If this blog has any raison d’être, then it is perhaps best described by Feynman’s wryful confession:
“We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover up all the tracks, to not worry about the blind alleys or describe how you had the wrong idea first, and so on. So there isn’t any place to publish, in a dignified manner, what you actually did in order to get to do the work … .”
… Richard P. Feynman, in his Nobel Lecture, 1966
If, further, this blog has any purpose, then that is perhaps best reflected in Gowers’ observation:
“If you ask a philosopher what the main problems are in the philosophy of mathematics, then the following two are likely to come up: what is the status of mathematical truth, and what is the nature of mathematical objects? That is, what gives mathematical statements their aura of infallibility, and what on earth are these statements about?”
… W. T. Gowers in his talk, Does mathematics need a philosophy?, presented before the Cambridge University Society for the Philosophy of Mathematics and Mathematical Sciences, 2002.
More specifically as to purpose, in these posts I shall attempt to address standard interpretations of the formal reasoning and conclusions of classical first order theory—based primarily on the work of Cantor, Gödel, Tarski, and Turing—which argue that the satisfiability and truth of the propositions of a formal mathematical language, under an interpretation, is subjective, in the sense of being essentially unverifiable constructively.
I shall, however, argue that if mathematics is to serve as a universal set of languages of both adequate expression and effective communication, then such interpretations may need to be balanced by an alternative—constructive and intuitionistically unobjectionable—interpretation of classical foundational concepts in which satisfiability and truth are defined objectively, in the sense of being finitarily verifiable.
And finally, if this blog has any philosophy, I can only ascribe it with gratitude to what was once quoted to me many years ago by my late friend and mentor, Ashok Chadha:
“Let not posterity judge us as having spent our lives polishing the pebbles and tarnishing the diamonds.”