«Omnia numerorum videntur ratione formata». A ‘Computable World’ Theory in the Early Medieval Philosophy Luigi Catalani University of Salerno, Italy

The digital philosophy is strictly speaking a tional paradigm’. At the end of the tenth new speculative theory, developed in recent century, this paradigm becomes the theo- decades by Edward Fredkin, Gregory Chai- retical background for the development of a tin and Stephen Wolfram, who place the bit concept that, although not in a systematic at the foundation of reality and explain the form, outlines the contours of an ordered evolution of reality as a computational pro- vision of the world that updates the Py- cess. This theory actually reinterprets some thagorean dream. previous philosophical intuitions, starting The paper focuses on the works of au- from the Pythagorean theory of numbers as thors such as Abbo of Fleury (945-1004) the beginning of all things and as a criterion and Gerbert of Aurillac (946-1003). Abbo, for the comprehension of reality. monk and abbot of (near Or- Significant antecedents of this com- léans), is the author of a comment on the putational philosophical approach, how- Calculus, a manual of calculation wrote in ever, can be found in the tradition of late the fifth century by Victorius of Aquitaine, antiquity and in the early Middle Ages according to which the arithmetic is the sci- too. In particular, in the Western thought, ence of unity. The theoretical basis of the there is a path that goes from Augustine of work of Abbo is the famous verse of Wis Hippo (354-430) to the school of Chartres 11, 21 (Omnia creata sunt in numero mensura (twelfth century), passing through Cassio- et pondere): Abbo believes that the man dorus (485-580) and Severinus Boethius can, starting from the contemplation of the (480-524), who defines thequadrivium number, size and weight, go back to the and in particular the study of mathematics knowledge of the principles of the cosmos. a means to get closer to perfection and to Gerbert of Aurillac ( Sylvester II) is perceive the infinite De( institutione arith- the author of many mathematical writings metica). (Libellus de numerorum divisione, De geome- One of the less investigated chapters tria, Regula de abaco computi, Liber abaci) set of this ‘pre-history’ of the digital philoso- in a logical and metaphysical framework. phy is placed in the so-called Ottonian Re- He, too, believes that the natural world is naissance, when we can identify theorists governed by mathematical relations, so the of what has been called – in reference to study of numbers is not for its own sake modern authors as Leibniz – ‘computa- in itself but the best way to access to the

29 Accepted abstracts laws that govern the universe. His passion This amazing epistemological value of for arithmetic arises from the awareness medieval mathematics is the result of an that «the numbers contain within them, or approach to the numbers, typical of these originate, the beginnings of all things», ac- authors, in which the practical problems cording to a principle expressed in many of (the computus, the land surveying, the as- his writings, so the knowledge of numbers trology) are based on theoretical issues of is set at the beginning of any further knowl- the first order. This speculative attitude edge. is not unusual in the history of Western It would not be inappropriate to apply thought, but it is significant that it will oc- to these philosophers the modern concept cur again in this era – frequently consid- of mathesis universalis (universal mathemat- ered among the darkest ones – through the ical science), which is the project of a gen- double reference, on the one hand to the eral science modeled on mathematics that scientific tradition that is rooted in ‘numeric leads to a certain knowledge (the term was Pythagorean exemplarism’, the other side to employed by Leibniz to describe his combi- the (neo)Platonic tradition. natorial art, or characteristica universalis).

Sources [s1] Severinus Boethius, De institutione arithmetica, (ed.), Oxford University Press, Oxford, 2003. H. Oosthout, J. Schilling (eds.), Brepols, Turnhout, [s3] Gerberti postea Silvestri II papae Opera Mathema- 1999. tica, N. Bubnov (ed.), Friedlander, Berlin 1899, repr. [s2] Abbo of Fleury and Ramsey, Commentary on the Olms, Hildesheim, 1963 (2005). «Calculus» of Victorius of Aquitaine, A.M. Peden

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