On Hegel’s ‘Science of Logic’ : A Realm of Shadows — part forty six.
‘And would you fain the reason know’
by Philip Rosseter, (1567/8–1623)
And would you fain the reason know,
Why my sad eyes so often flow ?
My heart ebbs joy, when they do so,
And loves the moon by whom they go.
And will you ask, ‘Why pale I look?’
’Tis not with poring on my book :
My mistress’ cheek, my blood hath took,
For her, mine own hath me forsook.
Do not demand, ‘Why I am mute?’
Love’s silence doth all speech confute.
They set the note, then tune the lute ;
Hearts frame their thoughts, then tongues their suit.
Do not admire, ‘Why I admire?’
My fever is no other’s fire :
Each several heart hath his desire ;
Else proof is false, and truth a liar.
If why I love you should see cause!
Love should have form like other laws,
But Fancy pleads not by the clause :
’Tis as the sea, still vext with flaws.
No fault upon my love espy :
For you perceive not with my eye ;
My palate, to your taste may lie,
Yet please itself deliciously.
Then let my sufferance be mine own :
Sufficeth it these reasons shown :
Reason and love are ever known
To fight till both be overthrown.
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Georg Wilhelm Friedrich Hegel, (1770–1831). ‘The Science of Logic’.
The Syllogism of Reflection.
Recall the result of Judgment: I = {I, P, U}; I ≠ {I, P, U}. Four judgements were required because I had to be counted twice — as abstract and then as notional Individuality. The Syllogism of Reflection, where I is the middle term, is more advanced than the parallel Judgment of Reflection, which entailed merely an abstract /. Syllogism has now dissolved into UUU (E). The subject is therefore all of Syllogism. As in the Judgment of Reflection, the Syllogistic version starts with the proposition that the subject is nothing. Predicate is everything. But in Syllogism of Reflection, the subject is a notional nothing — UUU (E). It is in this way that the syllogism of reflection is the first to possess genuine determinateness of form, in that the middle term is posited as the totality of the terms.
‘From this determinateness of the extremes, which belongs to the course of the determination of the judgment, there results the more precise content of the middle, which is what counts most in the syllogism, for it is the middle that distinguishes the syllogism from judgment. The middle contains (1) singularity; (2) but singularity expanded into universality, as an ‘all’; (3) the universality that lies at the basis, uniting singularity and abstract universality in itself, the genus. — The syllogism of reflection is thus the first to possess genuine determinateness of form, for the middle is posited as the totality of determinations; the immediate syllogism is by contrast indeterminate because the middle is still only abstract particularity in which the moments of its concept are not yet posited. — This first syllogism of reflection may be called the syllogism of allness.
The Syllogism of Allness. The first Syllogism of Reflection is Allness. Its form is UPIR. Here, the subject (U, or UUU (E)) is the member of a class. It has external manifestation (I) through the medium of P. The particularizing trait of Syllogism is that each depends on external reflection. In the Syllogism of Allness, P is a notional P. UUU (E) has erased itself and displaced its Being into P. The Particularity of Syllogism is that external reflection decides which member of UUU (E) is really U, P, or I. For this reason, Hegel says that the extremes of Syllogism generally are Syllogism of Allness determinations of the judgement of reflection. That is, they are Singular Judgments.
‘The syllogism of allness is the syllogism of the understanding in its perfection, but more than that it is not yet. That the middle in it is not abstract particularity but is developed into its moments and is therefore concrete, is indeed an essential requirement of the concept. But at first the form of the allness gathers the singular into universality only externally, and conversely the singular behaves in the universality still as an immediate that subsists on its own. The negation of the immediacy of the determinations which was the result of the syllogism of existence is only the first negation, not yet the negation of the negation, or absolute immanent reflection. The singular determinations that the universality of reflection holds within still lie, therefore, at the basis of that universality — in other words, allness is not yet the universality of the concept, but the external universality of reflection’.
- ‘The Science of Logic’
Syllogism of Allness (UPI (G))
External reflection points and says, this part of the Syllogism is I, that one is P, etc. Indexicality depends on external reflection. For this reason, Hegel names P (external reflection) as genus, which determines the species.The Syllogism of Allness counts as the syllogism of understanding in its perfection. The middle term is no longer abstract particularity but is developed into its moments and is therefore concrete, a state that is an essential requirement for the Notion. P is now UUU (E) = I. External reflection has become internal to Syllogism. But the Syllogism of Allness has a flaw: the form of allness gathers the individual externally into universality. It] still preserves the individual in the universality as something possessing immediately a separate self-subsistence. Single determinations still form the basis of the universality of reflection that embraces them within itself. Allness is still not the universality of the Notion but the external universality of reflection. Dialectical Reason points out that I is the true mediator — not P. Nothing in the Syllogism of Allness assures us of the truth that all Syllogisms depend entirely on external reflection to make them work.
