothing will so quickly reveal the emptiness of thought as a succession of glittering generalities which admit of no particular application or definite verification. And on the other hand, also, it must not be overlooked that if the significance of the individual is to be adequately interpreted, it must be possible to refer it unerringly to some universal. The work of the scholar or of the man of science is not complete when he has collected facts, however numerous they may be; he must relate fact to law and rise above the particular results of his investigation to the appreciation of the universal which they embody. This relation of the individual object to the universal, Hegel illustrates by showing that it was only when the world came to recognize every man, whether Greek or barbarian, bond or free, as possessing an infinite and universal nature, that man’s real significance for himself and for society was fully understood and properly valued. The recognition of a man as a person and not a thing is simply the recognition that the principle of personality is in reality a principle of universality. The universal is not to be conceived, therefore, as merely the sum total of the various elements which a number of individuals have in common; it is rather that active principle which specifies and determines the individuals, building them together in a unity with itself. As Hegel says, “Things are what they are through the action of the notion immanent in them and revealing itself in them."[24] Thus every individual in the midst of all his particular traits of character and conduct reveals the universal strain of humanity.
Corresponding respectively to the three moments of universality, particularity, and individuality are the three categories which were found to constitute the fundamental elements of the idea of essence, – namely, that of identity, of difference, and of ground. Thus the universal is, in its nature essentially self-identical, – that is, perfectly homogeneous throughout and without distinction as to the particular varieties which embody and illustrate it. It is, however, under an irresistible compulsion of thought (gesetzt) to break up into particular varieties or species, and this it does through the process of differentiation according to the category of difference.
But in these particular manifestations it is the underlying universal which is always present. Moreover, the universal can manifest itself as an identity in the midst of all differences only in that which can form the common ground of such a union, – namely, in a series of different individuals.
When the universal subjects itself to the natural compulsion of thought, and becomes more specific by manifesting the various aspects of its particularity, then we have the notion developed in the form of a judgment. To judge is to make definite and specific the complete nature of the notion.
This specification of the notion which is the essential function of the judgment, is a process of breaking up the homogeneity of the notion in its purely universal features, and showing that it admits of a varied manifestation in respect to a number of particular instances of the universal, each ranking as a distinct species within the all-embracing genus.
To specify these particular instances in detail, and give at the same time their differentiating characteristics, would necessitate a series of judgments whose sum, when complete, would exhaust the full significance of the universal notion as such. The German word for the judgment is das Urteil, – that is, the primary division, – and thus signifies most strikingly the original breaking up of the notion into the particular forms of its manifestation, which, as we have seen, constitutes the essential function of the judgment.
The judgment when expressed in words naturally shapes itself in the following form, “The individual is the universal.” This asserts an underlying identity between the universal, as such, and its particular manifestation in some concrete individual instance.
Hegel’s conception of the essential function of the copula will be found to be in complete accord with the view of the modern logic. The copula does not signify that the subject and predicate of a proposition have been brought together merely by a juxtaposition of thought, and thus connected by a convenient thought form. Its function is rather to emphasize the fact that the two seemingly separate elements, appearing as subject and predicate terms, respectively, are in reality identical, and that their fusion into one is indicated by their union in one and the same judgment through the connecting copula. The subject and predicate terms must not be regarded as two independent extremes. Nor is the predicate to be conceived as a general characteristic, lying outside the subject, and having a separate existence somewhere in our heads. It is an essential phase of the subject itself.
It must be remembered in this connection that the judgment is merely an expanded form of the notion. There is an obvious unity attaching to the essential nature of the notion. This unity is not lost, therefore, when the notion puts itself in the more explicit form of the judgment. The seemingly separate terms which the copula connects have no really separate subsistence apart from their underlying connection. When we say “This rose is red,” we mean that the particular rose now in the field of perception partakes of the nature, and is a specific instance, of the universal red; and on the other hand, that the universal red, in connection with this particular rose, manifests itself in the specific shade of red which characterizes this special rose in question.
In general, it may be said, that in every judgment the subject and predicate so blend together that the particularity of the subject partakes of the nature of the universality expressed in the predicate, and that on the other hand the universality of the predicate in turn partakes of the nature of the particularity expressed in the subject. The identity of the subject and predicate, thus bound together in one, constitutes what Hegel calls the specific content of the judgment (der bestimmte Inkalt des Urteils). It is that which constitutes the judgment’s essential significance.
