THE AFTERMATH OF SYLLOGISM – Book Sample
Introduction – THE AFTERMATH OF SYLLOGISM
Marco Sgarbi and Matteo Cosci
LOGICIAN: Here it is an example of a syllogism. “The cat has four paws.
Isidore and Fricot both have four paws. Therefore, Isidore and Fricot are cats.”
OLD GENTLEMAN: Well, my dog has got four paws. LOGICIAN: Then it’s a cat.
OLD GENTLEMAN: So then, logically speaking, my dog must be a cat?
LOGICIAN: Logically, yes.
But the contrary is also true.
E. Ionesco, Rhinocéros, act one (1959)
“A syllogism,” according to Aristotle, “is an argument in which, certain premises being posited, something other than what was laid down results by necessity because these premises are.” In the book entitled Prior Analytics, from which this initial definition comes (I, 24b, 18), the first theory of syllogistic reasoning was set forth, and it was presented in a way that was already highly developed.
The syllogistic heritage left by Aristotle, however conspicuous, was discussed and reworked by his pupil Theoprasthus while he was still alive.
Syllogism and its possibilities of inference were tested and developed even more during the Hellenistic age, mainly by Stoics, during the imperial age due to the prominent contributions by later Peripateticians such as Aristo of Alexandria and Boethus of Sidon, and during late antiquity and the early middle ages, with many exegetes and commentators who profitably commented on the Aristotelian texts.
These latter in particular often reformulated Aristotle’s teachings in syllogistic-ish fashion and overall expanded upon his original reflection on the matter through their eager activity of retake, criticism and ordering. In this way they originated a very elaborate set of syllogistic doctrines (although not always well integrated and consistent).
A very strong impulse on this object of study was certainly that given by Severinus Boethius, by way of his twofold translation of Prior Analytics and his own treatises, the De syllogismo cathegorico, the De hypotheticis syllogismis and the Introductio ad syllogismos cathegoricos. As time passed, scientific syllogism became the logical key-structure of demonstrative knowledge; its preeminence lasted and flourished with neither interruption nor competitors for centuries.
The purpose of the present volume
The purpose of the present volume is to analyze the lines of continuity and/or discontinuity that the fortune of scientific syllogism enjoyed in the history of philosophy and particularly in the long period of time from Avicenna to Hegel. What follows is a short introductory overview on its manifold contributions on the matter, leaving to the reader the reference to the subsequent essays needed for further depth on the subject.
The first essay of this collection deals with the age of Medieval Islamic philosophy, in which the incubation and development of the Aristotelian logical knowledge is strong. In his contribution, Allan Bäck examines the reception and reworking of the syllogistic doctrine by Avicenna, considering some of his additional specifications.
In particular, Avicenna’s presupposition of the actual existence of the involved terms is noteworthy, together with his introduction of some complex variables, such as the temporal duration implied in existential assertions, the modal value in effect, and the status of the “quiddities” under analysis (whether the essence of the object should be understood in itself, in re or in intellectu).
Taking into account such additional conditions has inevitable repercussions on the following conversion rules, as in the case of mixed-modal syllogisms. Regarding the latter, Avicenna chose to maintain the stance set by Aristotle, Alexander and Philoponus against the innovatory corrections being brought by the majority of the remaining commentators.
Without going into detail, it is interesting to ascertain that some of the logical positions defended by Avicenna actually depend on metaphysical views (not vice versa) as, for example, the fact that the existential condition required by propositions of logical necessity seems to be satisfied, if not by a hypothetical existence in the intellect, by an actual existence within the divine mind, being it the supreme guarantor of the kingdom of necessity.
After the splendour of medieval logic, and scholastic logic in particular, the fortunes of syllogism were largely reduced by a certain humanistic ideology that was hostile, as a matter of principle, to the excessive formalism of Christian aristotelianism which had been felt as the West thought’s cumbersome inheritance.
Such a humanistic ideology was carried out in an increasingly prejudiced way against scholasticism, its logic, and everything one might presume it represented (verbosity, sophistry, murkiness and so on). As we can learn, for instance from Lorenzo Valla as stated in his Dialectical Disputations, various accusations were addressed at that time against scholastic logic. Apparently, those accusations self-nourished until they became so widespread that they have influenced even our sector of studies up until a few decades ago.
The content of those critiques were basically the charges of excessive formalism, of making abstractions without actual meaning, of ruining the beauty of classical Latin in favour of an almost made-up technical language whose grammar did not take into account the mundane and which disregarded the ordinary common manner of speaking. In this way the preconceived stereotype was reinforced, with the result that scholastic logic and syllogism as its key instrument were basically regarded as useless and worthless exercises.
