While I agree that these are titans of 20th c. philosophy, particularly of the philosophy of mathematics and logic, the overarching school they belonged to (logical positivism) has been thoroughly and rightly criticized, and it is informative to read these criticisms to understand why a view of life that is overly mathematical is in many ways inadequate. Your comment still argues from a very limited perspective. There is no reason that correct application of Gödel s theorem should be any indication of the richness of someone's philosophical views unless you are already a staunchly committed reductionist who values mathematical arguments above all else (why? can maths help you explain and understand the phenomena of love in a way that will actually help you experience love? this is just one example ___domain where it does not make much sense), or unless they are specifically attempting a philosophy of mathematics. The question of whether or not we can effectively model cognition and human mental function using mathematical models is not a question of mathematical philosophy, but rather one of epistemology. If you really want to head a spurious argument, read McCulloch and Pitts. They essentially present an argument of two premises, the brain is finite, and we can create a machine of formal "neurons" (which are not even complete models of real neurons) that computes a boolean function, they then conclude that they must have a model of cognition, that cognition must be nothing more than computation, and that the brain must basically be a Turing machine.

The relevance of mathematics to the cognitive problem must be decided outside of mathematics. As another poster said, even if you buy the theorems, it is still an empirical question as to whether or not they really model what they claim to model, and whether or not that model is of a fidelity that we find acceptable for a definition of general intelligence. Often, people reach claims of adequacy today not by producing really fantastic models but instead by lowering the bar enormously. They claim that these models approximate humans by severely reducing the idea of what it means to be an intelligent human to the specific talents their tech happens to excel at (e.g. apparently being a language parrot is all that intelligence is, ignoring all the very nuanced views and definitions of intelligence we have come up with over the course of history. A machine that is not embodied ina skeletal structure and cannot even experience, let alone solve, the vast number of physical, anatomical problems we contend with on a daily basis is, in my view, still very far from anything I would call general intelligence).