The relation, moreover, in which the subject and predicate become one is not due to our thinking, which, as it were, imposes this connection externally upon things. The relation, on the contrary, exists in the very nature of the things themselves, and our thought about them is only our discovery of a relation already existing. If the notion is to be regarded, as Hegel insists, as the constructive force immanent in all things, then the judgment is merely the definite manifestation of the indwelling potentiality of the notion in an explicit manner and in certain specific instances.
It is an actual manifestation, moreover, and one which is subjectively revealed to be that which it is in its objective reality.
In this connection Hegel distinguishes between a judgment and a proposition (der Satz). The proposition contains an assertion in reference to a given subject, which does not stand in any relation of universality to its predicate, but expresses some single state or action which is the result of a contingent relation of subject and predicate, as the so-called narrative judgments, such as “Caesar crossed the Rubicon,” or “It rained last evening.” In the judgment proper, the connection between subject and predicate is freed from any disturbing element of contingency.
This distinction does not obtain, however, in the formal logic, as the proposition is a term there employed to indicate merely the judgment as expressed in language in the form of a sentence.
Hegel divides the judgment into three types, which correspond to the three main divisions of the Logic –
(1) The Judgment of Being.
(2) The Judgment of Essence.
(3) The Judgment of Notion.
These types of judgment form a series of progressive development.
The distinctions between them are due in each case to the logical significance of the predicate. There is, for instance, a manifest difference in logical value between the two judgments – The rose is red.
The statue is beautiful.
The former is the result of a simple perception, while the latter is the result of a more complicated thought process which is based upon comparison between the object of perception and the kind of being which we conceive it ought to realize, – that is, its ideal or its essential notion.
Corresponding to the category of being, we have the qualitative judgment (das qualitative Urteil).
Corresponding to the category of essence, we have two judgments, – that of reflection, and that of necessity (das ReflexionsUrteil, das Urtieil der Notkwendigkeit).
Corresponding to the category of the notion, we have the notional judgment (das Urteil des Begriffs).
The qualitative judgment, or the judgment of being, Hegel defines as one which ascribes to the particular subject a quality which is universal, and yet which does not characterize all the individuals of the same class to which the subject belongs. For instance, when we say, “The rose is red,” the universal quality of redness is ascribed correctly to the rose in question, but it is not possible to extend that ascription to all roses generally. Therefore, in asserting “The rose is red,” we imply that some roses exist which are not red. Consequently, for every affirmative judgment of this kind there must be a possible negative judgment which parallels it. The predicate, in other words, belongs to the special subject under consideration, but not to the underlying universal notion of which the subject is a particular manifestation.
It is proper, therefore, to characterize a qualitative judgment as correct or incorrect, but never as true or untrue. For to affirm that a judgment is true means that the predicate is an essential element of the underlying notion to which the subject must be referred. Hegel says, “In the judgment of the notion the predicate is, as it were, the soul of the subject by which the subject as a body is characterized through and through."[25] If, instead of starting with an affirmative judgment and deducing by necessary implication a corresponding negative judgment, we should start with the negative judgment, such as “This rose is not red,” we are as necessarily constrained to deduce the implied affirmative; for the negative statement that the rose is not red implies some other color.
Inasmuch as the subject in such cases is not a universal, the negative either expresses an empty identity, that the rose which you see has the color which you see, or else it is to be regarded as a so-called infinite judgment in which an absolute incompatibility is set forth such as might be expressed in the judgment “A circle is not a tree.” In the formal logic, such a judgment is regarded as representing the reductio ad absurdum of irrelevant negation. But Hegel insists that a judgment of such a nature may possess some significance as the description of certain concrete relations whose nature can only be thus characterized. For instance, death is the infinite negative as regards life, since death signifies a total negation of life. Disease, on the other hand, represents merely a simple negation, inasmuch as certain functions may be only temporarily impaired, that is, contingently negatived; and this negation is at once overcome when with returning health the normal functioning is resumed, but not so with the negation which is expressed by death.
When we come to the judgment of reflection, we find that Hegel defines this type of judgment substantially as one in which the subject no longer appears as a special case or particular instance, but is represented as related to something else which is implied in the predicate.
