He claims that not-3 implies that 1 is useless and 4 will only give incorrect results
By that, it seems like he is saying that being right is useless, and that the right answer yields incorrect results... that first bit would be rather horrible if true, and the last bit is just silly outside of the context of trying to nail down exactly how and why not-3 is true.
Could you rephrase 'philosophically wrong' (as your friend means it) more clearly? I don't want to attack a straw man, but it seems like it could be going in a ridiculous direction.
I think he is trying to say that it's more important to understand how humans currently perform cognitive tasks than to try to formulate a robust way to perform cognitive tasks that has mathematical guarantees about accuracy. This same friend has some vague, new-agey type beliefs about "emotions" and I think he takes the evidence about emotions being major players in decision making a little too far. He sees attempts to quantify what he calls "human decision making" with the same tools that we use for "computational decision making...
I have recently been corresponding with a friend who studies psychology regarding human cognition and the best underlying models for understanding it. His argument, summarized very briefly, is given by this quote:
I am having trouble synthesizing a response that captures the Bayesian point of view (and is sufficiently backed up by sources so that it will be useful for my friend rather than just gainsaying of the argument) because I am mostly a decision theory / probability person. Are these works of psychology and neuroscience really illustrating that human emotion governs decision making? What are some good neuroscience papers to read that deal with this, and how do Bayesians respond? It may be that everything he mentions above is a correct assessment (I don't know and don't have enough time to read the books right now), but that it is irrelevant if you want to make good decisions rather than just accept the types of decisions we already make.