Description Fitting and Alan Turing
Date:
Joint talk with Stephen Perry.
One classic question of 20th century philosophy, inspired by Wigner’s classic 1960 paper, is “Why is mathematics, something abstract, so applicable to the sciences, something empirical?” A new analytical tool, description fitting, seeks to ease our mind about such questions. There is no one, singular way that applied mathematics works. Rather, the particular goals relative to each project inform how each piece of applied mathematics “works”. Applied mathematicians will massage, or “fit” their description of the natural world, sometimes in very idealized or even false ways, in order to make that description amenable to formalization.
In this talk, we aim to apply this tool to the works of Alan Turing and his theory of computation. We will show that Turing’s account of “human computable” in his 1936 paper is “fitted” as described above. Moreover, we show that understanding how his fitted descriptions function is crucial for understanding the success of his project, especially relative to mathematically equivalent but distinct formalisms of “computable functions”. We conclude by gesturing at future work, which considers Turing’s work here as an exemplary case of formal epistemology. In so doing, we hope to be able to compellingly address frequently made attacks against formal epistemology on the grounds that it is over-idealized, and to better understand how and why formal epistemology is successful and enlightening when it is.