<p>Several models of cognition were developed by different researchers at different levels of account (brain versus mind). While useful insofar as they account for a wide swath of empirical findings, they are often viewed separately, perhaps even in an adversarial sense. Yet, we show them to be formally nested within a more general mathematical framework which is partially derived from the Hodgkin-Huxley models. Mathematical analysis of this framework indicates these equivalent systems are a coherent family of models that describe the mind, on the one hand, and brain, on the other, providing statistically accurate descriptions and predictions of observed data. On this fact, our findings support a parallelism or monism between mind and brain. We conjecture that a key link in this formal equivalence is Luce’s Existence Theorem, suggesting that different mind/brain phenomena arise from a competitive system in which behaviors are stochastically generated.</p>