Synthetic Philosophy and Deductive Engineering
It is surely a commonplace that the solution of difficult intellectual problems requires focus. This is of course, just the opposite of what we see in LLMs, which are trained on massive datasets and are not only costly to train, but also not cheap to apply to simple problems. Problems which require deep thinking are explicitly provided for in many models by getting the LLM to think twice (or more) and reflect upon its results, or by combining the talents of multiple LLMs in a “chain of thought” or “reasoning chain” to solve problems which are beyond the capabilities of any single LLM. Away from the generality of LLMs, AI has lately had success in narrower domains by using more focused methods. Deepmind’s alpha-zero has shown the benefits of focus most clearly in those domains which constitute “perfect information spaces”.
Alongside the effectiveness of focus in some narrow domains, it sometimes happens that the solution of a relatively broad problem set may be facilitated by focus on certain key subproblems. A special case of this comes with the idea of “the singularity”, the point at which AI becomes capable of redesigning itself leading to progressive acceleration of the AI design cycle and hyperexponential growth in the capabilities of artificial superintelligence. Here we see that focus on the problem of AI design may be expected to advance capability in design across the board, and the potential suggests talking of this as a benefit of singular focus.
It may be that the benefits of focus, and the possibility of singular focus, can be turned into architectural models and strategic plans, and that is the purpose of this note.
There are two kinds of focal thinking which contribute to the proposed architecture. These come as a focal tower and a focal hierarchy which are discussed in turn.
The focal tower as described above loosely correlates with the epistemological stack in the following way:
As we ascend the focal tower, the self development capability which is being leveraged to achieve advancement becomes broader. So we begin with purely logical capability of a formal deductive system, which defines a recursively enumerable set of truths as the closure of a set of axioms under a set of operations which are the inference rules of the system. This becomes a singular focus when the deductive system is used to reason metatheoretically about its own reasoning, and find more effective and efficient algorithms for deriving truths in the system.
There are multiple levels of capability in the purely logical sphere, as we continue to address reasoning about how to effectively exploit deductive theories, but a clearer extension of functionality arises when we use formal model to reason about the design of digital electronics, and thereby obtain a capability for a material embodiment of artificial intelligence to contribute to the design of a better physical AI system. Such a capability would in the first instance be predicated on the availability of semiconductor fabs. It would be far short of a system capable of self-reproduction, or self-proliferation. There will be many increments in capability subject to self improvement with progressively diminishing constraints on the context in which the system can operate, ultimately leading to systems capable of interstellar or intergalactic proliferation, selecting some suitable remote target environment in which to design and construct a new generation of self-proliferating intelligent systems.
The connection with the epistemological stack is related to the different kinds of knowledge which are required to achieve the different levels of capability. At the lowest level the required knowledge is logical and may be obtained by reasoning alone. At some stage as the capability advances to involve physical systems, the required knowledge will include empirical knowledge of the physical world. Beyond that, though not necessarily confined to the highest levels, normative considerations will become significant, and in these matters we go beyond logical and empirical knowledge into more murky epistemological territory, though hopefully not entirely beyond the reach of reason.
It might be thought that deductive methods are confined to the purely logical level, but that is not the case. Application to higher levels in the epistemological stack can be factored into two parts, the establishment of appropriate formal models of the relevant domains, and the application of deductive methods to those models. The deductive methods, work in tandem with empirical observations both in establishing models (by deriving testable consequences of a theory) and in applying them (dual terminology for scientific method which reflects these is hypothetico-deductive and nomologico-deductive, reflecting the difference between testing hypotheses and applying laws).
In a SPaDE repository (and in any ITP like reasoning system) there is a natural hierarchy of theories, each theory building on its parents. Each theory is a perfect information space, since all answers all the information which can be used in determining theoremhood is available in the theory or its parents. The cumulative aggregate of the extensions in a theory and its ancestors is called in SPaDE a context, and each context is a perfect information space, suitable for focal reasoning by a specialist in that context. Since the theories are arranged in a hierarchy, the contexts are also arranged in a hierarchy. In SPaDE, the hierarchy is mirrored by a hierarchy of reasoning specialists which continuously learn both by undertaking reasoning tasks subcontracted to them, and by independent exploration of their context.