A single counter-example destroys the proof.
All men are mortal
Gaius is a man.
Therefore Gaius is mortal.
In this Syllogism, all men is a set of empirical Individuals. How do we know that all men are mortal? Only external observation, which provides incidents of mortality, can be brought to bear. Perhaps the major premise is right and perhaps it is wrong. Nothing in the Syllogism of Allness can establish the truth of the major premise. The conclusion (therefore Gaius is mortal) is brought to the table by the major premise — not by Syllogism as such. The major premise presupposes its conclusion.
‘It followed from the concept of the syllogism, with regard to the syllogism of existence, that the premises, as immediate, contradicted the conclusion, that is to say, contradicted the mediation that the concept of the syllogism requires; that the first syllogism thus presupposed other syllogisms, and conversely these presupposed the first. In the syllogism of reflection this result is posited in the syllogism itself: the major premise presupposes its conclusion, for it contains the union of the singular with a predicate that would have to be a conclusion first’.
- ‘The Science of Logic’
This is ‘no inference at all but a simple tautology’, says Burbidge. What we have in the Syllogism of Allness ‘is only an external, empty show of syllogizing’ adds Burbidge. The dynamic was supposed to be objective, but the essence of this syllogizing rests on subjective individuality.
‘What we have here in fact can therefore be expressed by saying that the syllogism of reflection is only an external, empty reflective semblance of syllogistic inference; that therefore the essence of the inference rests on subjective singularity; this singularity thus constitutes the middle term and is to be posited as such: singularity which is singularity as such and possesses universality only externally. — Or what has been shown on closer inspection of the content of the syllogism of reflection is that the singular stands connected to its predicate immediately, not by way of an inference, and that the major premise, the union of a particular with a universal, or more precisely of a formal universal with a universal in itself, is mediated through the connection of the singularity that is present in the formal universal, of singularity as allness. But this is the syllogism of induction’.
- ‘The Science of Logic’
Individuals — subjectively brought together in a supposed Universal set — are therefore the true middle term of the Syllogism of Allness, which Dialectical Reason takes to be external to Syllogism. The major premise stands only so long as induction does not falsify it. As a result, the truth of the Syllogism of Allness is induction.
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La Düsseldorf ‘Cha Cha 2000’. ‘Menschen’:
The Syllogism of Induction. The true middle term of the Syllogism of Allness was not P but I. Hence, the Syllogism of Induction follows the form UIPR. So far, I and P are notional, but U is abstract. That is to say, both I and P are proven because they have been the middle terms in the first two Syllogisms of Reflection. U remains unproven. The Syllogism of Induction asserts UP through the mediation of I. For example, in all men are mortal, mortality is claimed as the predicate — the Particularity — of every individual man. The other extreme (all men) is the universality — but only an abstract U subjectively derived. Abstract U erases itself and admits that its being resides in the class of individuals that has been subjectively brought together. This erasure in favour of the empirical class proves that I=[i, i, i. . . ] is notional. The middle term between U and P — the proof — is the class of all individuals. Syllogism of Induction (UIP (E)) shows a Spurious Infinity as the middle term between a Particular predicate and the claim to Universality. The class of individuals is a Spurious Infinity because one never knows if Syllogism of induction all individuals have been enumerated. Some (UIPR) unenumerated individual might exist to destroy the truth of the induction.
As always, Spurious Infinity is a sign that something is amiss. Nevertheless, UIP (R) is an advance over UIP (E). Earlier, I was not the subsuming term or predicate. (Remember in the translation I am using I = S).
‘The second figure of the formal syllogism, U-S-P, does not correspond to this schema, because the S that constitutes the middle term did not subsume or was not a predicate. In induction this deficiency is eliminated; here the middle term is “all singulars”; the proposition, U-S, which contains as the subject the objective universal or the genus set apart as an extreme, has a predicate which is of at least equal extension as the subject and is consequently identical with it for external reflection. Lion, elephant, etc., constitute the genus of quadruped; the difference, that the same content is posited once in singularity and again in universality, is thus just an indifferent determination of form — an indifference which in the syllogism of reflection is the posited result of the formal syllogism and is posited here through the equality of extension’.
- ‘The Science of Logic’
I was an immediacy, not the relation of U and P. Now induction claims perfect unity between U and I. UI (the subject) is coextensive with its predicate (IP). The subject (all men) is comprised by the set of all individual men. The two are taken as the same thing; the same content is posited once in individuality and again in universality. All men and all these men bear a mere formal difference, but substantively they are taken as the same. Induction from a set of individuals is based on experience — the subjective taking together of the individuals into the genus and of conjoining of the genus with a universal determinateness because this is found in all the individuals.
