 What does a model involving distortions tell us about reality? Laymon (1991) formulated a theory which understands idealizations as ideal limits: imagine a series of refinements of the actual situation which approach the postulated limit, and then require that the closer the properties of a system come to the ideal limit, the closer its behavior has to come to the behavior of the system at the limit (monotonicity). If this is the case, then scientists can study the system at the limit and carry over conclusions from that system to systems distant from the limit. But these conditions need not always hold. In fact, it can happen that the limiting system does not approach the system at the limit. If this happens, we are faced with a singular limit (Berry 2002). In such cases the system at the limit can exhibit behavior that is different from the behavior of systems distant from the limit. Limits of this kind appear in a number of contexts, most notably in the theory of phase transitions in statistical mechanics. There is, however, no agreement over the correct interpretation of such limits. Batterman (2002, 2011) sees them as indicative of emergent phenomena, while Butterfield (2011a,b) sees them as compatible with reduction (see also the entries on  intertheory relations in physics  and  scientific reduction).