John R. Welch

Llull and Leibniz both subscribed to conceptual atomism: the belief that the majority of concepts are compounds constructed from a relatively small number of primitive concepts. Llull worked out techniques for finding the logically possible combinations of his primitives, but Leibniz criticized Llull’s execution of these techniques. This article argues that Leibniz was right about things being more complicated than Llull thought but that he was wrong about the details. The paper attempts to correct these details.

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 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

How can the objectivity of an argument’s conclusion be determined? To propose an answer, this paper builds on Betz’s view of premises as hedged hypotheses. If an argument’s premises are hedged, its conclusion must be hedged as well. But how? The paper first introduces a two-dimensional critical grid. The grid’s vertical dimension is inductive, reflecting the argument’s downward flow from premises to conclusion. It specifies the inductive probability of the conclusion given the premises. The grid’s horizontal dimension is epistemic, focusing on the premises without dropping down to the conclusion. It evaluates the epistemic probability of the premises when conjoined. This two-dimensional grid is then applied to three kinds of cases: vertical and horizontal evaluations rely on point-valued probabilities; vertical and horizontal evaluations rely on interval probabilities; vertical and horizontal evaluations rely on non-numeric plausibilities. The result is that, in each case, the argument’s conclusion can be assigned a credence tag, as it were, that reflects a critical appraisal of its objectivity. Reference Betz, Gregor. 2013. “In defence of the value free ideal.” European Journal for Philosophy of Science 3, 207–220.