Overview
Formal analytic philosophy using X-Logic, rationality and deduction, X-Logic foundations.
OpenMind applies formal methods and tools to analytic philosophical problems, explores the relationship between logic and rationality, and provides both applications of and foundations for X-Logic.
To underpin an understanding of Rationality, and as a philosophical foundations for The Semantic Web, we propose develop a new "Theory of Knowledge".
Foundation systems for formal analysis play the same role as logical foundations for mathematics but are aimed at a broader range of applications.
Introduction
OpenMind applies formal methods and tools to analytic philosophical problems, explores the relationship between logic and rationality, and provides both applications of and foundations for X-Logic.
Formal Analytics
Bertrand Russell, after his mammoth essay in the formalisation of mathematics, thought that the methods of logic could enable analytic philosophy to move on from indecisive sophistry to solid scientific (but not empirical) results. It hasn't happened. Here at OpenMind, that's what I intend to do.
Rationality
David Hume appears in some of his writings to have supposed that beliefs are rational only when supported by demonstrative proof. That this excludes all beliefs about the external world suggests that a better account of the relationship between rationality and deduction is desirable. A more liberal account might suggest that a collection of belief's can rationally be held provided only that they are logically coherent (which is not a coherence theory of truth). The concept of rationality is of central importance to The Open Society, and for that reason, eventually I hope to address this at OpenMind.
X-Logic
The X-Logic project may be thought of as a project to develop technological support for rationality. Be that as it may, it certainly is intended to provide support for (inter alia) formal analytic philosophy, and OpenMind is intended to become a showcase for philosophical applications of X-Logic technologies. However, the relationship between X-Logic and OpenMind is closer than that, for OpenMind is to provide philosophical and logical foundations for X-Logic. This is an exercise in "analytic philosophy as design", in which the same work can be viewed either as the formalisation of philosophical theories about language and logic, or as an architectural design for the semantic web, eventually to be realised in software.
The Theory of Knowledge
To underpin an understanding of Rationality, and as a philosophical foundations for The Semantic Web, we propose develop a new "Theory of Knowledge".
Introduction
Philosophically, OpenMind passes over half a century of modern analytic philosophy most closely associated with Quine and Davidson, returning to the ethos of Russell and Carnap.
Fundamental Dichotomies
To ease the reader into formality with the simplest possible models, we re-formalise here using X-Logic and ProofPower a model of the Analytic/Synthetic and Necessary/Contingent dichotomies.
Wittgenstein's Tractatus
To provide a slightly more substantial connection between these formal theories and traditional analytic philosophy, some aspects of Wittgenstein's Tractatus Logico-Philosophicus are formalised. The scope of this early work of Wittgenstein is matched by the scope of our conception of "the semantic web", and the theory which we need to underpin the semantic web and X-Logic may be thought of as in the same philosophical tradition.
Metatheory for X-Logic
In order to be able to reason soundly in a multi-lingual environment we propose to develop formal models of language. These models will then provide the semantic domains in terms of which we define the metanotation which we call XL-glue. The purpose of XL-glue is to permit sound integrated multi-lingual solutions to problems, in which an overall result is synthesised from the results of a multiplicity of language or domain specific problem solvers.
Foundations of Analytics
Foundation systems for formal analysis play the same role as logical foundations for mathematics but are aimed at a broader range of applications.
Introduction
Our preferred starting point is the formalisation of set theory in Higher Order Logic. This provides a universal semantic foundation for X-Logic, and a suitable framework for further formal foundational experiments.
Well-Founded Systems
Some experiments in foundation systems intended to deliver pragmatic features like polymorhphism and structured name-spaces without rocking the boat.
Reflexive Foundations
The identification of functions with well-founded graphs is both fruitful and cumbersome. Is it possible to reconcile this classical framework with a more liberal notion of "rule"?
Proof and Computation
Formal foundation systems are normally associated with fixed sets of rules and axioms. For X-Logic, liberalisation is proposed, yielding a closer relationship between proof and computation.
Where the Buck Stops
The attempt to define semantics formally leads either to infinite regress or to meta-circular semantics. We propose the latter.

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