A few weeks ago, the famous French-born German mathematician Alexander Grothendieck passed away at the age of 86. While his death left most people nonplussed, mathematicians around the world mourned. Why? After much thought and research, Gorthendieck came to establish that underlying every algebraic formula was what one writer called a "schema," an "invisible" structure without which the formula could not exist. In other words, these inviolate formulas could not be so unless something even "more" inviolate existed as well.
The British mathematician and philosopher Bertrand Russell once voiced his frustration that he had to accept various mathematical formulas without any proof for their validity. These formulas just "were." The American philosopher Richard Rorty insisted that he was an anti-foundationalist: he had no starting point. Nor did he want one. He claimed that he arrived at every choice in an epistemological vacuum.
Russell and Rorty's positions demonstrate the necessity and importance of Grothendieck's conclusions. Nothing, not even the most basic of mathematical formulas, stands in isolation from everything else. Nothing exists in a vacuum. Nothing exists outside of a medium bigger than what it is. Nothing. As medieval theologian Thomas Aquinas pointed out long ago, unless we posit a non-starting starting point, we will never be able to begin. Mathematicians may call it "schemas," philosophers may call it a Form, and theologians may call it God. Either way, outside of a series of "experiences," we can make no sense of temporal contingency without the eternality of something that never began.
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