A Philosophical and Mathematical Model of Truth or #NewOrganon
Back in the early ’90’s, the great logician, Graeme Forbes, with impeccable Balliol irony, had a one-panel comic taped to his office door which crudely depicted Rodin’s The Thinker above the caption, “Aristotle Trying to Think of Frege.” Naturally, this suggested the straightforward doctoral project of thinking my way back in the other direction, from the principle results of Mathematical Logic to somewhere in the vicinity of Metaphysics Μ & Ν. Sometime around 1996, my resulting dissertation prospectus was approved by Graeme and a committee of readers with the modest title, “A Philosophical and Mathematical Theory of Truth.” Alas, in temperament, I have always been more like the mad Wittgenstein than the stoic Frege, while in techné, more like the foolhardy Xenophon than the careful Plato, so the project took 20 years. Nevertheless, it has now been completed as promised with the small exception that, instead of a theory of Truth, it became a model. Rather, twenty years ago I loosed that arrow of Truth and now it is up to the careful reader to see how close I have come to my mark.
Definition 1: #NewOrganon is a model of Truth, T = <D, I>, in which every well-formed formula on this page is a member of D, as well as every well-formed formula Referenced by any member of D, and I is the interpretation function which is given by the members of D.