Question To whom it may concern; I thank you in advance for your assistance. I had a discussion with some of my colleagues regarding a problem that I identified. Basically, I got two different and contradictory results of the same problem (i.e., a paradox) using different but equally valid methodologies and rationales in our area of research. I propose to resolve this paradox by making some adjustments to the methodologies in order to make them consistent. As you know, when paradoxes are found, solutions have to be advanced in order to resolve the inconsistencies, and this in turn strengthens the whole methodology. The problem is that I identified the aforementioned paradox by means of a simulated, laboratory-type of study, in which ideal conditions are assumed and simulated. Since my area of research is business studies, my colleagues allege that the “paradox” I found is not valid, because it is not based on data from real firms. They added that for the paradox to be valid, real data would have to be used. I argue that on the contrary, the problems raised by the paradoxical situation I found are very likely to “get worse”, so to speak, in studies with real firms, since the data and conditions under which those studies are run are going to be far from the ideal situation I simulated. In short, my argument is that “if it is bad under ideal situations and conditions (i.e., lab study), it can only get worse when less than ideal situations and conditions are expected (i.e., studies with real firms), thus the paradox I found is even more relevant in studies with real data”. The last sentence in the above paragraph is based on my own logic and intuition. It makes so much sense to me, that I am surprised that my colleagues do not see it that way. Therefore, I would like to know if there is any “theorem” or “law” or “argument” in the philosophy and/or logics fields that would back up my rationale. Since my area of research is an empirical field mainly, I thought that maybe there is a logical or philosophical argument, theorem or law that would assert something along the lines of “if the results obtained by a lab study (i.e., ideal conditions) are inconsistent, an empirical study with real firms (i.e., less than ideal conditions) are expected to be also inconsistent”. I apologize for perhaps not using the appropriate terminology and concepts, and also for the lengthy question. I hope you can help me with my query. Regards.

Accepted:
May 14, 2008

Comments

I don't think that there is or could be a general principle that says that a paradox arising from idealizations will inevitably carry over (much less become worse) when the idealizations are relaxed. In some cases, the paradox will disappear when the idealizations are removed. In other cases, the paradox will persist (or become worse). There is no general rule here. It depends entirely on the details of the case.

For example, various paradoxes result in classical electromagnetic theory when pointlike charged particles are used. Point charges are a convenient idealization for many purposes, but the energy in such a field is undefined (the integral blows up). However, if we go to charge densities and extended charged bodies rather than point charges, these problems disappear. Likewise, in cosmology, Newtonian gravitational theory is afflicted with various paradoxes if we assume an infinite universe with a homogeneous, isotopic distribution of matter. Remove these idealizations and the problems go away.

These are intended merely as examples to show that sometimes paradoxes arise because of the idealization. In other cases, they arise despite the idealization. The matter can only be resolved in a case-by-case way, given the details of the particular paradox.