Ramon Llull was acutely aware of Islamic and Jewish divergences from Christian belief. He undertook a quest for "necessary reasons" to show that, where these belief systems diverged, Christian belief is true. Though largely self-taught, Llull managed three (perhaps four) stays at the University of Paris. Encounters between the incandescent Mallorcan and academic orthodoxy contributed hugely to Llull's changing conception of necessary reasons. These changes are abundantly documented in Anthony Bonner's The Art and Logic of Ramon Llull.
Llull's understanding of necessary reasons is different in the Ars magna's quaternary phase, its ternary phase, and a post-Art logical phase. In the quaternary phase, necessary reasons are often presented as demonstrative; fully ten works use the term in their title. Although Llull meant 'demonstration' in a sense broader than Aristotle's, Parisian academics objected, mistakenly thinking he was trying to prove dogmas like the Trinity and Incarnation through Aristotelian demonstrations propter quid and quia. As Bonner conjectures, this may be why no work from the ternary phase mentions demonstration in its title and why demonstration is given a "very reduced role" in this phase (187). Finally, in the post-Art phase, necessary reasons take syllogistic form to approximate Aristotelian demonstrations and engage Averroists of the Faculty of Arts on their own ground.
In these shifting configurations, then, necessary reasons are frequently understood as demonstrative. But Llull used broad and narrow senses of 'demonstration'. The broad sense includes any persuasive argument (267). The narrow sense, which is "discussed almost obsessively throughout [Llull's] career" (269), admits three types of demonstration: propter quid, quia, and per aequiparantiam (65, 266–69). The first two are the classic Aristotelian structures; the third is Llullian.
To see what Llull meant by demonstratio per aequiparantiam (demonstration by equivalence), recall his view of the divine "dignities" such as goodness, greatness, power, will, justice, etc. He refers to three of these dignities in the following sketch of demonstration by equivalence (DBE):
[W]hen a demonstration is made by means of things equal to one another, as for instance when one demonstrates that God cannot sin because his power is of the same essence as his will, which in no way desires to sin, and this will is of the same essence as justice, which is completely opposed to sin, which accords with injustice.(65)
Although Llull emphasizes the theological uses of DBE, he indicates non-theological applications as well (65, 221–22, 224). Potentially, then, DBE is an extremely fecund idea. But here we encounter both the chief virtue and major limitation of this volume. The virtue is that the work succeeds admirably in the aim announced in its subtitle: to provide a user's guide to Llull's Art and logic. In particular, it lets us see how DBE was supposed to work. The corresponding limitation is frankly acknowledged by Bonner from the start. His aim, he says, "has not been to defend Llull, but rather to remain neutral in the matter of possible judgments upon his Art and logic" (xiv). Hence the critical evaluation that DBE demands is not undertaken here.
Critical points that might be developed include the following. (i) In the above-quoted passage, Llull says the dignities have the same essence; elsewhere, that they are "one in number" (271, 286). Are essential identity and numerical identity coextensive? Or does numerical identity imply essential identity, yet not the reverse? (ii) Could DBE function with a weaker relation like material equivalence? (iii) Because the dignities are supposed to be essentially and numerically equal, they convert: goodness is great, and greatness is good. But how could even divine goodness be equivalent to divine greatness? Bonner cites Cornford's view that Platonic Forms blend and suggests that this is also true of the dignities (203–04). Perhaps so, but this would require defense of a specific form of Neoplatonism. [End Page 313] (iv) Such a defense would seem to presuppose that truth is structured more like...