‘Induction, therefore, is not the syllogism of mere perception or of contingent existence, like the second figure corresponding to it, but the syllogism of experience — of the subjective gathering together of singulars in the genus, and of the conjoining of the genus with a universal determinateness on the ground that the latter is found in all singulars. It also has the objective significance that the immediate genus has determined itself through the totality of singularity as a universal property and possesses its existence in a universal relation or mark. — But the objective significance of this syllogism, as it was of the others, is at first only its inner concept, and is not as yet posited in it’.
- ‘The Science of Logic’
Syllogism of Induction (UIP (E))
Undoubtedly, the individuals are made into allness by mere external reflection. Universality remains a problem.
‘On the contrary, induction is essentially still a subjective syllogism. The middle terms are the singulars in their immediacy, the collecting of them into a genus through the allness is an external reflection. Because of the persisting immediacy of the singulars and because of the externality that derives from it, the universality is only completeness, or rather, it remains a task. — In induction, therefore, there recurs the progression into the bad infinity; singularity ought to be posited as identical with universality, but since the singulars are equally posited as immediate, the intended unity remains only a perpetual ought; it is a unity of likeness; the terms which are supposed to be identical are at the same time supposed not to be identical. The a, b, c, d, e, constitute the genus only further on, in the infinite; they do not yield a complete experience. The conclusion of induction thus remains problematic’.
- ‘The Science of Logic’
‘The process of reflective inference produces only a problematic conclusion’, says Burbidge. But induction assigns the role of genus to Spurious Infinity of all individuals. Winfield suggests that genus is not proper to induction, because genus determines the species. Rather, class membership is the issue. A class has no substance of its own and is whatever the class members bring to it. In this sense, induction presupposes its conclusion. Induction is accepted as valid although the perception is admittedly incomplete.
‘But induction, by expressing that perception, in order to become experience, ought to be carried on to infinity, presupposes that the genus is in and for itself conjoined with its determinateness. In this, it in fact rather presupposes its conclusion as something immediate, just as the syllogism of allness presupposes the conclusion for one of its premises. — An experience that rests on induction is assumed as valid even though the perception is admittedly not complete; it may be assumed, however, that there is no counter-instance to the experience only if the latter is true in and for itself. Inference by induction, therefore, is based indeed on an immediacy, but not on the immediacy on which it is supposed to be based, not on a singularity that exists immediately, but on one that exists in and for itself, on the universal. — The fundamental character of induction is that it is a syllogistic inference; if singularity is taken as the essential determination of the middle term, but universality as only the external determination, then the middle term would fall apart into two disjoined parts, and there would be no inference; this externality belongs rather to the extremes. Singularity can only be a middle term if immediately identical with the universality; such a universality is in truth objective universality, the genus. — The matter can also be viewed in this way: universality is external but essential to the determination of the singularity which is at the basis of the middle term of induction; such an external is just as much immediately its opposite, the internal. — The truth of the syllogism of induction is therefore a syllogism that has for its middle term a singularity which is immediately in itself universality. This is the syllogism of analogy’.
- ‘The System of Logic’
The fundamental character of induction is that it is a syllogism. In it, I (as the set of all I’s) unites Particulars and proclaims them Universal. Yet the forgathering of I’s into I is a subjective judgment, which asserts (but does not prove) the immediacy which is in and for itself the universal immediacy. Induction takes Universality as essential to its truth. ‘That is, it has implicitly formed the demand that only speculative philosophy can satisfy: the demand that universality be concrete, present in and as the experienced Other’, says Peter Simpson. ‘Logical induction has rightly identified the goal of a concept that is one with its instances … but lacks the appropriate standpoint for recognizing that identity’. If, per Karl Popper, individuality is taken as the essential, but universality as only the external determination of the middle term, then the middle term would fall asunder into two unconnected parts and we should not have a syllogism. Induction is a Syllogism only if I = U. Such universality is properly objective universality, the genus. For induction, then, universality is external but essential. As essential, Universality is just as much internal to induction as external. The truth of Induction is therefore Universality — IUP (R). This Hegel labels the Syllogism of Analogy.
The Syllogism of Analogy. With the Analogy section we arrive at the invocation of moon men. Hegel simultaneously denounces and praises analogy as empirically worthless and spiritually necessary. Induction entails a class of Individuals with the same predicate, which is logically put forth as the Universal. Hence what really mediates induction (Popperian caveats notwithstanding) is Universality. Universality of predicates is what the Syllogism of Analogy puts forward. In analogy, ‘the universal is seen in the individual case’, says Clark Butler. According to Hegel’s definition, if two objects agree in one or more properties, then a property which one possesses also belongs to the other. Hegel gives a selenic example:
The earth is inhabited [PU],
The moon is an earth [UI],
Therefore the moon is inhabited [PI].
