My current project is one which seeks to explicate how it is that the works of the three "wise men" of the past century, Brouwer, Wittgenstein and Turing provided a means of completely revamping theory in neuroscience, and, conversely, how more intimate acquaintance with state of the art neuroscience provides a means of extending their works, which, sadly, in all three cases, were left uncompleted.
We speak here of neuroscience in an extremely "NON-reductionist" manner, but where the understanding of how the gaps in neuroscience narratives and the gaps in philosophy and foundations of mathematics, are not at all inconsistent with each other and how the shared patterns of their incompleteness can point to remodeling both areas of "way finding".
For us 'metaphysics" of the classic sort needs to be bypassed (entirely) if possible. Brouwer and Wittgenstein alerted our civilization to that need, Turing (not saying much) however presented a model of writing/exposition which made him, for us, the first 'meta-metaphysical" option.
In a fundamental sense, they could be said to have been "saying the same thing", but that claim would itself have been deeply immersed in classic modes of speaking. Instead, they all spoke in terms which demonstrated a common refusal to be drawn into the vortex of common, ordinary language, classic Euclidean/Platonic mythologies. So they managed to be alert to sidestepping the landmines of typical intellectual discourse
The first major phase of Turing's work was, simply put, aimed at developing a way of talking of "machines' which could, in their outputs (linguistic/logically founded) emulate how humans would proceed and thus implicate "intelligent" function.
The later aspects of Turing's work are not fully appreciated yet. In those years, he began to be curious in the reversal of that emulation, that is, how it might be that the matrix of tissue known as the brain could somehow emulate the outputs of the most powerful computational machines.
Ultimately any meaningful tackling of the question of "mathematics' itself....it's complete mysteriousness ....is intimately related to the question of how it is that the brain can be spoken about in a manner than leads to the further speaking of "minding".
Rather brutally phrased, these are "aspects of the same" more profound problem. That of the escaping the prevalent inadequacy of our society/s tendency to rely on the speaking of 'truth" and/or 'knowledge" as fundamental rather than as what those notions are, that is, mythologies inherited from Platonic misinterpretations of Euclidean based efforts at 'understanding".
