In Modern Philosophy, we have begun with the father of the movement, Descartes himself. In his Discourse on the Method, he sets forth a new sort of epistemology, a way of knowing. It is a sort of reductionism, the sort that tells us to take nothing for granted and to deconstruct everything into its smallest possible components.
In his First Meditation, Descartes sets out to call every one of his opinions into question. He presents possible outcomes and challenges in two tones, hopeful and doubtful. Painters are brought up by the doubtful voice. Descartes has called into question the reality of our perceived existence. In a scenario completely borrowed from the Matrix (I do realize the opposite is true!), he asks, “What if this is all just a dream?”
This mightn’t be such a problem, though. Descartes points out that just as a painter must refer to extant creatures when dreaming up a fantastical one, experienced reality, if it is indeed an illusion, still must refer to some further reality. Even if an artist goes so far as to imagine wholly new forms, the artist must depend on the physical properties of light and shape to give his new idea life.
Some problems are presented here. If reality cannot be distinguished via the senses, then methods of knowing based on the senses cannot be trusted. However, the simpler, more theoretical studies may still hold the key to unlocking something about actual, rather than perceived, existence. Perhaps the "useless" study of mathematics provides humanity with the only way of actually knowing something about reality.
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