Announcement: Chris Langan has published a new paper, "An Introduction to Mathematical Metaphysics", in the journal Cosmos and History.
Problem of induction
The problem of induction refers to the lack of justification for generalizing from the part to the whole in the empirical realm. Observation and experimentation, the standard empirical methods of science, may tell us that "all X observed so far are Y", but they do not allow us to then conclude that "all X are Y (across the whole universe)". Because of this problem, we cannot prove universal laws of nature using the scientific method, but only provisionally confirm or falsify them.
Langan's approach with the CTMU is to circumvent the problem of induction by using deduction instead. That is, he proposes to use the deductive methods of logic and mathematics to draw conclusions about reality. Instead of starting with a limited set of empirical observations and provisionally theorizing about them, he starts with logic, adjoins certain analytic truths (see below), and extracts the implications for the whole of reality. Among the results he claims to have mathematically deduced are "nomological covariance, the invariance of the rate of global self-processing (c-invariance), and the internally-apparent accelerating expansion of the system".
The keys to Langan's approach are the three analytic principles which he uses to relate logic to reality. These principles are associated with three properties which a theory of reality must inevitably possess: closure, comprehensiveness, and consistency. The principles in question are supposed to be true of reality as defined on the model-theoretic level, i.e. on the level of the general correspondence between a theory of reality, and reality itself. For more information about these principles and properties, see the Three Cs / Three Ms.
As a final note, Langan does not claim that at the current stage of its development, the CTMU can be used to demonstrate every empirical truth, and he acknowledges the role that empirical methods may play in refining his theory. Since those methods remain subject to the problem of induction, it is perhaps better to say that the CTMU transcends the problem, rather than doing away with it entirely.
- Langan 2002, p. 32.