Existing academic and para-academic discourses leave no attempts in splitting any organic communication between fields. The current piece and my overall work in life has been to attempt in bridging these split communications, to render visible insights and intersections that otherwise would remain dormant.
This is certainly not an entirely novel disposition to have, rather, much of my work is to communicate what has already existed in forgotten discourses. Specifically, the spirit of the current work embodies that of the Graeco-Roman world, i.e, classical antiquity and it’s rebirth through the European Renaissance movement in the XV century. The ad absurdum approach to this would be to reduce such a disposition to being a generalist.
Moreover, while the spirit remains with those specific periods and ideas, the content embodies them in different ways. Plato’s philosophy of mathematical objects, is just as crucial as Meinongian nonexistent objects; or Peacock’s version of formalism in the XVII century is just as pertinent as Hilbert’s of XIX century; or Berkeley’s critique of Newtonian approach to the infinitesimals remains as valuable as Omar Khayyam’s treatment of Euclid’s parallel postulate. Thus, one can reinvent the unifying spirit across different contexts, including those of modern, ‘‘postmodern’’ (which I consider to be an oxymoron yet indicative), and all the other subversive approaches.
It might also seem that since the fields that were prevalent in those periods have given birth to newer forms that even the most foresighted thinker would’ve only occasionally dreamt of, this limitation might also carry over to the current investigations. It does not. Through the minds of Leibniz, Babbage and Lovelace, was born a child that was to embody the mathematical principle of computation. And in this precarious creation not only mathematics and electrical engineering but also foundations of philosophy and logic were of equal parts. Alonzo Church, Turing’s doctoral advisor, did not consider his protégé’s work as deviation of his own, but rather as a different means of achieving something similar. Even though, to the uninitiated, Turing might appear as an ‘‘applied mathematician’’, he is a first-grade pure logician and mathematician as is apparent from his publications on type theory ála Church. Similar arguments can be made for innumerable thinkers, such as Gödel, Tarski, John McCarthy, Marvin Minksy, Dana Scott, Raymond Smullyan or to list a few recent names, Seymour Papert, Douglas Hofstadter and John MacFarlane.
Thus, computer science is a vivid epicenter of intersections between the three subjects of our interest, one only has to discern it amidst the literature about it that surrounds us today. The current work is the author’s attempt to nudge the needle towards that direction.