This paper discusses and compares a number of influential definitions of the syllogism in the history of logic. We start with Aristotle, and offer a dialogical interpretation of his definition of a syllogism in the Prior Analytics. We then briefly discuss Boethius and Robert Kilwardby, and finally focus on Ockham and Buridan’s respective definitions. What we observe in these authors over the centuries, especially with Ockham (but with the exception of Boethius), is a diminished focus on the pragmatic dimension of applying syllogisms in certain contexts, in particular but not exclusively dialectical/dialogical contexts. We also observe increased focus on the formal properties of the syllogistic system, in particular the notions of figure and mood (though not in Buridan). And thus, taken as a whole, this analysis may be taken to illustrate a general tendency to move away from logic conceived as a tool for specific applications, and towards a focus on logical theories conceived as objects of study in their own right.
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It gives me great pleasure to contribute to this volume in honor of Claude Panaccio. He may not even remember, but Claude played a key role in the development of my career at its early stages. In 2000, I was writing my master’s thesis at the Institute for Logic, Language and Computation in Amsterdam; perhaps foolishly, I had chosen medieval logic, and Ockham’s supposition theory in particular, as my topic, even though there was no one there with the right expertise to supervise me. Fellow Brazilian philosopher Ernesto Perini put me in touch with Claude, and immediately Claude offered me guidance per email, which turned out to be crucial for the whole thesis-writing process. After this, we stayed in touch, and in 2002 he put me in touch with Luisa Valente, who was organizing the European Symposium for Medieval Logic and Semantics in Rome. Thanks to Claude’s introduction, I could attend the Symposium, the first of seven in a row. Claude and I only met in person for the first time a few years later, if memory does not fail me at the European Symposium for Medieval Logic and Semantics in Cambridge (2004). Since then, we had the opportunity to meet on a number of occasions, including two of his yearly workshops on medieval philosophy in Montreal. Throughout, Claude has had nothing but words of support and encouragement, and the occasional well-placed criticism of my work (much welcome!). Besides being a fantastic scholar, Claude is a very generous person, and this reveals itself in particular in his infallible support for young scholars. With his retirement, I suspect Claude will remain as active as always, and I look forward to continuing our conversations on medieval philosophy and other matters. Thank you, Claude!
I’ve benefited greatly from engaging with the work of P. Thom on the topic, in particular (Thom 2016); indeed, there is quite some overlap between my analysis and his.
Notice however that the study of the (meta-)properties of the system is also undertaken by Aristotle himself in APri (though the bulk of the text is dedicated to applications), and applications remain of crucial importance for later authors too.
In what follows I will use the neologism “syllogismos” when referring to Aristotle’s notion. This is because his own use of the term appears to be broader than what we now understand as a “syllogism” (i.e. covering arguments that do not have the familiar two premises, one conclusion structure, all of which are categorical sentences of the A, E, I, O forms), but it is narrower than our current notion of a deduction. (Striker translates it as “syllogism,” Smith as “deduction”; we arguably need something in between.)
This gloss should not be understood in the sense that a unique set of premises is what allows for the derivation of a given conclusion; often, alternative sets of premises are equally able to produce a given conclusion. Rather, it should be understood as stating that the set of premises is sufficient for the necessary truth of the conclusion (no “hidden premises”), and that the removal of any of the premises from the set would make the conclusion no longer deductively derivable. (I owe this point to P. Thom.)
See Barnes’ interpretation (1969) of Aristotle’s theory of demonstration presented in APo, according to which the primary use of this theory was didactic, thus referring to a teacher-pupil form of interaction.
“It [a syllogismos] is a demonstration whenever the syllogismos is from true and primary things or from similar things that have attained the starting point of knowledge about themselves through true and primary things. Dialectical syllogismoi syllogise from reputable opinions.” (24a30–b3, as quoted in Duncombe 2014, 442).
There are issues pertaining to propositional identity arising in connection with this requirement (e.g. are logically equivalent propositions such as AiB and BiA the same?), but we will set those aside for the present purposes.
Boethius, De syllogismo categorico, 821A: “Syllogismus est oratio in qua positis quibusdam atque concessis, aliud quiddam quam sint ea quae posita et concessa sunt, necessaria contingit per ipsa quae concessa sunt” (my translation).
According to Thom (2016), this approach echoes that of Averroes.
Ockham, SL III-1, c.1, OPh I, 59–61: “Syllogismus est oratio in qua ex duabus praemissis, dispositis in modo et in figura, de necessitate sequitur conclusio. Et ad istam definitionem nihil refert an praemissae sint verae vel falsae” (my translation).
This seems to be presented as a subdivision of the fallacies extra dictionem; one wonders if the distinction would also apply to the fallacies in dictione.
Ockham, SL III-4, c. 15, OPh I, 2–4: “Post fallacias penes quas peccant argumenta peccantia in forma dicendum est de fallaciis penes quas non peccant argumenta sophistica, sed penes quas peccat opponens in arguendo contra respondentem” (translation by P. Thom).
Ockham, SL III-4, c. 15, OPh I, 5–7: “Quarum prima est petitio principia, quae tunc accidit quando opponens, quamvis inferat conclusionem quam intendit, tamen non potest convincere respondentem, eo quod accipit quod deberet probare” (translation by P. Thom).
Buridan, SD, 5.1.3, 308: “Syllogismus est oratio in qua quibusdam positis necesse est aliud accidere per ea quae posita sunt, ut ‘omne animal est substantia, omnis homo est animal; ergo omnis homo est substantia’; hoc totum est una oratio in qua quibusdam positis, scilicet duabus praemissis, necesse est aliud accidere, id est sequi, scilicet conclusionem” (translation by G. Klima).
Buridan, Quaestiones 1, q. 3: “Item, notetis quod quamuis omnes communiter dicant quod haec dictio ‘positis’ debet glossari id est dispositis in debito modo et in debita figura, ad excludendum inductionem et multas alias consequentias inordinatas, tamen ego credo quod illa expositio non sit conueniens: quia non debet declarari quid est syllogismus ex eo quod est in bono modo et in bona figura, immo ex ista definitione declarabitur qui sunt modi debiti et qui sunt inutiles. Nec est uerum quod omnes syllogismi sint in istis tribus figuris de quibus determinatur in isto libro, ut postea uidebitur. Et ideo credo quod quotienscumque aliquibus praemissis positis sequitur de necessitate conclusio, non solum uocaliter, sed etiam mentaliter ab illis praemissis et ab unaquaque illarum diuersa, tunc semper est bonus syllogismus, dum tamen sit consequentia formalis, de qua semper intelligimus in hoc libro” (translation by P. Thom).
This is again the delicate issue of propositional identity noted above.
For example, the conversion rules may be interpreted as non-syllogistic because “No A is B” ultimately means the same as “No B is A,” as they are logically equivalent. Other than this, I have not found much in Buridan’s discussions pertaining to the multiple-premise requirement.
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Dutilh Novaes, C. (2017). The Syllogism as Defined by Aristotle, Ockham, and Buridan. In: Pelletier, J., Roques, M. (eds) The Language of Thought in Late Medieval Philosophy. Historical-Analytical Studies on Nature, Mind and Action, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-66634-1_14
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