Godehard Link (MCMP, Munich)
I start with giving a non-Platonist account of general mathematical truth that does justice to our strong anti-formalist intuitions without embracing what W. Tait calls a "superrealist" ontology of a Model-in-the-Sky as the eternal truth-maker of mathematical statements. "Non-Platonist" instead of "anti-Platonist" is meant to indicate that I intend to sidestep the opposition of Platonism vs nominalism. In fact, I argue that almost all revisionist stances in the philosophy of mathematics are rather unattractive, in particular formalism, intuitionism, and so-called fictionalism. Instead, the conception of mathematical truth I favor is highly the- oretical, continuous with science, locally semantic (or interpretive), and globally coherentist. Since I am also unconcerned about the indispensability argument, I am in line with much of modern set-theoretical practice where the techniques of forcing and inner models play a dominant role. However, in the face of the plethora of models generated by these technical tools suggesting relativism of some sort, I still think that a substantive notion of set-theoretic truth can be defended along the lines proposed here. In this context I will give my take on Hugh Woodin’s quest for the Ultimate-L.