Truth, modality and intersubjectivity

Is there something more frozen than A foundations B ? A quick glance at the list A foundations of mathematics B : http ://www.cs.nyu.edu/mailman/listinfo/fom shows a paradigm close to archaic astronomy : truth is a primitive (like Earth), around which several systems and meta-systems gravitate (like the epicycles of Ptolemy). This being orchestrated by Doctors of the Law, in charge of the latest developments of Hilbert’s program, i.e., of a certain form of finitism obsolete since Gödel’s theorem (1931 !), but still in honour in this sort of Jurassic Park. Let us put it bluntly : these people confuse foundations with prejudices. Of course, it cannot be excluded that the deep layers behave accordingly to our preconceptions ; but who thinks in that way should draw the conclusions and quit. My personal bias, the one followed in this paper, is that the real hypostases are very different from our familiar (mis)conceptions : I shall thence propose a disturbing approach to foundations. This viewpoint is by