THE PRINCIPLE OF HOPE

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rationalist scholastic Ramon Lull had made a device around 1300 by means of which every kind of deductive derivation was to be discovered and checked. The device
(‘Instrumentum ad omnis scibilis demonstrationem’) consisted of a system of concentric circles, on each of which a group of concepts was spread in the shape of a fan.
By moving these circles all possible combinations whatsoever between subject and predicate were supposed to be achieved; whereby the number of possible subjects
and that of possible basic predicates (predicables), and consequently the quantity of discs was fixed. There was thus a Figura Dei which ‘contained’ the whole of
theology, a Figura animae which ‘contained’ the whole of psychology, and a Figura virtutum with the seven virtues and deadly sins in alternately blue and red chambers
(v. the details in J. E. Erdmann, Grundriss der Geschichte der Philosophie I, §206, 4–12; table in Stöckl, Geschichte der Philosophie des Mittelalters II, 1865, p. 936).
The Lullian art thus sought to give instructions for discovering what is categorially definable, scientifically distinguishable, combinable, and provable in every object. And
Lull's hope was simply that the deduction machine of knowledge should encompass and exhaust every variation of cognition that was at all meaningfully possible. It
demonstrates literally ad oculos, so that anyone eager for knowledge can also see and not merely understand the arch­rationalist derivation of individual definitions from
ideas. All this in the most abbreviated mode of deduction, based on Aristotelian topics, though also not unconnected with the Plotinian, indeed cabbalistic doctrine of
emanation of the world from ideas. At any rate the most astonishing machine was in fact produced, that of an ‘Ars magna’ as both Ars inveniendi and Ars
demonstrandi, portrayed in symbols, circles, tables, in the reductions of a kind of logical logarithmic clock. Giordano Bruno sought to improve the Lullian art by
decreasing the circles, and Pico della Mirandola connected it for the first time with Pythagorean arithmetic. The need in bourgeois calculation for an arithmetical
universal derivation of all that is given from a few logical elements or principles (‘first truths’) ensured that the Lullian art was not forgotten anyway, at least with regard
to its intention. Leibniz began his career with the work ‘De arte combinatoria’, 1666, in which, following Lull and Bruno, he treated the modes of combination of
concepts as calculable; so that one would be able to demonstrate an error in reasoning with the same clarity and certainty as an arithmetical error. Throughout his life
Leibniz searched for the valid combination theory composed of an ‘alphabet of ideas’, according to which new truths can be found mechanically as it were. This ‘Ars
combinatoria’