The advance of mechanism in science and philosophy in the 17th century created a great interest to machines or automata. Leibniz was no exception - in an early memoir Drôle de pensée he wrote admiringly about a machine that could walk on water, exhibited in Paris. The idea of automatic processing in general had a large role in his thought, as can be seen, for example, in his invention of the binary code and the so-called Calculemus!-model for solving controversies. (...) In metaphysics, the idea of an automata was expressed most clearly in the 1695 article New System of the Nature of Substances and their Communication, and the ensuing correspondence with, among others, Foucher, Bayle, Lamy, Jaquelot and Masham. In the article Leibniz discusses the soul as a spiritual machine in the context of pre-established harmony, arguing that God can "give to a substance at the outset a nature or internal force which could produce in it an orderly way (as in spiritual or formal automaton; but a free one, in the case of a substance which is endowed with a share of reason) everything that is going to happen to it, that is to say, all the appearances or expressions it is going to have, and all without the help of any created thing." The basic idea of Leibniz's spiritual machine is that the soul or entelechy is an autonomous and spontaneous unity, consisting of internal active force and producing its own perceptions (both confused and distinct). It is a self-moving machine, driven by its perceptions and appetites, but it follows (without being conscious of it) a lawful series or programme created by God. The entelechy remains the same despite undergoing an infinite number of changes. To Foucher he explained that each state of the individual substance is a consequence of its preceding one, "as if there were only God and the substance in the world". Despite this, the spiritual machine is related not only to God, but through the pre-established harmony to bodies or natural machines. However, as it is not dependent on them, the spiritual machine is superiot to natural machines. In this paper I concentrate on three moral themes related to the spiritual machine: moral deliberation, moral identity and the goal of moral action. All these themes are more or less implicit in the New System, but are discussed in more detail in the ensuing correspondence after the publication of the article. Finally, the themes are given an extended discussion especially in the second book of New Essays on Human Understanding (1704, published 1765), written partly at the same time as some of the correspondence and unpublished related material. I will first give an overview of Leibniz's position concerning the spiritual machine or automaton in the New System and then go on to explore the three moral themes one by one, as they feature in the subsequent correspondence and in the New Essays. I will show that the three topics are essential to the function of the spiritual machine – to Sophie Charlotte Leibniz wrote: "...let us say that everything in bodies happens mechanically, or in accordance with laws of motion, and that everything in the soul happens morally, or in accordance with perceived good or evil." There are many texts that anticipate the views in the New System (notably the unpublished memoir De Affectibus of 1679) and Leibniz continued to discuss its themes later on (in addition to correpondence, for example, in Theodicy of 1710 and Monadology and Principles of Nature and Grace of 1714). Here I focus on the short-term development of Leibniz's views on the topic (around 1695-1705), but I argue that his basic view of the spiritual machine did not change much after finishing the dialogue with Locke in 1704. (shrink)

In 1685, in The Art of Discovery, Leibniz set down an extraordinary idea: "The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate [calculemus], without further ado, to see who is right." Calculemus.

In 1932 Kolmogorov created a calculus of problems. This calculus became known to Deleuze through a 1945 paper by Paulette Destouches-Février. In it, he ultimately recognised a deepening of mathematical intuitionism. However, from the beginning, he proceeded to show its limits through a return to the Leibnizian project of Calculemus taken in its metaphysical stance. In the carrying out of this project, which is illustrated through a paradigm borrowed from Spinoza, the formal parallelism between problems, Leibnizian themes and Peircean (...) rhemes provides the key idea. By relying on this parallelism and by spreading the dialectic defined by Lautman with its ‘logical drama’ onto a Platonic perspective, we will attempt to obtain Deleuze's full calculus of problems. In investigating how the same Idea may be in mathematics and in philosophy, we will proceed to show how this calculus of problems qualifies not only as a paradigm of the Idea but also as the apex of transdiciplinarity. (shrink)

In this contribution we propose an agent architecture for theorem proving which we intend to investigate in depth in the future. The work reported in this paper is in an early state, and by no means finished. We present and discuss our proposal in order to get feedback from the Calculemus community.