Transcultural Philosophy and Its Foundations in Implicate Logic

This article provides a transcultural, “transversal” investigation. It starts from the philosophical problem of knowing non-knowing. In chapters 1 and 2, the first expressions of this problem by Confucius and Socrates are considered. Against this background, new transcultural working concepts are developed. A new key term to be established here is that of an “implicate logic”. It refers to the reflection of unity of unity and difference and therefore to the very condition of the possibility of (differentiating) thinking as such. In chapters 3 and 4, this train of thought is further developed under the influence of Nicolaus Cusanus, by reflecting on the first chapter of the Daodejing, and in view of important remarks by Niklas Luhmann. In chapter 5, the outcome is related to the idea of transversal reason in the philosophy of Wolfgang Welsch. As the most basic principle of (self-referential) thinking, implicate logic is to be discerned from Aristotelian (or similar traditions of) logic and Hegelian dialectics—albeit both are being tied to the former’s principle in one way or the other. In the end, an introductory outlook of a comprehensive work by the present author provides the starting point to validate the logical foundations of knowing non-knowing as a methodological foundation to further develop the fields of transcultural-comparative, trans-comparative, and global philosophy

A Decidable Class of Nested Iterated Schemata (extended version)

Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called "iterated schemata", allow to express such patterns. Schemata extend propositional logic with indexed propositions, e.g. P_i, P_i+1, P_1, and with generalized connectives, e.g. /\i=1..n or i=1..n (called "iterations") where n is an (unbound) integer variable called a "parameter". The expressive power of iterated schemata is strictly greater than propositional logic: it is even out of the scope of first-order logic. We define a proof procedure, called DPLL*, that can prove that a schema is satisfiable for at least one value of its parameter, in the spirit of the DPLL procedure. However the converse problem, i.e. proving that a schema is unsatisfiable for every value of the parameter, is undecidable so DPLL* does not terminate in general. Still, we prove that it terminates for schemata of a syntactic subclass called "regularly nested". This is the first non trivial class for which DPLL* is proved to terminate. Furthermore the class of regularly nested schemata is the first decidable class to allow nesting of iterations, i.e. to allow schemata of the form /\i=1..n (/\j=1..n ...).Comment: 43 pages, extended version of "A Decidable Class of Nested Iterated Schemata", submitted to IJCAR 200

Reasoning on Schemata of Formulae

A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists, the trees etc.). A proof procedure is proposed to relate the satisfiability problem for schemata to that of finite disjunctions of base formulae. It is shown that this procedure is sound, complete and terminating, hence the basic computational properties of the base language can be carried over to schemata

Identity in ellipsis: an introduction

Theoretical and Experimental Linguistic

Plotinus and Wang Yangming on the Structures of Consciousness and Reality

In this paper, particular key aspects of the philosophies of Plotinus and Wang Yangming have been analysed comparatively on the basis of important passages of their works. The method used for this investigation can be defined as that of transversal comparative induction, in which the focus is more on working out the details of affinities and similarities. As this means a first step in an encompassing systematic context, differences will be introduced more briefly. The present investigation aims to provide a foundation for a more differentiating and therefore complementing second part, which will consider other contents and topics in both philosophies. The present analysis is performed in three systematic steps and with regard to three basic philosophical ideas: (1) the idea that human consciousness is a central medium in the universal process and interrelatedness of (biological) life as a whole; (2) the idea that the self-unfoldment of reality represents a meta-cognitive process beyond the limits of subjectivity and finite consciousness; and (3) the idea that it is our major task to perfect and know ourselves by means of a “return” to the highest underlying foundation of this universal process. In their own ways, Plotinus and Wang Yangming both show that by enfolding human reflexivity toward the ineffable source of all reality in thought, feeling, human activity, and natural processes, namely by actively pursuing the path of moral and intellective perfection, we become fulfilled mediators of a universal process and of that which all of it represents

Rising Waves, Breathless Wind. Lacan, Zen and Adolescence: Illuminating Śūnyatā in the Dualism of Education

Practising Receptance moves beyond simply receiving or accepting, as action in thinking, as intention towards openness to the other. Representations of us contrasted to the ‘real’ transcendental properties, founded in śūnyatā, sees us at the intersection of Lacan, Gadamer, and Zen Buddhism, where we have objects as they appear to us and objects that exist independently of us. How might we apprehend the reality of others and discern this reality from what we see