The key issues raised by Bill Lawvere may be further specified if we try to make explicit the different "philosophical projects" which underlie the Set Theory vs Category Theory debate. ST is "newtonian": it proposes a fixed-absolute universe (ZF or alike) where all of present (and future!) mathematics should be embedded (described). Its perspective is (basically) "laplacian": given the (current) axioms of set-theory (or arithmetic) we can prove/decide/predict all future states of affairs (theorems of mathematics). CT originates from a rather different perspective. Riemann first proposed to found mathematics (geometry) on key regularities of the world to be turned into conceptual invariants, as "hypothesis" about the structure of physical space (connectivity, continuity, isotropy ... ; H. Weyl added symmetries to this). Then, one had to single out the "invariant preserving transformations" (Kleine, Clifford, Poincare' ...). The objects, as structural invariants, and the morphisms of CT, as transformations (including isomorphisms ...; functors; natural transformations ...), came out directly from this tradition; that is, CT followed the riemannian project who had replaced the absolute axioms/universe of euclidean geometry by the "relativizable" notions of invariant and transformation (as founding manifolds). In CT, the unity of mathematics, not as an absolute pre-fixed universe, but as an open world of ongoing new concepts and structures, is constantly re-constructed, by (interpretation) functors, which relate new categories to old ones (moreover, natural transformations (adjunctions ...) help to correlate these functors). Clearly, Newton and Laplace were immense scientific personalities, but ..., since then, many things have happened. In Physics, of course, but also within ... ST or in the proof-theory of Arithmetic, such as the independence theorems or the remarquable results on the "unremovability of machinery", which, even if within ST, force us outside the "rational mechanics" of PA .... More on this may be found in a two pages note of mine on "Laplace (vs Hilbert)" (or, reflections on rational mechanics and incompleteness), an item inserted in the Dictionary at the end of JY Girard's paper "Locus Solum" (MSCS, n. 11.3, to appear) and in a paper on "The reasonable effectiveness of Mathematics ..." (both downloadable from my web page). Giuseppe Longo Lab. et Dept. d'Informatique CNRS et Ecole Normale Superieure (Postal addr.: LIENS 45, Rue D'Ulm 75005 Paris (France) ) http://www.dmi.ens.fr/users/longo et : CENtre d'Etude des systemes Complexes et de la Cognition de l'ENS (CENECC) http://www.cenecc.ens.fr/ e-mail: longo@dmi.ens.fr (tel. ++33-1-4432-3328; fax -2151)