‘When we consider the syllogism of analogy with its major premise expressed as above, namely, ‘if two subject matters agree in one or more properties, then a further property of one also belongs to the other’, it may seem that this syllogism contains four terms, the quaternio terminorum — a circumstance that brings with it the difficulty of how to bring analogy into the form of a formal syllogism. — There are two singulars; for a third, a property immediately assumed as common, and, for a fourth, the other properties that one singular possesses immediately but the other first comes to possess only by means of the syllogism. — This is so because, as we have seen, in the syllogism of analogy the middle term is posited as singularity but immediately also as the true universality of the singularity. — In induction, the middle term is, apart from the extremes, an indeterminate number of singulars; this syllogism, therefore, required the enumeration of an infinite number of terms. — In the syllogism of allness the universality in the middle term is still only the external form determination of the allness; in the syllogism of analogy, on the contrary, it is as essential universality. In the above example, the middle term, ‘the earth’, is taken as something concrete which, in truth, is just as much a universal nature or genus as it is a singular’.
- ‘The Science of Logic’
‘This syllogism has the third figure of the immediate syllogism, S-U-P, for its abstract schema. But its middle term is no longer some single quality or other but a universality which is the immanent reflection of a concreted term and is therefore its nature; and conversely, since it is thus the universality of a concreted term, it is at the same time in itself this concreted term. — Here, therefore, a singular is the middle term, but a singular taken in its universal nature; there is moreover another singular, an extreme term, which has the same universal nature as the other which is the middle term. For example:
The earth has inhabitants,
The moon is an earth,
Therefore the moon has inhabitants.’
— ‘The Science of Logic’
According to David Gray Carlson: ‘Analogy is a strange part of the SL, with its reference to moon men’ and this syllogism of analogy is a ‘dubious example’. But in fact this example is not original with Hegel and very likely was a common trope at the time. One can find it, for instance, in Antonio Genovesi, ‘Elementa artis logico-criticæ’, Liber V, 1749, and also, by the same author, ‘Gli elementi dell’arte logico-critica’, 2nd edn., 1783. In Genovesi’s treatise, syllogism of analogy follows immediately upon the treatment of probability, exactly as it does in Hegel.
In this example, Analogy degrades reason to the sphere of mere representation.
‘Analogy is all the more superficial, the more the universal in which the two extremes are united, and in accordance with which the one extreme becomes the predicate of the other, is a mere quality or, since quality is a matter of subjectivity, is some distinctive mark or other and the identity of the extremes is therein taken as just a similarity. But this kind of superficiality to which a form of understanding or of reason is reduced by being debased to the sphere of mere representation should have no place in logic. — Also unacceptable is to present the major premise of this syllogism as though it should run: ‘That which is similar to an object in one distinctive mark is similar to it in other such marks as well’. On this formulation, the form of the syllogism is expressed in the shape of a content while the empirical content, the content properly so called, is together relegated to the minor premise. So, for example, could also the whole form of the first syllogism be expressed as its major premise: ‘That which is subsumed under another thing in which a third thing inheres has that third thing inhering in it too; but now … etc.’ But what matters in the syllogism as such is not the empirical content, and to make its own form the content of a major premise makes just as little difference as to take any other empirical content for that purpose. Nothing of consequence follows for the syllogism of analogy from a content that contains nothing but the form peculiar to that syllogism, just as nothing of consequence would have followed for the first syllogism from having as its content the form that makes the syllogism a syllogism. — What counts is always the form of the syllogism, whether the latter has itself or something else for its empirical content. So the syllogism of analogy is a form peculiarly its own, and it is vacuous not to want to regard it as such on the ground that that form could be made into the content or matter of a major premise whereas matter is no concern in logic. — What might tempt one to this view in regard to the syllogism of analogy, and perhaps in regard to the syllogism of induction too, is that the middle term in them, and also the extremes, are more determined than they are in the merely formal syllogism, and therefore the determinations of form, since they are no longer simple and abstract, must also take on the appearance of a content determination. But that the form determines itself to content is first of all a necessary advance on the part of the formal side, and therefore an advance that touches the nature of the syllogism essentially; secondly, such a content determination cannot, therefore, be regarded as any other empirical content, and abstraction cannot be made from it’.
