Analog and Discrete Systems in the Brain
I hypothesize that there are two systems in the brain: discrete and analog. Syntax and symbol manipulation abilities (e.g., language and arithmetic) are realized in the discrete system. In a typical human brain, formal theories of folk physics, folk biology, etc. are embodied in the discreet system. Symbols, which are meaningless per se, are endowed with meaning due to the causal link connecting the discrete system through the analog system to the world. Reasoning in the discrete system is symbol manipulation according to rules, which is specified by mental logic theory.
Analog computation, such as physical simulation is realized in the analog system. People can reason by constructing mental models in the analog system.
There is a division of labor between the two systems in reasoning and understanding the world. E.g., one can simulate and predict the trajectory of a football by constructing a mental model of physics in the analog system or she can solve the same problem by calculation based on physical axioms in the discrete system (although rarely). The correlation between them is specified by semantics.
I survey the difference in analog number processing and discrete number processing as empirical evidence that the distinction between the two systems exists.
The philosophical framework outlined here also sheds light on the symbol grounding problem. It explains how concepts, semantics, and thought attribution are realized in the brain.
 László E Szabó, “Meaning, truth, and physics,” In Making it Formally Explicit, pages 165–177. Springer, 2017.
 Carruthers, P, “The cognitive functions of language,” Behavioral and brain sciences, 2002.
 Johnson-Laird, Philip N, “Mental models and human reasoning,” Proceedings of the National Academy of Sciences 107.43 2010.