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 While Historians­-of-Mathematics antedate formulae and proofs, from years (Boole to Peirce) to centuries (Borda to Lull), graphs and schemas prove a spot of bother. While an odd Oxfordian still mistakes Bruno for Harry Potter (if not Dee), Wildgen cuts to the chase: “Bruno’s parallel work on cosmology and artificial memory [formed] a new model of semantic fields which was so radical in its time that the first modern followers (although ignorant of this tradition) are the Von­-Neumann automata and neural net systems.”—and, more plain to the eye, the diagrams of Venn (Euler), Hasse (Vogt) et al. Being technologists, not historians, we defer to sharper quills—to wit, Eco 1994: “Lull [reiterates] that if metaphysics considers things as they exist outside our minds,” (i.e. schematic ontology, not ‘New Age’ astro­-magick frippery) “and if logic treats them in their mental being, the art can treat them from both points of view [hence] to more secure conclusions than logic alone, ‘[thus] the artist of this art can learn more in a month than a logician can in a year’. What this audacious claim reveals, however, is that, contrary to what some later supposed, Lull’s art is not really a formal method.”

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fig.70—Lull’s “cognates” | our media mix | Lull’s “dissonants”


—if not formal, then how is it? Unlike Bruno’s figurae, Lull’s combinatoires are mechanically transparent—even if both are theoretically opaque. Lull married topological diagrams to lexical tables by strict vows, lest “the virtuous student” dial up dastardly queries like ‘Will full extension of God’s Glory end in eternal privation?’ Yikes! In more practical terms: in 1679, by divorcing notational form from denoted content, Leibniz surmised that “all derived concepts originate from the combinations of primary ones, and those further compounded from the combination of the compounded; but care must be taken, lest useless combinations be made by joining together things that are incompatible with one another.” Nevertheless, we sample a ninefold of concepts from Lull’s Ars­ Infusa as filed under Æqualitas. As we no longer fear the Church will hang us by the thumbnails, we may contemplate terms of mediation: while armed to the lexical teeth, we still need to slice ad verba every “Universe of Discourse” (Boole) from Orthodoxy to Hydrodynamics to post­-Nietzscheism. 

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