- ‘The Science of Logic’
In terms of its content, analogy “should not find a place in logic at all. According to Burbidge, the problem with the moon analogy is that ‘the inference itself cannot establish whether the fact that the earth has inhabitants follows from its essential nature as satellite, or is simply accidental. It is this contingency that frustrates the syllogism and prevents it from symbolizing a necessary inference’ he says. Analogy’s importance, Hegel declares, itself does not depend on the empirical content. The form of the Syllogism is the main thing. In analogy, Speculative Reason finds that Universality, the implicit middle term in induction, now mediates expressly in the form IUP (R). As mediator, U is now proven as the very nature of the thing. The thing is a concrete object — an Individual — but U is now taken as genuinely in the thing. For this reason one may suppose Errol Harris to e in error when he finds the point to be that analogy can be ‘a fruitful stepping-stone to scientific discovery, if used with care and circumspection’. The utility of analogy is not at stake, but rather the role of U in mediating between P and Iwhich interests Hegel. Admittedly, Hegel does praise the utility of analogy in science, but this is not his speculative point.
Here, then, the middle term is an individual but an individual taken in its universal nature. ‘In this process, reflective thought rises above bare denotation [i.e., assignment of an individual to a class] and assumes that there is an objective ground for conjoining class and determinate characteristics’, says Burbidge. Analogy is a relation between two Individuals, such as the moon and earth. These Individuals share some Universal trait (such as inhabitation). When analogy is based on mere similarity, however, it is not notional. Hegel reorganizes analogy so that its empirical content (all earths are inhabited) is demoted to the minor premise. The major premise is that which is subsumed under some other thing in which a third inheres, and has also that third inherent in it. In our case, the major premise is the moon is an earth. The moon is subsumed by the earth. The earth has a third (inhabitation) and this third inhabits the moon. The conclusion (therefore the moon is inhabited) shows that the Individual (moon) is continuous with the earth and so is a Universal Individual.
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In the meantime what was previously formal Syllogism must now appear as a determination of content. That is to say, in the Syllogism of Analogy, Universality objectively mediates and therefore is proven. This makes Analogy (IUP (R)) an advance over IUP (E)) which yielded abstract Universality. It may seem, Hegel suggests, that analogy contains four terms, the quatemio terminorum. Quatemio terminorum is a logical mistake with this form:
A = B
C = D
A = D
In Hegel’s which isn’t really Hegel’s example, there are two individuals (earth and moon), a (third) property in common (they are both heavenly bodies). The quatemio terminorum is therefore all the other properties of the one individual (including inhabitation) which are now attributed to the second individual. For example:
1. The earth is inhabited (PI).
2. The earth is a heavenly body (IU).
3. The moon is a heavenly body (PU).
4. Therefore the moon is inhabited (PI).
If analogy has four terms, how could it be a Syllogism, which has only three? The answer is that Universality is immediately also as the true universality of the Individuals. The apparent four terms are really only three. Earth and moon really do share a Universal — their nature as heavenly bodies. The second and third term are really one single middle term. Compare this with induction, where the middle term was a set of individuals. Such a mediator was a mere ought-to-be which ought to be enumerated. Even further back, in the Syllogism of Allness, the middle term was purely external (hence less than an-ought-to-be). Now, however, essential universality mediates. The Individuals share Particulars which are Universals (or so analogy claims). In short, successful analogy requires the presence of a notional Universal. Analogy still suffers from externality, which means that it is still a Syllogism of Reflection. That two things share some aspect (earth and moon are heavenly bodies) does not prove that they share all aspects (such as inhabitation). Only external reflection can decide whether habitation is particular or universal. If individuality and universality are immediately united, then external reflection simply asserts that the predicate (habitation) is Universal, not Particular.
‘From this aspect, the quaternio terminorum would not make analogy an imperfect syllogism. But it would make it so from another aspect; for although the one subject has the same universal nature as the other, it is undetermined whether the determinateness, which is inferred to pertain also to the second subject, pertains to the first because of its nature in general or because of its particularity; for example, whether the earth has inhabitants as a heavenly body in general or only as this particular heavenly body. — Analogy is still a syllogism of reflection inasmuch as singularity and universality are united in its middle term immediately. Because of this immediacy, the externality of the unity of reflection is still there; the singular is the genus only in itself, implicitly; it is not posited in this negativity by which its determinateness would be the genus’s own determinateness. For this reason the predicate that belongs to the singular of the middle term is not already the predicate of the other singular, even though the two singulars both belong to the one genus’.
- ‘The Science of Logic’
In such a case, analogies fail as objective proof. Syllogism, however, is about mediation. And mediation requires a positing, not of the immediate being, but of genus. So far, the Universal (heavenly body) is only implicitly genus; it must become so expressly. The moon is inhabited. This was the conclusion (PI). But the earth is inhabited is also PI. Earthly habitation is the major premise brought to the table by external reflection. Since the major premise is the conclusion, the major premise is presupposed, not proved. Hence this syllogism is the demand for itself to counter the immediacy [i.e., unprovenness] which it contains.