The relation which is thus stated is true not only for the particular subject in question but for all others of the same class universally. The following is a judgment of this type – “This plant is edible.” This signifies a universal connection between all plants of the same kind represented by the subject and a certain effect which it is possible for them to produce upon a definite part of the great world system to which they belong, – namely, the gustatory and digestive processes of man. it is called a judgment of reflection, because it is only in the light of something else brought into relation to it that the adjective edible can be applied to a plant. Its edibility is a characteristic which arises simply from its being brought into relation with man.
This type of judgment in general breaks up into three varieties –
(1) The Singular Judgment.
(2) The Particular Judgment.
(3) The Universal Judgment.
If we have a singular judgment such as the following, “This plant is wholesome,” there is implied in this that there are some other plants also which are wholesome. This latter form would then be a particular judgment.
In some cases, moreover, the nature of the particular judgment is such that it may be found possible upon further investigation to enlarge it to such an extent that it will embrace the universal as well. The progress of knowledge is from the singular to the particular, and then from the particular to the universal. For instance, we start with the judgment, “This metal conducts electricity.” Then we advance to the larger statement in the form of a particular judgment “Some other metals conduct electricity.” Finally we reach the universal, “All metals conduct electricity.” These judgments represent widening circles of knowledge. Thus the individual merges its seemingly individual characteristics with those which are common to the other members of the same species, to every one of which the same predicate may be applied as was primarily applied to the individual in the form of a singular judgment. There are predicates, moreover, of such a nature that, when ascribed to an individual subject, imply not merely an advance to a particular, but to an all-embracing, universal judgment. In such cases there are no negative instances, and therefore the individual is to be regarded as a type of the whole class. As Hegel puts it, “The individual man is what he is in particular only in so far as he is before all things a man as man and in general."[26]Any property which belongs to the individual, and at the same time to every other member of the same species, ranks as a necessary attribute. It is universal for the very reason that it is necessary. The judgment of reflection which expresses a universal relation between an attribute and the subject as a whole, must be consequently a judgment of necessity as well. And thus the transition from the judgment of reflection to the judgment of necessity is a natural one.
Hegel discusses the judgment of necessity under its three aspects, as, –
(1) Categorical. (Das kategorisehe Urteil.)
(2) Hypothetical. (Das hypothetische Urteil.)
(3) Disjunctive. (Das disjunctive Urteil.)
In the categorical judgment, the predicate expresses the essential nature of the subject. It represents the essence of the subject, moreover, in respect to the most elemental of the categories of essence, that of substantiality. Thus, in the judgment of simple assertion, which is the characteristic feature of the categorical judgment, such as “Iron is a metal,” the idea of metallity is regarded as the underlying substance which constitutes the essential nature of iron. The categorical judgment, however, lacks completeness, inasmuch as it does not embrace in its statement the elements of particularity, – that is, of definite and specific description.
When we introduce the specifying element which renders a general statement more particular and therefore more definite, we have always the hypothetical form of judgment, – if A is B, C is D, – that is, where the subject only under specified conditions leads to its necessary consequent.
This specified condition gives to the subject a particular aspect.
In the hypothetical judgment the relation which is set forth is that of cause and effect, the second of the categories of essence.
When, however, the subject, regarded as a genus, is completely specified through an exhaustive division into its component species, we have the disjunctive judgment. It is of the form, “A is either B, or C, or D.” In such a judgment the predicate is coextensive with the subject, the genus always being equal to the sum total of its several species. Therefore the genus is expressed in its totality, and the totality of any genus is its notion. This marks the point of transition to the judgment of the notion.
In this latter class of judgments the subject is regarded as conforming more or less adequately to its ideal, – that is, to its notion. The predicates which are available in this form of judgment are such as the adjectives good, true, beautiful, wise, perfect, and the like. Each one implies a norm which the subject in question is judged as completely illustrating; and in the negative judgments, of course, as failing to illustrate.
The judgment of the notion divides into three classes –
(1) The Assertory Judgment. (Das assertorische Urteil.)
(2) The Problematic Judgment. (Das problematiseke Urthel.)
(3) The Apodictic Judgment. (Das apodiktiache Urteil.)
The assertory judgment is one which contains the bare statement that a given subject is in full accord with its ideal. Such a judgment, however, may be challenged by one who holds an opposite opinion.
This gives rise to the second form, the problematic judgment.
