Abstract
This chapter elaborates and develops the thesis originally put forward by Mary Morgan (2005) that some mathematical models may surprise us, but that none of them can completely confound us, i.e. let us unable to produce an ex post theoretical understanding of the outcome of the model calculations. This chapter intends to object and demonstrate that what is certainly true of classical mathematical models is however not true of pluri-formalized simulations with multiple axiomatic bases. This chapter thus proposes to show that - and why - some of these computational simulations that are now booming in the sciences not only surprise us but also confound us. To do so, it shows too that it is needed to elaborate and articulate with some new precision the concept of weak emergence initially due, for its part, to Mark A. Bedau (1997).