‘S-P (‘the moon is inhabited’) is the conclusion; but the one premise (‘the earth is inhabited’) is likewise S-P; in so far as S-P is supposed to be a conclusion, it entails the requirement that that premise also be S-P. This syllogism is thus in itself the demand to counter the immediacy that it contains; or again, it presupposes its conclusion. One syllogism of existence has its presupposition in the other syllogism of existence. In the syllogisms just considered, the presupposition has been moved into them, because they are syllogisms of reflection. Since the syllogism of analogy is therefore the demand that it be mediated as against the immediacy with which its mediation is burdened, what it demands is the sublation of the moment of singularity. Thus there remains for the middle term the objective universal, the genus purified of immediacy. — In the syllogism of analogy the genus was a moment of the middle term only as immediate presupposition; since the syllogism itself demands the sublation of the presupposed immediacy, the negation of singularity and hence the universal is no longer immediate but posited. — The syllogism of reflection contained the first negation of immediacy; the second has now come on the scene, and with it the external universality of reflection is determined as existing in and for itself. –Regarded from the positive side, the conclusion shows itself to be identical with the premises, the mediation to have rejoined its presupposition, and what we have is thus an identity of the universality of reflection by virtue of which it becomes a higher universality’.
- ‘The Science of Logic’
Presupposition here is reflective — contained within the totality. Presupposition has declined since the Syllogism of Existence, where one Syllogism resupposed all other Syllogisms. Each Syllogism was immediate and abstracted from the other. Now presupposition is proven to be a structural part of Analogy. The major premise is the conclusion. The Syllogism of Analogy bears the structure of a Determination of Reflection — a unity between immediacy and mediation. Speculatively, an advance has been made. Analogy works when the conclusion is also the major premise. If this occurs, then mediation ha coincided with its presupposition. Hegel insists that analogy is a negation of the negation. How precisely is this so? Recall that the Syllogism of Existence failed to be what it claimed. External reflection (P) made it work. Yet P involved a foregathering of Individuals in induction. I, not P, mediated. But I mediated only because all I’s were universally the same. Every individual Syllogism [i, i, i… ] operated by externality. But Analogy is the truth of induction. All Individuals have Universal attributes. ‘All Syllogisms work by external reflection’ is the same as saying that external reflection is inside the Syllogisms. Analogy is therefore a negation of the negation. It brings Syllogism’s externality inside. U is now proven. It has become the middle term of analogy. When I yields to U, the syllogism of reflection has passed over into the syllogism of necessity’.
‘Reviewing the course of the syllogism of reflection, we find that mediation is in general the posited or concrete unity of the form determinations of the extremes; reflection consists in this positing of the one determination in the other; the mediating middle is thus allness. But it is singularity that proves to be the essential ground of mediation while universality is only as an external determination in it, as completeness. But universality is essential to the singular if the latter is to be the conjoining middle term; the singular is therefore to be taken as an implicitly existing universal. But the singular is not united with it in just this positive manner but is sublated in it and is a negative moment; thus the universal is the genus posited as existing in and for itself, and the singular as immediate is rather the externality of the genus, or it is an extreme. — The syllogism of reflection, taken in general, comes under the schema P-S-U in which the singular is still as such the essential determination of the middle term; but since its immediacy has been sublated, the syllogism has entered under the formal schema S-U-P, and the syllogism of reflection has thus passed over into the syllogism of necessity’.
- ‘The Science of Logic’.
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Some further thoughts on Inference, Syllogism and Conclusion.
The verb schliessen means to shut, close, conclude, draw a conclusion, infer. A noun derived from it, Schluss (close, closure, end, conclusion, inference), was used by Jakob Böhme (1575–1624, noted for Boehmian theosophy, (not to be confused with Bohemian Rhapsody), the mystical being of the deity as the Ungrund (unground, the ground without a ground)) for the Latin conclusio, and by Gottfried Wilhelm (von) Leibniz, (1646–1716), and Christian Wolff (1679–1754), for the process of inference. Hegel exploits this link between closing and inferring, and also the fact that schliessen forms, with the prefix zusammen (together), zusammenschliessen (to unite, combine, connect).
