Here is something to prepare you for what will be said in the next paragraph. I may be mistaken in what I am saying because I am connecting what is rational and ethical as pretty much the same thing. Dostoyevsky claims that the conclusion of that the underground man came to makes him irrational. Not so much the process by which he gets to the conclusion. Dostoevsky seems to associate what is ethical with what is rational. For example the doctor says it is rational to get treatment because it is in your best interest, and it is ethical for you as an individual to act in your best interest. That is where I get my connection between the rational and the ethical.
I believe that The problem with Dostoevsky's argument for freewill is that he claims that there is only one universal definition of what counts as rational. He claims that working against rationality proves that we have free will. He claims that turning down a liver operation proves that he is not a logic calculator. However he never asks by what standard is he acting irrational. There are many different philosophies that discuss which action are ethical, and which actions are rational. Kant for example says that reason should dictate ethics. He says that we should "act as if the maxim from which you act were to become through your will a universal law". He says that it is rational and ethical to act in a way that is applicable to everybody, and to not act in this way is a violation of the rational, and the ethical. He says that if you do not act in a universal way you violated what reason should tell you. A Hedonist claims that a rational man will maximize pleasure and minimize pain. Among the many philosophies there are many different criteria people have for rational people.
I am asking by what standard is the underground man acting irrationally? Is what is rational defined by what benefits a person as an individual? Is what is rational defined by what can be applied to everyone universally like Kant said? To Kant you are not using reason if you decide to live like a hedonist. To a hedonist the same thing can be said about kant. I make say these things to demonstrate that many different philosophies have their own idea of what is rational.
The underground man Dostoevsky discusses is not acting irrationally and thus proving his free will, he merely makes his own version of rationality. He decided that he was going to take the doctor’s version of rationality and do the exact opposite.He made a rational idea that says it is ethical he should do the opposite of whatever the doctor says will help him, so as to prove he has free will because he did not have to follow the other guys rational idea. He still used logic to come to his conclusion. The underground man still acts rationally; It is just by his own definition. Using this new definition of reason he concludes that his action is ethical because it will make him think he has freewill. I think if you agree with me that the underground man had his own definition of reason, then the argument for whether or not someone has freewill completely changes.Hopefully you comments will help me iron out my argument.