Announcement: Chris Langan has published a new paper, "An Introduction to Mathematical Metaphysics", in the journal Cosmos and History.
In the most general sense, a theory is just a description of something. A theory can be good or bad, fanciful or plausible, formal or informal, true or false. If the theory can be used to relate the components of its subject to other components in revealing ways, then it is said to have "explanatory power". If it can be used to make correct predictions about how its subject behaves under various conditions, then it is said to have "predictive power".
A theory which makes falsifiable, experimentally testable predictions about the world is called a "scientific theory". Langan contends that due to the problem of induction, the standard methods by which scientific theories are constructed cannot establish a truly general theory of reality.
The problem of induction is very real; it is [...] why no general theory of reality can ever be reliably constructed by the standard empirical methods of science. Unfortunately, many scientists have either dismissed this problem or quietly given up on the search for a truly general theory, in neither case serving the long-term interests of science. In fact, the problem of induction merely implies that a global theory of reality can only be established by the rational methods of mathematics, specifically including those of logic.
In contrast to the standard methods of science, in which theories are constructed from a limited set of observations, the CTMU is established by logical properties of the process of theorization itself.
Because all theories have certain necessary logical properties that are abstract and mathematical, and therefore independent of observation - it is these very properties that let us recognize and understand our world in conceptual terms - we could just as well start with these properties and see what they might tell us about objective reality. Just as scientific observation makes demands on theories, the logic of theories makes demands on scientific observation, and these demands tell us in a general way what we may observe about the universe.
The CTMU is intended to be a truly general theory of reality, or Theory of Everything.
In other words, a comprehensive theory of reality is not just about observation, but about theories and their logical requirements. [...] The CTMU is such a theory; instead of being a mathematical description of specific observations (like all established scientific theories), it is a "metatheory" about the general relationship between theories and observations…i.e., about science or knowledge itself.