The Greek syllogismos, from the verb syllogizesthai (to infer), is also associated with the ideas of concluding and combining or putting two and two together. Hence Hegel’s usual word for inference, Schluss, he uses Syllogismus only occasionally, is often translated as syllogism. The disadvantage of this rendering is that while syllogismos originally meant inference, it has come to refer only to those inferences recognized as valid by Aristotle and to similar inferences added by logicians in the Aristotelian tradition. While most of the types of inference considered in Hegel’s Logic fall more or less under this heading, some, notably the inductive inference, do not. (Aristotle recognized induction, but not as a valid form of syllogism.)
Hegel, like Kant, held that formal logic had made no significant progress since Aristotle. In fact, eighteenth-and early nineteenth-century logic contained several Stoic and medieval additions to Aristotle’s logic. For example, Aristotle recognized only syllogisms whose premisses and conclusion take one of these forms: (1) Universal affirmative: ‘All A’s are B’; (2) Universal negative: ‘No A’s are B’; (3) Particular affirmative: ‘Some A’s are B’; (4) Particular negative: ‘Some A’s are not B’. But the logic of Kant’s and Hegel’s time added to these the Individual judgement forms: (5) ‘This A (e.g. Socrates) is B’; (6) ‘This A is not B’. An Aristotelian syllogism has two premisses and a conclusion. For example;
1 All men are mortal
2 All Greeks are men
3 All Greeks are mortal
1 is the major premiss (in German, der Obersatz), 2 is the minor premiss (der Untersatz), and 3 is the conclusion (der Schlusssatz). It also involves three terms or concepts, here man, Greek and mortal. The term that appears in both premises, here man, is the middle term (in Hegel, often just die Mitte, the middle, mean); the other two terms are the extreme; the extreme in the major premise, here ‘mortal’, is the major term, that in the minor premise, Greek, is the minor term. Aristotle divides the syllogism into three schemata or figures (a fourth was added later, supposedly by Galen), which differ according to the positions of the middle, major and minor terms.
The above example is in the first figure, since the terms occur in the following positions: 1 Middle-Major; 2 Minor-Middle; 3 Minor-Major. The two (or three) other figures vary the order of the terms in the premises (though not in the conclusion). Each figure is then divided into several moods, according to the propositional form of the premisses and conclusion. Thus the above syllogism is in the first mood (of the first figure) since its premises and conclusion are all universal and affirmative. Hegel’s account of the inference, in his Logic, considerably alters both Aristotle’s logic and the formal logic of his own day. Aristotle was concerned with the ways in which a proposition can be validly derived from two other propositions. But, in accordance with his reinterpretation of the Judgement as an original division of the Concept into the Universal, Particular and Individual, Hegel reinterprets the forms of inference as successively more adequate ways of restoring the unity of the concept. Thus it is crucial for Hegel that an inference should contain a universal, a particular and an individual term. For example, an inference of Existence (Dasein) in the first figure is this:
1 All men are mortal
2 Caius is a man
3 Caius is mortal
Here, the middle term, man, is particular; the major term, mortal, is universal; and the minor term, Caius, is individual. The individual term is combined with the universal by the mediation of the particular (UPI). The second figure of the inference of Dasein differs from the first, in that it unites the universal with the particular, by way of the individual (PIU); and the third figure unites the individual with the particular by way of the universal (IUP). (The terms of the less significant fourth figure, the ‘mathematical inference’, are all universal.)
Hegel rejects Aristotle’s moods as an unnecessary complication, and proceeds from the inference of Dasein, in which the terms are external to each other and contingently connected, to the inference of reflection, in which the terms are more closely connected. The first form is the inference of allness (Allheit), an improved version of the first figure of the inference of Dasein. The second is the inference of induction, which unites the particular with the universal by way of individuals, and the third, the inference of analogy, unites the individual with the particular by the universal.
Finally, in the inference of Necessity, the relation between the terms is even closer: The categorical inference, a further improved version of the first figure of Dasein, unites an individual with its genus by way of its species (IPU). The hypothetical inference unites the species with the genus by way of the individual (PIU): e.g. ‘If Fido is a dog, then Fido is an animal; Fido is a dog; so Fido is an animal.’ Finally, the disjunctive inference unites the individual with the species, by way of the genus (IUP), which is exhaustively divided into its subordinate species: e.g. ‘Fido, being an animal, is either a dog or a cat or a horse, etc.; he is not a cat or a horse, etc.; so he is a dog.’ This inference, on Hegel’s view, fully restores the unity of the concept, and we can now turn to the realm of Objectivity.