The problematic judgment is one which is qualified by the modal copula, may be, implying obviously the possibility also that it may not be. However, if the relation between the subject and predicate is reinforced by a subsidiary statement, either expressed or implied, which indicates the ground of their connection, we have the third form, the apodictic judgment.
The apodictic judgment is one which asserts that the relation between subject and predicate is such that it must be true. It is no longer a matter of opinion, but of necessity. When the reason which reinforces the cogency of a judgment is fully elaborated, we pass by a natural transition to the syllogism. For example, the judgment that a certain law will prove harmful to the best interests of the community, can be shown to be an apodictic judgment, – that is, necessarily true, if we show that it is essentially unjust, – and our judgment would then be put in the following form: – “This law, being obviously unjust, must necessarily prove harmful to the best interests of the community.” Expanded into the form of a syllogism, it would run as follows – All unjust laws are harmful.
This law is unjust.
It must prove harmful.
Whenever a judgment under challenge reveals its underlying ground as its justification, we have a syllogism. The statement that anything must be true is justifiable only when it can be shown that there is a sufficient reason to warrant it. The syllogism, therefore, is merely the expanded form of the apodictic judgment.
A syllogism is a judgment which is accompanied by its own proof.
In the apodictic judgment, we have an individual subject whose particular characteristics warrant our reference of it to its universal. In its elaborated form, as expressed by the three terms which make up the syllogistic structure, the individual and universal are brought together by means of a common term, the traditional middle term of the formal logic, in such a way as to form together a logical unity. In the major and minor premises we have separate judgments, their point of articulation being the middle term; this separation of the major and minor terms in the premises is completely overcome in the conclusion, and we have a return to the unitary notion which holds the major and minor terms together in one judgment. Thus Hegel defines the syllogism as the unity of the judgment and the notion,[27] – that is, the separate judgments of the premises coalesce in the one notion which underlies the conclusion. The statements contained in the two premises are the result of the analytic function of thought. The fusion of the major and minor terms in the conclusion is, however, the result of the synthetic function.
The syllogism should not be regarded as an arbitrary or artificial grouping of judgments together in thought. We do not, properly speaking, construct syllogisms. The syllogistic process is rather the universal mode in which the phenomena of the universe manifest themselves. It is, moreover, a true description of the endless activity by which the Absolute ever manifests Himself. Hegel means by this that all being and all activity of the universe are to be regarded as the manifestation of a universal by means of certain particular and specific characteristics which it reveals in the sphere of some definite concrete individuality. The syllogism is merely an expression in general of the process which provides for the varied interplay of the universal, the particular, and the individual in their manifold relations. Every notion as a universal manifests itself in individual instances through particular characteristics which differ with the various species which it embraces. And on the other hand every individual reveals its full significance only when it may be referred to its corresponding universal by virtue of its particular characteristics.
It seems to be of the very nature of thought to bind together in one the three ideas of universality, particularity, and individuality, which is nothing more or less than the syllogistic process. Therefore, reason by its very nature tends to express itself in the form of a syllogism; and as it is of the essence of reason, according to Hegel, to manifest itself dynamically as the essential constructive force of the universe, it follows that the syllogistic principle underlies the active processes of all nature and of all mind.
Hegel discusses the syllogism under its three aspects as follows: –
(1) The Qualitative Syllogism. (Der qualitative Schluss.)
(2) The Syllogism of Reflection. (Der Reflexions-Schluss.)
(3) The Syllogism of Necessity. (Der Schluss der Notwendigkeit.)
In the qualitative syllogism the subject of the conclusion as an individual is referred to its predicate, a universal because of a certain quality which it possesses.
The qualitative characteristics are expressed by the middle term, which is of the nature of a particular.
Thus in the form of the syllogism the subject of the conclusion, which is always the minor term, is the individual.
The predicate of the conclusion, which is always the major term, is the universal.
The middle term, which does not appear in the conclusion but in each of the premises, is the particular. All this Hegel expresses in the formula I-P-U, which means that P, the particular, is the middle term between I, the individual as minor term, and U, the universal as major term. In similar formulae the same order is preserved to designate all possible varieties of syllogistic structure, – namely, the first letter always represents the minor term; the last, the major term; and the middle letter, naturally, the middle term[8] Expanded into the form of a syllogism, the formula I-P-U would become : –
An individual has certain particular characteristics.
All such particular characteristics belong to a certain universal.
