Abstract
In his Tractatus de Consequentiis, the 14th century logician John Buridan states a theorem, which reads like a refutation of Aristotelian Syllogistics. Syllogistics in its usual form, indeed, faces problems when propositions about the divine persons are involved, and, in some cases, when past- or future-tense propositions occur. Buridan offers different ways of overcoming some of these obstacles. The first aim of this paper is to analyse these ways, the second aim is to draw some conclusions concerning Buridan’s understanding of logic and its relation to theology.
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Notes
Words in this paper that are written in capital letters cannot be found in the text of Buridan.
More detailed: ‘Under the guidance of Pope Innocent III, a Paris-trained theologian, the Fourth Lateran Council condemned Joachim, and enshrined the Trinitarian formulation of Peter Lombard as the standard of orthodoxy for centuries to come: “we believe and confess with Peter Lombard that there is some one highest thing, incomprehensible and ineffable, that is truly Father, Son, and Holy Spirit; three persons at once, and singly each of them; and therefore in God, there is only a Trinity, not a quaternity; since each of the three persons is that thing, namely substance, essence, or divine nature [...].” (Denzinger and Schonmetzer, Enchiridion symbolorum, 261-262 (nos. 803—808))’ (Shank 2014, p. 61). Compare also Maierù 2005, p. 402.
Note that ‘formal to the form’ includes syllogisms with no counterexamples at all. Translation by S. Read (Buridan 2015, p. 119). The original passage in Hubien (1976, p. 86) is: [E]go de cetero uocabo syllogismos formales contra quorum formam non erit dare aliam instantiam quam in terminis diuinis.
Buridan describes this in the first sentence of Buridan (2015, Book III, Ch. 4).
The positive theoretical effects of this convention are discussed in Parsons (2008, pp. 162-164).
At this point, we should note that Buridan is not strictly separating consequences from conditionals and inferences in the text. We refer the reader to Dutilh Novaes (2007, p. 100) for more details on this matter. Furthermore, it is not completely clear to which extent Buridan distinguishes between syllogistic consequences and consequences as defined in Book I of Buridan (2015). Since he is not particularly clear in drawing distinctions between consequences and conditionals, we assume that he extends his notion of consequence on the fly, so to speak, when he comes to the matter of syllogistics in Book III.
A difference is, for example, that Buridan’s notion is more general in the sense that his definition includes the case in which propositions of relevance to the consequence are not mentioned by a speaker. (See Dutilh Novaes 2007, p. 92)
Buridan calls it bona consequentia. (See Hubien 1976, p.21)
It can be argued that Buridan has a modal notion of consequence. Of course, exploring the logical status of his necessity requirement and, therefore, the identification of a suitable semantics would need an extensive discussion we cannot give in the narrow scope of the present paper. We therefore have to leave it by assuring the reader that this does not affect matters here. Furthermore, it can be argued that (sometimes) Buridan means true/valid consequences by ‘consequentiae’ (see Bos 1976, p.63). However, this does not change matters in our context, either.
Buridan’s treatment of material and formal consequence is extremely interesting and is discussed at length in Dutilh Novaes (2007); however, we do not need to concern ourselves with the finer details here.
‘Deinde [...] supponenda est quaedam diuisio consequentiarum, scilicet in materialem et formalem.’ (Hubien 1976, p.22)
This restriction will be explained in the next section.
There is a printing error in the translation by S. Read in Buridan (2015, p. 73). We have added the part in parentheses because the passage in Hubien (1976, p. 29) reads: ‘Quia haec: “B est A” si praedicatum non sit ampliatiuum, non habet causas ueritatis nisi quia quod est B est A; sed haec: “B erit A” habet causas ueritatis uel quia quod est B erit A uel quia quod erit B erit A.’
Buridan considers this sentence to be true: ‘Item, ad remotionem dubii, notandum est quod cum dico ‘homo est mortuus’ non opertet quod praedicatum supponat pro praesentibus, immo supponit pro praeteritis, eo quod ipsum est praeteriti temporis; tamen oportet, cum uerbum sit praesentis temporis, quod supponat pro his quae respectu huius praesentis sunt praeterita.’ (Hubien 1976, p. 29).
The original passage from Hubien (1976, p. 42) reads: ‘Quia licet ista concedatur in diuinis: “quod est pater est filius” tamen ista non concederetur: “Pater est filius” sed hoc est speciale sanctae trinitati, eo quod ipsa simul est trinitas et indiuisa unitae, quod non uiderunt communiter philosophi gentiles.’
We think that the signification changes as well, but ultimately it is supposition that must change in order to make the point.
Burdian does not explicitly say that this consequence is not a good one, however, he does mention good consequences several times in this context. He does not explicitly say that the first sentence is false, either, only that it is not granted. (See Buridan 2015, pp.83-84)
This is so, even if the consequence relation is to be understood modal, since it seems appropriate to assume that truths about the divine persons are necessarily true. Note that when \(\Box \varphi \vee \Box \neg \varphi \) and \(\Box \psi \vee \Box \neg \psi \) are true, then \(\Box (\varphi \rightarrow \psi )\) is equivalent to \(\varphi \rightarrow \psi \).
Note that Buridan does not allow for higher types of objects or identities of predicates etc. (see Section 2.1).
This treatment of the Trinity exposes a possible tension between Buridan’s nominalisitic account on supposition theory and the doctrine of the Holy Trinity. One might wonder if his approach solves this problem only at the cost of splitting the Trinity further up: instead of three divine persons which are one in essence Buridan’s treatment leads to four distinct entities in a strange ‘equivalence relation’.
Buridan differs from Aristotle in his identification of valid syllogistics, but the details do not bother us here.
Buridan says ‘moods in which one can infer a conclusion in the customary way of speaking’, but as he has stated in the First Conclusion that there are no such moods, he must mean the usual Aristotelian valid moods, in which no divine terms and no ampliation occurs.
For the history and the background of this problem see also Marshall (2014).
Or, should we say: He who is the Essence is the Father?
‘Syllogistic moods’ is used as per the standard terminology of syllogistics, which makes a distinction between moods and figures of a syllogism. Note that using ‘qui/quod est’ to block ampliation does not alter the mood through its restrictive usage (see Appendix).
‘Since university statutes forbade arts masters from teaching or writing about theology, Buridan produced no theological works.’ (Zupko 2018) Moreover, Buridan was a skilled teacher, and it seems appropriate to stop students at a point where they may want to go deeper into a ‘big debate’ by reminding them of the narrower scope of the present course.
Even if Buridan meant ‘qui/quod est’ by ‘another way of speaking’, this could still have a polemic touch (‘I offer you “qui/quod est”, if this still doesn’t fit for your purposes, then good luck finding a more appropriate way of speaking – speaking of something that is obviously very hard to speak about in reasonable terms’).
See Bröcker 1964, p.221.
Perler argues that Bacon’s view of logic was not so negative as it is usually claimed, see Perler2005, pp. 394-397.
In Zupko (1998) it is argued that the common view according to which the theologians were better philosophers than the Arts Masters is wrong.
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Toppel, M., Ramharter, E. Buridan’s Secular Demarcation of Logic. Philosophia 49, 1267–1288 (2021). https://doi.org/10.1007/s11406-020-00270-x
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DOI: https://doi.org/10.1007/s11406-020-00270-x