Unlike Aristotle, Hegel sees each type of inference, except the last, as having defects which can be resolved only by moving to the next type of inference. For example, the first figure of Dasein (IPU), exemplified above, has these defects: (1) It is entirely contingent that we pick ‘man’, ‘mortal’ and ‘Caius’ as our terms. We could have deduced Caius’ mortality from different premisses (e.g. ‘All farmers are mortal’ and ‘Caius is a farmer’). This defect is resolved, on Hegel’s view, by the ever closer relation between the terms in successive types of inference. (2) The premisses of the inference, ‘All men are mortal’ and ‘Caius is a man’, are not yet demonstrated, and cannot be demonstrated in the first figure. Hegel, like J. S. Mill, even objects that the syllogism involves a petitio principii, since we cannot know that all men are mortal, unless we already know the conclusion, that Caius is mortal. This motivates the introduction, within each main type of inference, of the second and third figures (PIU) and IUP), since these can demonstrate the premisses of the first figure. But what he requires is not an infinite regress, in which the premisses of any inference are demonstrated by two further inferences, but a circle of inferences, in which any two figures demonstrate the premisses of the third.
But Hegel’s main deviation from Aristotelian orthodoxy is this: That inferences appear as a way of arguing from two propositions to a third is only their ‘subjective form’. Inferences of Dasein, owing to the contingency of their terms, are more susceptible to this subjective reading than are higher types of inference. But all inferences have also an ‘objective meaning’ the unification of universality, particularity and individuality which is not essentially or primarily propositional. Nor is the inference, as Aristotle held, essentially or primarily a form taken by our subjective thinking. On Hegel’s view, everything is an inference. Most basically, everything is an individual of a particular species and a universal genus. But a self-contained totality, such as the solar system (sun planets moons), the State, or the universe as a whole, are circular systems of three mutually supporting inferences, with a universal, particular and individual element each serving to unite the other two. The state, for example, involves the individual person (I), his needs (P) and a government (U), and each unites the other two. Similarly the universe involves the logical idea (U), nature (P) and spirit (I): in his system, Hegel presents them in the order UPI, but any order would be equally appropriate, since each term mediates the other two.
Hegel’s objectification of the inference is a part of his systematic transposition of terms traditionally associated with subjective thinking (e.g. Reason, judgement, concept, Contradiction, Truth) into the objective realm. Since, for example, reason is traditionally associated with the inference, and things, as well as thinking, can be rational and true, it is natural to suppose that things are also inferences. The motivation for the transposition is this: Thoroughgoing Idealism requires that things be not simply static projections of Thought, but that they embody the processes of thought as well. But in accordance with Hegel’s principle of Opposites, the doctrine is also an extreme realism, since things fully conform to our thoughts and thought-forms. A natural objection to the doctrine is that even if, e.g., the state does exhibit such a threefold structure, its relation to the inference is one of superficial analogy rather than of deep kinship.
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An example of a syllogistic fallacy from Shakespeare. Portia is arranged to marry whomever can correctly guess which of three caskets contains her portrait: the gold, the silver, or the lead casket. A prince comes to solve the riddle, and thinks he has worked out the answer upon reading the following inscription on the gold casket:
PRINCE OF MOROCCO:
‘Who chooseth me shall gain what many men desire’.
Why, that’s the lady, all the world desires her.
From the four corners of the earth they come
To kiss this shrine, this mortal breathing saint. — ‘The Merchant of Venice’, Act 2, Scene 7.
As a syllogism:
- All men desire Portia
- Many men desire what is in this chest.
- Ergo what is in the chest is (the portrait of) Portia.
But of course it isn’t. If only princes (like Harry for instance, too late for him now) were taught logic. The fallacy of the undistributed middle. Some A are B, and some C are A, ergo some C are B. But A is not distributed across the B and C in such a way that the B and C terms actually overlap. It is like reasoning thus: some cats are black, and some dogs are black, ergo some cats are dogs.
An example of some valid syllogistic reasoning from Shakespeare:
TIMON:
Away! What art thou?
FLAVIUS:
Have you forgot me, sir?
TIMON:
Why dost ask that? I have forgot all men;
Then, if thou grant’st th’art a man, I have forgot thee.
FLAVIUS:
An honest poor servant of yours.
TIMON:
Then I know thee not.
I never had honest man about me, I.
All I kept were knaves, to serve in meat to villains.
- ‘Timon of Athens’, Act 4 Sc. 3
As a syllogism:
- All men are men that Timon has forgotten.
- Flavius is a man.
- Ergo Flavius is a man that Timon has forgotten.
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La Duesseldorf — Rheinita:
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Dedicated to my One, my Everything.
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‘All love is wonder; if we justly do
Account her wonderful, why not lovely too?’
- from ‘Elegy II’, John Donne, (1571/72–1631)
And as a syllogism:
- All love is wonder.
- Kira inspires wonder.
- Ergo, Kira inspires love.
I say your name Kira.
Ich liebe dich.
❤️
Coming up next:
The Syllogism of Necessity.
To be continued …
