The Role of General Intelligence in Mathematical Reasoning

It offers optimality principles that govern the blending process. Blending has in particular been used to account for concepts in mathematics as well (Lakoff & Núñez, 2000; Guhe et al., 2011). Various computational implementations have followed the cognitive theory, formalizing its notions and principles (Eppe et al., 2018); and even a theoretical Category Theoretic formulation that unifies these various A.I. concretizations (Schorlemmer & Plaza, 2021). The phenomenon explored here, however, is treated as a very high-level (and rather peripheral) conceptual one, concerning (perhaps human-only) creativity. And the computational implementations are grounded in logic, accordingly. The different focus I suggest here is on such combination as a fundamental component of the cognitive construction of object-representations at large. In particular, how the regularities that govern the possibility and value of such combinations are handled, should be understood as part of the more general working of the system, picking up on and integrating statistical patterns into the construction of its ontology. In terms of A.I., this reflect the on-going quest to find the proper place for the symbolic within modern architectures, which are chiefly neural. Given the suggested picture, of how an object-centered system might in general come to attribute objecthood or break it apart, we can approach the development of our conception of numbers and account for a hidden, sub-symbolic intricacy in that conception.