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The original question had to be edited down. I think that one of the strongest philosophical perspectives that is raised through Nasar's work is the idea that reality can be constructed in different manners. John Nash's worsening schizophrenia illuminated the idea that reality in the modern setting is seen through different lenses. There is no totality that defines and governs reality in the absolutist manner. Even though Nash is a fervent devotee of logic and numbers, he clearly represents the idea that reality can appear different to individuals and this variance is what constitutes consciousness in the modern setting. Nash's idea of appropriating "mixed strategies" might not merely be an economic approach, but actually one that talks about how reality can be appropriated. This same philosophical perspective is seen in how Nash eventually deals with his condition. Nash and Alicia embrace the postmodern philosophical perspective of not dogmatically subscribing to standard medicine and blindly adhering to doctors. The philosophical approaches that emerge from Nasar's narrative reside in the realm of rejecting dogmatic notions of the good and rather understanding that a multiplicity of paths in the modern setting represent the pursuit of the good. This helps to establish a heavily Postmodern philosophical approach in understanding how a mathematician can embrace a pursuit that exists both within and outside of it.
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