The individual belongs to this universal.
It will be noticed in the above that the first premise stated is the minor, and the second the major. Reversing this order, and abbreviating, the syllogism runs as follows: –
All P is U.
I is P
I is U
This will be recognized as a syllogism of the first figure, in which the middle term appears as subject of the major premise, and as predicate of the minor. Now, in this syllogism, each premise in turn must be regarded in the light of a conclusion which has been previously mediated by some other middle term. In other words, if the ground of each premise is fully expressed, it necessarily reveals a syllogistic structure.
If, therefore, we should assume that the major premise, “All P is U,” is the conclusion of a subsidiary syllogism, the middle term in that case must be of the nature of an individual. Putting it, therefore, as the middle term between the particular as minor and the universal as major, the formula for this new syllogism would be, P-I-U.
If this formula should be elaborated so as to express fully the syllogistic structure, it would be as follows: –
Certain individuals have particular marks.
These individuals all belong to a certain universal.
These particular marks characterize this universal.
This syllogism is in the third figure, – that is, the middle term appears as subject in each of the premises. It will be observed that such a conclusion is valid only when the individuals examined are so numerous and of such a kind as to preclude the possibility of the discovery of any negative instances; otherwise the third figure can prove only a particular statement.
If in a similar way, we assume the minor premise of the original syllogism, “This I is P,” to be the conclusion of a subsidiary syllogism, then the remaining term which does not appear in this conclusion, – in this case the universal, – would be the middle term, and the syllogistic formula would be I-U-P. In its expanded form it gives the following syllogism –
The individual is the universal.
The particular is the universal.
The individual is the particular.
This is in the second figure, – that is, the middle term appears as predicate in each of the premises. The conclusion is not valid unless we regard the major premise as having the force of a judgment in the following form, “Only the particulars in question are the universal.” Otherwise, the second figure can prove only a negative conclusion. To secure from it an affirmative conclusion, the major premise must always be qualified in some such manner as is indicated above.
These transitions, which Hegel thus effects from figure to figure may be seen more clearly perhaps in the following concrete illustrations.
The syllogism in the first figure, corresponding to the formula IP- U, may be expressed as follows: –
This whale is a mammal.
All mammals are vertebrates.
This whale is a vertebrate.
In this syllogism I = whale (individual). P = mammal (particular species). U = vertebrate (universal genus).
The syllogism in the third figure proves as its conclusion the major premise of the above, “All mammals are vertebrates.” Its formula is PI- U.
It may be illustrated by the following: –
Certain individuals (I) are mammals (P).
The same individuals (I) are vertebrates (U).
All mammals (P) are vertebrates (U).
This conclusion follows only upon the supposition that the individuals examined warrant an inductive generalization upon the ground that the possibility of negative instances has been completely eliminated.
Again, the syllogism in the second figure, proving as its conclusion the minor premise of the original syllogism, “This whale is a mammal” may be illustrated according to the formula I-U-P as follows: –
Only mammals (P) suckle their young (U).
The whale (I) suckles its young (U).
The whale (I) is a mammal (P).
In these syllogisms the judgments all express an identity in spite of differences, as when we say “The individual is the universal.” Now, if in such judgments the element of difference is wholly eliminated, then the subject and predicate in every ease may be simply equated, and all the terms in the syllogism will become strictly identical, giving us the quantitative or mathematical syllogism which would appear in the following form: –
I = P.
P = U.
I =U.
The truth which is contained in such a syllogism may be expressed by the axiom, “Things which are equal to the same third thing are equal to each other.” This may be regarded as the limiting case of the syllogism proper.
In the qualitative syllogism the individual is represented under the aspect of some one of its attributes, and, therefore, an indefinite number of syllogisms may be formed in reference to any individual object of investigation or of interest, according as we choose to vary the several attributes which may for the time being happen to attract our attention.
Thus we say that a certain rose is red, or fragrant, or it is fading, or is not yet full blown, and so on indefinitely. When, however, we choose an attribute which is an essential property of all roses whatsoever, we have always the syllogism of reflection, – that is, the concept of a rose is illuminated by the light reflected upon it by one of its essential attributes.
