Situating Kant’s Pre-Critical Monadology: Leibnizian Ubeity, Monadic Activity, and Idealist Unity

This essay examines the relationship between monads and space in Kant’s early pre-critical work, with special attention devoted to the question of ubeity, a Scholastic doctrine that Leibniz describes as “ways of being somewhere”. By focusing attention on this concept, evidence will be put forward that supports the claim, held by various scholars, that the monad-space relationship in Kant is closer to Leibniz’ original conception than the hypotheses typically offered by the later Leibniz-Wolff school. In addition, Kant’s monadology, in conjunction with God’s role, also helps to shed light on further aspects of his system that are broadly Leibnizian, such as monadic activity and the unity of space

An Informational Interpretation of monadology

In this paper, I will try to exploit the implication of Leibniz's statement in Monadology (1714) that "there is a kind of self-sufficiency which makes them [monads] sources of their own internal actions, or incorporeal automata, as it were" (Monadology, sect.18). Leibniz's monads are simple substances, with no shape, no magnitude; but they are supposed to produce the phenomena resulting from their activities, which for us humans look as the whole world, the nature. The activities of a monad are characterized by mental terms, perceptions (internal states) and appetites (which change the internal state). By means of perceptions, a monad becomes a "perpetual living mirror of the universe"; it can receive the information of other monads and it can send its own, in turn, to others. The communication and interconnection thus produced result in the physical and the psychical phenomena observed by us, humans. According to Leibniz, all monads are governed by the teleological law given by the God, and the world of phenomena are governed by the causal and mechanical law. Leibniz argues that there is a pre-established harmony among the monads so that this double character is no problem. Now, I will propose an informational interpretation of monadology, which regards the monads as an automaton governed by the God's program and arranged appropriately; and I will argue that Leibniz's scenario can be defended in terms of this interpretation. The crucial part of this interpretation is that the God's program and the monads' activities are related with the phenomenal world by means of a coding by God. This interpretation is also defended on the textual basis, with a special reference to Leibniz's distinction between primitive and derivative forces. Drawing on R. M. Adams's careful reading of Leibniz's texts (Leibniz: Determinist, Theist, Idealist, 1994), I will argue that his rendering is quite in conformity with my interpretation, although he does not seem to be aware of the notion of coding

Initial Semantics for Reduction Rules

We give an algebraic characterization of the syntax and operational semantics of a class of simply-typed languages, such as the language PCF: we characterize simply-typed syntax with variable binding and equipped with reduction rules via a universal property, namely as the initial object of some category of models. For this purpose, we employ techniques developed in two previous works: in the first work we model syntactic translations between languages over different sets of types as initial morphisms in a category of models. In the second work we characterize untyped syntax with reduction rules as initial object in a category of models. In the present work, we combine the techniques used earlier in order to characterize simply-typed syntax with reduction rules as initial object in a category. The universal property yields an operator which allows to specify translations---that are semantically faithful by construction---between languages over possibly different sets of types. As an example, we upgrade a translation from PCF to the untyped lambda calculus, given in previous work, to account for reduction in the source and target. Specifically, we specify a reduction semantics in the source and target language through suitable rules. By equipping the untyped lambda calculus with the structure of a model of PCF, initiality yields a translation from PCF to the lambda calculus, that is faithful with respect to the reduction semantics specified by the rules. This paper is an extended version of an article published in the proceedings of WoLLIC 2012.Comment: Extended version of arXiv:1206.4547, proves a variant of a result of PhD thesis arXiv:1206.455

An algebraic basis for specifying and enforcing access control in security systems

Security services in a multi-user environment are often based on access control mechanisms. Static aspects of an access control policy can be formalised using abstract algebraic models. We integrate these static aspects into a dynamic framework considering requesting access to resources as a process aiming at the prevention of access control violations when a program is executed. We use another algebraic technique, monads, as a meta-language to integrate access control operations into a functional programming language. The integration of monads and concepts from a denotational model for process algebras provides a framework for programming of access control in security systems

Mind and Body

This chapter discusses Gottfried Wilhelm Leibniz’s philosophical reflections on mind and body. It first considers Leibniz’s distinction between substance and aggregate, referring to the former as a being that must have true unity (what he calls unum per se) and to the latter as simply a collection of other beings. It then describes Leibniz’s extension of the term “substance” to monads and other things such as animals and living beings. It also examines Leibniz’s views about the union of mind and body, whether mind and body interact, and how interaction is related to union. More specifically, it asks whether mind and body together constitute an unum per se and analyzes Leibniz’s account of the per se unity of mind-body composites. In addition, the chapter explores the problem of soul-body union as opposed to mind-body union and concludes by discussing Leibniz’s explanation of soul-body interaction using a system of pre-established harmony

Systems, Resilience, and Organization: Analogies and Points of Contact with Hierarchy Theory

Aim of this paper is to provide preliminary elements for discussion about the implications of the Hierarchy Theory of Evolution on the design and evolution of artificial systems and socio-technical organizations. In order to achieve this goal, a number of analogies are drawn between the System of Leibniz; the socio-technical architecture known as Fractal Social Organization; resilience and related disciplines; and Hierarchy Theory. In so doing we hope to provide elements for reflection and, hopefully, enrich the discussion on the above topics with considerations pertaining to related fields and disciplines, including computer science, management science, cybernetics, social systems, and general systems theory.Comment: To appear in the Proceedings of ANTIFRAGILE'17, 4th International Workshop on Computational Antifragility and Antifragile Engineerin

Leibniz, the Young Kant, and Boscovich on the Relationality of Space

Leibniz’s main thesis regarding the nature of space is that space is relational. This means that space is not an independent object or existent in itself, but rather a set of relations between objects existing at the same time. The reality of space, therefore, is derived from objects and their relations. For Leibniz and his successors, this view of space was intimately connected with the understanding of the composite nature of material objects. The nature of the relation between space and matter was crucial to the conceptualization of both space and matter. In this paper, I discuss Leibniz’s account of relational space and examine its novel elaborations by two of his successors, namely, the young Immanuel Kant and the Croat natural philosopher Roger Boscovich. Kant’s and Boscovich’s studies of Leibniz’s account lead them to original versions of the relational view of space. Thus, Leibniz’s relational space proved to be a philosophically fruitful notion, as it yielded bold and intriguing attempts to decipher the nature of space and was a key part in innovative scientific ideas