In his contribution, Alan R. Perreiah is capable of showing the superficiality of such judgements as “gratuitous, misleading, and demonstrably false,” and that, no matter how widespread, they were built on weak and self-conditioned foundations. In fact, during the Renaissance, there was an appreciation of the traditional logical studies which is proven by an impartial analysis of the publications and the editorial market on the subject between the fifteenth and sixteenth centuries.
During this time, printed works on Scholastic logic greatly outnumber that of humanistic literature intended for a broad audience (e.g. Latin and Greek classics).
This is a telling state of affairs that provides evidence in regard to a rather lively continuity of interest (and corrects much of what was believed up to a short time ago on this matter). So one can perhaps affirm that the history of syllogism in the Renaissance period remains to be fully covered beyond the reigning prejudice against it.
Such a history remains to be investigated more thoroughly, perhaps in universities or religious colleges—environments less exposed to the influence of those who would neglect the medieval acquisitions without being aware of, or willing to give credit to, those vertiginous philosophical developments previously reached in the field of logic and, notably, in the theory of syllogism.
Following this general prejudicial tendency, a progressive rejection of the empirical results of Aristotelian science is realized by the seventeenth century.
This happened together with a critical devaluation of syllogism, which had traditionally been the paradigmatic way of exposition favoured for those outdated outcomes. In fact, the reason which Descartes and his contemporaries adduced for this marginalization regarded the utility and the effectiveness of syllogism as such, flawed by the fact of not being functional for the growth of the body of scientific knowledge.
They objected to the fact that first, there was no certain criterium for distinguishing an informative syllogism from a non-informative one; and, secondly, the capacity to find something new by using such a logical structure was in doubt.
The state of the structure gave the impression of being simply apt at organizing previously acquired knowledges within its own schema without concluding anything that was not already given in the premisses or that was recreated as a posteriori reasoning on the grounds of previously ascertained conclusions.
In this sense, syllogism was perceived as an instrument more useful for reordering given data in a manneristic fashion, than producing new concepts. With so many discoveries being made and so much still to discover, what science required was content rather than form.
Hence, the expectations of Descartes for a strong way of knowing were such that it could allow something indistinct to be established as evident; above all he was expecting that such a way of knowledge could permit the recognition of an object as self-evident and that such a discovery might become the foundation for new, grounded, certainties.
From his point of view, syllogism failed to challenge intuitions on both a heuristic and a recognition level, neither being able to impose itself as the intellectual instrument to comprehend the evidence or for making new scientific detections. As is made clear by Stephen Gaukroger in his essay, Descartes’ syllogism is not “compressible” in a more immediate equation of non-inferential understanding. All in all, Descartes and the majority of his contemporaries basically contest the syllogism’s two characteristic qualities: (1) its prescriptive character and (2) its compulsory paths to which logicians of ascendant scholastics were obliged to bind their reasoning. That was why Cartesians and non-Cartesians alike found themselves favouring general common sense over what they regarded as the not-always-perceptible transparency of mnemonic schematisms and artefact figures of thought.
In his turn, Hobbes expressed other concerns about the merit of traditional syllogistic; because it seemed to be something, he said, that all men endowed with a good natural logic would have already been able to understand without such additional artifice.
Nonetheless, Hobbes recognized the value of such a doctrine with Aristotelian ascendence and in turn he offered an extensive treatment of syllogism, which we can still read in the first part of his De corpore.
In conformity with the general consensus on the matter, Hobbes set the value of syllogisms that were not of first figure aside, focusing on those with all the universal and affirmative premisses as well as concentrating his thoughts on them, with the bonus of grounding them in some of his own peculiar linguistic assumptions.
As Douglas M. Jesseph noted, a hobbesian study of syllogism availed itself of a proper nominalistic theory of words which had been previously developed and which were still operating in the background. Basically, it was the idea according to which names are just mere signs of things and because their attribution to external world items is arbitrary in substance, they remain effective solely on the merits of common convention.
Accordingly, although general names allow the designation of things in a universal fashion, that always happens with a meaning that works only in so far as it has been previously conventionally stipulated. The syllogistic structure too, as a superstructure with a logical-linguistic nature, is inevitably affected by this implicit stipulative assumption.
Therefore, some considerable consequences of this consideration follow, as the abandonment of the existential import that was sometimes supposed in the Aristotelian categorical syllogism, and the admission of equalizing hypothetical syllogisms to the categorical ones, based on the common speculative character that comes from an essentially arbitrary act such as the imposition of names to things.
Such arbitrary designations, however, do not impede the correct presumptions of inferences that may come from the associations of general names; this is exactly the role that, in Hobbes’ perspective, should
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