If we are to program a computer to think about its own methods for gathering information about the world, then it needs a language for expressing assertions about the relation between the world, the information gathering methods available to an information seeker and what it can learn. This leads to a subject I like to call meta-epistemology. Besides its potential applications to AI, I believe it has applications to philosophy considered in the traditional sense.
Meta-epistemology is proposed as a mathematical theory in analogy to metamathematics. Metamathematics considers the mathematical properties of mathematical theories as objects. In particular model theory as a branch of metamathematics deals with the relation between theories in a language and interpretations of the non-logical symbols of the language. These interpretations are considered as mathematical objects, and we are only sometimes interested in a preferred or true interpretation.
Meta-epistemology considers the relation between the world, languages for making assertions about the world, notions of what assertions are considered meaningful, what are accepted as rules of evidence and what a knowledge seeker can discover about the world. All these entities are considered as mathematical objects. In particular the world is considered as a parameter. Thus meta-epistemology has the following characteristics.
1. It is a purely mathematical theory. Therefore, its controversies, assuming there are any, will be mathematical controversies rather than controversies about what the real world is like. Indeed metamathematics gave many philosophical issues in the foundations of mathematics a technical content. For example, the theorem that intuitionist arithmetic and Peano arithmetic are equi-consistent removed at least one area of controversy between those whose mathematical intuitions support one view of arithmetic or the other.
2. While many modern philosophies of science assume some relation between what is meaningful and what can be verified or refuted, only special meta-epistemological systems will have the corresponding mathematical property that all aspects of the world relate to the experience of the knowledge seeker.
This has several important consequences for the task of programming a knowledge seeker.
A knowledge seeker should not have a priori prejudices (principles) about what concepts might be meaningful. Whether and how a proposed concept about the world might ever connect with observation may remain in suspense for a very long time while the concept is investigated and related to other concepts.
We illustrate this by a literary example. Moliére's play La Malade Imaginaire includes a doctor who explains sleeping powders by saying that they contain a ``dormitive virtue''. In the play, the doctor is considered a pompous fool for offering a concept that explains nothing. However, suppose the doctor had some intuition that the dormitive virtue might be extracted and concentrated, say by shaking the powder in a mixture of ether and water. Suppose he thought that he would get the same concentrate from all substances with soporific effect. He would certainly have a fragment of scientific theory subject to later verification. Now suppose less--namely, he only believes that a common component is behind all substances whose consumption makes one sleepy but has no idea that he should try to invent a way of verifying the conjecture. He still has something that, if communicated to someone more scientifically minded, might be useful. In the play, the doctor obviously sins intellectually by claiming a hypothesis as certain. Thus a knowledge seeker must be able to form new concepts that have only extremely tenuous relations with their previous linguistic structure.