Or in other cases, it may not be a specific property so much as an essential relation which the object of thought sustains; when, for instance, we fail to understand the essential significance of a certain tool until we discover the particular use to which it is adapted, and this is allowed to reflect its light upon the nature of the tool itself. In the syllogism of reflection, therefore, the quality which is taken as the middle term is not merely one of many attributes chosen at random, or through caprice, or suggested by some passing circumstance, but it should be an attribute of such a nature that it must necessarily belong to every other member of the same species which is represented by the individual, as well as to the individual itself. The significance of the species is thus reflected in its characteristic attributes which all its individual members possess in common. It is the bond of unity which holds together all individuals of the same class in one group.
The syllogism of reflection therefore may be divided into three subsidiary kinds: – (1) The Syllogism of Allness. (Der Schluss der Allheit.) (2) The Syllogism of Induction. (Der Schluss der Induktion.) (3) The Syllogism of Analogy. (Der Schluss der Analogie.) The primary form of the syllogism of reflection is a syllogism in the first figure, and. is known as the syllogism of allness. It endeavors to show what distinctive attribute or attributes are common to all members of a class. Hegel illustrates this by the traditional syllogism: –
All men are mortal.
Caius is a man.
Caius is mortal.
The weakness of this syllogism lies in the fact that the universality of the major premise, “All men are mortal,” obviously depends upon the tacit assumption that the conclusion is true. The major premise implies that a previous induction of an exhaustive nature has been made.
Thus a transition is effected by the necessities of thought to the inductive syllogism, such as the following: –
This man, and this man, and so on indefinitely, are mortal.
This man and this man, and so on indefinitely, constitute all men.
All men are mortal.
The formula for this syllogism would be
I.
U-I-P.
I.
etc., wherein is signified that the middle term (I) is indefinitely repeated, and is the sum of a number of individual cases. Passing from the individual instances, however numerous they may be, to the universal, which must necessarily transcend our experience, our reason rests upon the postulate that whatever is observed to be an essential property which a number of individuals have in common, will be found to obtain in all the individuals which resemble them sufficiently to be regarded as members of one and the same class, or species.
This gives us the third form of the syllogism of reflection, which expresses an underlying analogy as the warrant for the inductive generalization previously performed. In this syllogism of analogy the inference is based upon the logical principle that inasmuch as some things of a certain kind possess a certain well-marked quality, therefore the same quality will be found in the case of other things of the same kind. The individual instance under investigation may be regarded as a typical case, and, therefore, as standing for a class, it so far forth partakes of the nature of a universal. The common bond, moreover, which unites together objects of the same kind, and by virtue of which they are what they are, cannot be merely the result of a fortuitous coincidence of similar qualities, but is a necessary and essential characteristic of the very nature of the things themselves. This forms a natural transition to the syllogism of necessity.
The syllogism of necessity may be divided into three kinds: –
(1) The Categorical Syllogism.
(2) The Hypothetical Syllogism.
(3) The Disjunctive Syllogism.
In the categorical syllogism the individual is referred to its appropriate universal by means of the intermediate particular, or species to which it more proximately belongs. This syllogism would be in some such form as follows: –
A certain individual belongs to a particular species.
The species belongs to a certain genus.
The individual belongs to that same genus.
In the hypothetical syllogism the universal or the genus is represented as the ground of the particular or the species. Its major premise is of the form, “If A is, so is B.” The minor premise represents the presence or the absence of the necessary condition, and the conclusion the resultant realization of the effect, or the failure to realize it, as the case may be.
In the disjunctive syllogism the universal is resolved into its component parts. It is the highest form of the syllogism, for it represents an exhaustive manifestation of the full concrete essence of the universal.
The minor premise of this syllogism expresses what parts in any given cases are present or absent, and the conclusion expresses the resulting presence or absence of the other parts as thus determined.
This syllogism in its disjunctive form marks the natural transition also to the category of the notion in its second aspect, that of objectivity; for an exhaustive manifestation of the universal shows not merely the sum total of its thought relations, – that is, in reference to its purely subjective aspect, for then its manifestation would be partial and not exhaustive, but it furnishes as well scope for its external actualization in the world of reality. The notion represents a totality, and that, too, is the essential function of the disjunctive syllogism, – to represent the given object of thought in its totality. Moreover, there is no such thing as a totality which is not realized in all of its concrete fulness. The notion, therefore, as a fundamental constructive principle, is not to be regarded as a force operative in vacuo, but in the concrete system of things, of persons and of events, in life and its wealth of inexhaustible possibilities.