Organizational Computing is a computational model for using the principles, practices, and methods of human organizations. Organizations of Restricted Generality (

ORGs) have been proposed as a foundation for Organizational Computing.

ORGs are the natural extension of Web Services, which are rapidly becoming the overwhelming standard for distributed computing and application interoperability in Organizational Computing

*. *The thesis of this paper is that large-scale Organizational Computing requires reflection and strong

paraconsistency for organizational practices, policies, and norms.

Strong

paraconsistency is required because the practices, policies, and norms of large-scale Organizational Computing are pervasively inconsistent.

By the standard rules of logic, anything and everything can be inferred from an inconsistency,

*e.g.,* “

*The moon is made of green cheese*.” The purpose of strongly

paraconsistent logic is to develop principles of reasoning so that irrelevances cannot be inferred from the fact of inconsistency while preserving all natural inferences that do not explode in the face of inconsistency.

Reflection is required in order that the practices, policies, and norms can mutually refer to each other and make inferences. Reflection and strong

paraconsistency are important properties of Direct Logic [Hewitt 2007] for large software systems.

Gödel first formalized and proved that it is not possible to decide all mathematical questions by inference in his 1

^{st} incompleteness theorem. But the incompleteness theorem (as generalized by

Rosser) relies on the assumption of consistency! This paper proves a generalization of the

Gödel/

Rosser incompleteness theorem:

*theories of Direct Logic are incomplete*. However, there is a further consequence. Although the semi-classical mathematical fragment of Direct Logic is evidently consistent, since the

Gödelian paradoxical proposition is self-provable,

*every theory in Direct Logic has an inconsistency*!

The published paper with the above abstract appears in the excellent Springer LNCS volume Coordination, Organizations, Institutions, and Norms in Agent Systems III (edited by Jaime Sichman, Pablo Noriega, Julian Padget and Sascha Ossowski) and can be found at SpringerLink.

A version with some typos corrected is here: Large-scale Organizational Computing requires Unstratified Reflection and Strong Paraconsistency.