Don Boudreaux reminds us of a quote by great economist W.H. Hutt over at Cafe Hayek discussing mathematics and its role in the economic science (for the sake of space, I will refrain from posting the whole quote here). What follows is my two cents on the matter.
Mathematics is a useful tool in understanding our world if, for no other reason, that to help us separate the probable from the merely possible.
But, despite the old cliche, facts do not speak for themselves. Without a good theory underneath, the data are meaningless. A theoretical framework, well-grounded and logical, is important to putting information in context and helping to determine whether an outcome is reasonable or not. Of course, if data run afoul of theory, then both must be considered. Is there a problem with the theory or with the data?
I think this is what we’re running into now in regards to minimum wage. In recent years, there have been some data to suggest that minimum wage may not have the negative consequences theory would predict (although there is also data to suggest the outcome is exactly what one would predict).
So, then, is the Law of Demand wrong? Possible, but given its consistency on many other subjects (including wages at higher-skilled positions), unlikely. Is there something unique about low-skilled labor? Also possible (and some have suggested that unique conditions like monopsony power do exist). However, given the specificity of these conditions, I think unlikely on any grand scale.
This question I think should be answered with mathematics and statistics. But I also think the evidence should be overwhelming before overturning theory. To rule simply by mathematics is to lose sight of the previous body of knowledge, which can lead to disastrous conclusions.