The Theory of Knowledge
Overview
To underpin an understanding of Rationality, and as a philosophical foundations for The Semantic Web, we propose develop a new "Theory of Knowledge".
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.
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.
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.
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.
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.
Carnap v. Quine

Quine's "Two Dogmas of Empiricism" is the paper most closely associated with the overthrow of the Russell/Carnap perspective on Philosophy. This was a counter-revolution, begun by Wittgenstein when he repudiated his Tractatus, but completed by the mugging of Carnap by Quine and Tarski. The counter revolution was by the then greatest philosophical authorities on logic, against logic itself, and against Russell's scientific conception of philosophy. If you think this was a philosophical advance, you may find OpenMind an unpleasant site to read, for here I attempt to move forward as if this last half century of analytic Philosophy had never happened.

Part of this is to return a concern with knowledge to center stage, pushing the philosophy of language into an important but subordinate position. However, the Theory of Knowledge we envisage bears little resemblance to modern epistemology.

Tractarian Epistemology

The kind of theory I have in mind is best approached from Wittgenstein's Tractatus. This is of course, very much about language, but it is all encompassing, it covers philosophical logic, mathematical philosophy, philosophy of science, and even touches upon moral philosophy.

This is Theory of Knowledge in that broad sense which intends it to subsume all other kinds of knowledge rather than be a narrower special discipline.

My own primary concern is not with philosophy at all. It is with changing the world, and, as a means of doing so, in the design of things that know. These "things that know" are software agents inhabiting the semantic web which is growing as web content semantically well-defined notations become increasingly deployed on the World Wide Web.

Formal Analysis
The approach is here, as throughout OpenMind, formal. We aim to develop formal models which cast light upon the theory of knowledge. In the first instance we propose to exhibit simple models which are illustrative of the use of formal models in this domain and which provide some kind of connection into conventional analytic philosophy. However, the main thrust will be on formal meta-theory for the semantic web, which provides foundations for the design of X-Logic technologies. This is "formal analytic philosophy as design".
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.
Poisoned Wells
You don't get off square one in OpenMind until you have grasped the analytic/synthetic dichotomy. That it now appears to be received opinion that this dichotomy is untenable (maybe it isn't I don't watch very closely) boggles my mind. Its certainly hard (for me) to have a conversation with a philosopher who takes this view.
Untenable?

What does it mean to say that a dichotomy is "untenable"? We explore this question by showing some very simple formal models in which the notions of analytic and synthetic are given a formally precise meaning, and in which it is trivially true that they constitute a dichotomy. The point is made, that to make a dichotomy is extraordinarily easy.

There is a lot more which could be said, but I'm not proposing to do it. The primary purpose of this little exercise is just to provide an example of the simplest imaginable bit of formal modelling applied to philosophy.
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.
Logical Truth
In the first instance I have in mind just looking at Wittgenstein's account of logical truth. According to the Tractatus propositions are truth functions of atomic propositions, and necessary propositions are tautologous in the sense that the truth function involved allways yeilds true whatever the truth values of the atomic propositions (i.e. it is a constant valued truth function). This makes the Tractarian notion of logical truth equivalent to that of first-order validity (which was not defined until later). To say that logical truths are tautologous (in this particular sense) is the same thing as to say that the atomic propositions are logically independent.
Wittgenstein later repudiated this conception, apparently because colour exclusion gave necessary truths which were incompatible with the logical independence of atomic propositions (though he must surely have had some previous qualms about his treatment of mathematics in the Tractatus, which is pure fudge). I'm not expecting there to be a lot to learn here, but it does seem to me fertile ground for illustrating the application of formal modelling to analytic philosophy. I hope that a bit of formality will make more definite the relationship between the tractarian semantics and first order model theory, and maybe the connection between the independence of atomic propositions and the thesis that logical truth is tautologous.
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.
Two Aspects of X-Logic

There are two aspects of the X-Logic which get you into philosophy. The basic idea is that you can work coherently in a multi-lingual environment if you know the meaning of all the languages which you are working with. A formalist position doesn't really work, if you know the proof rules for each language that doesn't allow you to integrate them, but if you know the semantics of the languages, that does.

Metatheory

The first fundamental concern is with a metatheory which justifies this claim (that semantics does the trick), and which tells us how to integrate reasoning in different languages. This is our present concern, with the use of formal modelling to provide such a metatheory. It is also intended that this formal metatheory will lead us directly to a language which we can use to glue together solutions (or conclusions) from problems where subproblems (or lemmas) have been solved (or proven) in different languages (or logics).

Semantics

The other fundamental concern, assuming that the metatheory is OK, is with how the semantics of languages can be defined. This problem will be addressed by OpenMind elsewhere (somewhere under "Foundations of Analytics" probably. Formally is the answer, but of course, there are difficulties.


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