The system of syllogism
| Author | Richard Dien Winfield |
| Position | Distinguished Research Professor of philosophy at the University of Georgia |
| Pages | 245-268 |
Page 245
Since Aristotle, syllogism has cast a fateful shadow upon the power of reason. Recognized to be the great conveyor of rationality, syllogism has equally been acknowledged to be beset by limits.
Neither Plato, nor his greatest pupil, Aristotle, see fit to restrict reason to syllogistic inference. Given how every syllogism operates with premises, they recognize that if reason were confined to syllogizing, it could never account for the assumptions on which its conclusions ultimately rested. Any attempt to ground those premises would require further inferences whose own premises would always stand in need of further deduction. The unconditioned knowledge required for philosophical wisdom would instead depend upon transcending the limits of syllogism, something Aristotle and Plato sought by employing an intuitive understanding of first principles-those privileged givens that allegedly have an absolute immediacy mediating everything else that is and can be known. Such intuitive cognition would then empower syllogism to infer what would follow from the first principles.
The role of syllogism takes on a different cast, though, once the intuitive understanding of first principles is called into question. Privileged givens can never be shielded from sceptical challenge since immediacy can be ascribed to any content and no immediacy can be justified by anything else without forfeiting its alleged primacy. If the repudiation of intuitive understanding leaves reason with no resource other than syllogism, philosophical argument is condemned to an empty formality, where every inference rests upon premises that can never be fully proven. At best, syllogism becomes a regulative imperative, leaving reason ever seeking, but never attaining, the unconditioned condition of judgments.Page 246
Whether syllogism be supplemented by an intuitive intelligence or left alone as reason's solitary device, it can hardly account for its own defining nature, let alone provide an exhaustive treatment of its particular types. Inference cannot be inferred without taking itself for granted. Further, because inference employs premises that are given rather than derived, it can no more legitimate its own concept than that of its premises. Moreover, no empirical survey of inference can reliably locate its own nature, since what observed examples share may be contingent rather than necessary commonalities.
To be logically accounted for, syllogism must be determined apart from any contingent content. This does not mean that syllogism per se is completely formal. It does have a content consisting minimally in the mediated succession of terms comprising inference. Commonly, these terms are identified as three successive judgments, which are just as commonly assumed to be determined in their own right and only externally related through the inference to which they belong. The connection of inference thereby appears to be something subjective, rather than objective, residing not in the content of the judgments themselves, but in the arrangement imposed upon them from without, by some syl-logizer. Even if a conclusion is necessitated by the major and minor premises, these enter into the inference as givens. Nevertheless, the immediacy they possess is just as much superseded by the inference of which they are a part. To the degree that the conclusion follows within the syllogism -from them and them alone- it certifies that their connection is not just subjective, but inherent in their content.
Yet how are the terms, which are both initially immediate and posited as mediated, further determined in syllogism per se? To the degree that syllogism incorporates judgments, these judgments must themselves enter in only as they are necessarily determined. To eliminate all empirical contingencies, the logical investigation of judgment must consider the subject, as such, and the predicate, as such. Instead of predicating some particular universal, judgment per se predicates the universal, as such, and does so not of some contingent subject, but of the individual or particular, as such. Similarly, if inference is to be categorized independently of all contingent content, its constituents must be as equally conceptually determined as those that comprise the terms of judgment. Moreover, if the minimal nature of syllogism involves the universal, the particular, and the individual per se, then any differentiation of types of syllogism will be necessary and exhaustive only if it relies upon nothingPage 247 but the generic types of judgment they contain and the types of universality, particularity, and individuality that distinguish these judgments. If differentiation of forms of syllogism is to be non-arbitrary, it must emerge from what minimally characterizes syllogism. Otherwise their differentiation will be alien to the nature of syllogism and contingent upon some extraneous factor.
Although philosophers since Aristotle have freely employed syllogism as a central fixture of philosophical investigation, a systematic account of it has been wanting. The great exception to this neglect is Hegel. To escape arbitrariness, Hegel attempts to think through how the differentiation of judgment achieves closure when a type emerges whose connection overcomes the immediacy of judgment's copula, transforming itself into the mediated connection minimally comprising syllogism. Having thereby provided an alleged non-arbitrary account of syllogism per se, Hegel then proceeds to think through the differentiation of its forms. He does so by following how the minimal relationship of syllogism engenders a series of self-transforming forms of inference that exhausts itself by reaching a shape that eliminates the type of mediation constitutive of syllogism.
Not surprisingly, the forms of syllogism arise in an order that largely follows the order of the forms of judgment incorporated within them. Yet one glaring discrepancy stands out. Whereas judgment successively takes the form of judgments of determinate being (qualitative), of reflection (quantitative), of necessity (modal), and of the concept (normative), syllogism takes only three forms correlating with the first three of the four forms of judgment. In Hegel's account, the first form of syllogism is that of determinate being, relating qualitative judgments involving abstract universals, particulars and individuals. This form of inference transforms itself into the syllogism of reflection, linking quantitative judgments involving class membership. The syllogism of necessity follows, containing genus/species relationships. What is lacking is a form of syllogism that might correlate with judgments of the concept whose normative relations involve the concrete universal. Instead, the syllogisms of necessity allegedly exhaust the necessary forms of inference by eliminating the difference between what is concluded and that by which it is inferred. This purportedly undermines the mediation constitutive of syllogism, removing the remaining externality of its connections, in which its abiding subjectivity resides. With the universal andPage 248 particular relations of individuals now completely posited, the category of objectivity has emerged.
The only way to evaluate the anomaly between the series of judgments and syllogisms is to think through their determinations and establish whether they transform themselves as Hegel suggests. Doing so will allow us to determine to what degree a systematic account of inference has been achieved.
In drawing upon Hegel's investigation to comprehend syllogism, the logical starting point is the examination of whether syllogism does arise from the self-engendered closure of the judgment forms, and if so, with what character it emerges. This may allow us to lay hold of the minimal determination of syllogism, which no less becomes a particular form of syllogism as other forms arise from it.
On Hegel's account, the forms of judgment achieve closure through the connection posited in the apodeictic judgment. Apodeictic judgment, like the assertoric and problematic judgments from which it arises, involves the concrete universal, which unites particularity and universality. This correspondence of particularity and universality is predicated of the individual in all three of these judgments of the concept. Because the assertoric judgment makes this connection immediately, providing no ground for the individual to fit this correspondence, the individual may or may not fit, depending upon what particularity it has. The problematic judgment posits just this, which yields the apodeictic judgment insofar as the latter specifies that the individual has the unity of particularity and universality by containing the appropriate particularity. As a consequence, both subject and predicate now take on the form of judgments, containing an immediate connection between individual and particular (the erstwhile subject), and particular and universal (the erstwhile predicate). Moreover, the identity posited by the apodeictic judgment resides no longer simply in the immediate connection of the copula, expressed by is. What connects the individual in the subject with the universal in the predicate is instead the particularity both equally contain, which is why the connection is not contingent upon some subjective association, but necessary and objective.
Although the apodeictic judgment nominally has the form of a subject/predicate relation, the connection it effects leaves judgment behind. More precisely, judgment is incorporated in a more concrete me-Page 249diation of the...
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