Ceteris Paribus: On The Virtues and Vices of Simplification

Ceteris Paribus is a handy Latin expression, used most often in economics, which means "with other things the same" or "all other things being equal." This particular simplifying assumption is an attempt to eliminate, for purposes of comparison or analysis, those niggling factors and error terms that result from the simple fact that all other things are never really equal. Given the rather esoteric use of this particular expression, I am concerned with the practical implications of this simplification, and what it means for our attempts to understand the complexity of our world. Consider this, therefore, a philosophical sort of post.

One of the fundamental axioms of my own life can be summed up with the following phrase: "there is an easy answer, and it is invariably wrong (or, at best, incomplete)." Given the contingent nature of so much in our lives, and the complexity that surrounds us at every turn, the certainty that so many people attach to such doubtful things is an area of deep concern to me. Is the faith of people that strong, or is it that others are so ignorant of the complex details and so confident in their ability to fill in the gaps that they do not recognize how little we really know about ourselves and our world? Indeed, the faith of those that deny the reality of God and the existence of anything beyond the material realm far exceeds the considerable faith of the most devout believer in the inerrancy of Holy scripture. What gives people the logical wherewithal to cast aside such great aspects of reality to comfort themselves with an apparent (and false) simplicity? Often, it is simplifying assumptions like "ceteris paribus" that allow people to toss aside the nasty unpleasantries of reality to focus on the comforting apparent similarities between two cases.

In some ways, this reliance on proof by analogy (of which ceteris paribus is one element) is necessary in logic and proof for lack of better alternatives. By virtue of the Pareto principle, a few crucial factors have a hugely disproportionate impact on something than the vast majority of other factors. In other words, the vital few have an explanatory power that far exceeds that of the trivial many. Who, though, gets to decide which elements are the vital few and which are the trivial many? Who gets to cut through the complexities of a matter and simplify it down to a reasonable and manageable level so that analysis can be undertaken to better understand the matter at hand? What grounds are acceptable for this simplification?

These are not particularly easy questions to answer when we get down to business. Let us consider a continuum between the messy and complicated truth, of which our knowledge is limited and finite on one side and an exceedingly simple but incomplete model of this truth on the other side. The more easily we seek to make the problem that reality presents us, the less our conception of the problem corresponds with the actual reality. The more closely we try to approximate that reality, though, the more difficult we make our given task on ourselves. Where do we draw the line between the quest for absolute truth and the awareness of our human limitations in comprehension and analysis? There appears to be no easy or definite answer to this question, though it behooves us to recognize the simplifications we make, the factors we ignore, and maintain a humble attitude towards the complexity and uncertainty that remain, even if we are pleased with the simplicity and accuracy of our chosen models.

In the final analysis, the test of models is how they correspond with reality itself. A robust model makes predictions about a given aspect of the real world. The more ambitious the model, the more claims it makes, and higher its ability of being falsified by reality. While absolute metaphysical certainty remains beyond the grasp of humanity (as much as we pretend otherwise), we act on our faith by testing our ideas and theories against reality. If they come out successfully, approximating what we expect from the world around us, and using as few simplifications as possible, and capturing as many features of analogous phenomena as possible, we can be confident that our theories and models are true. If we, however, wall ourselves off from empirical tests for fear our cherished theories will not be able to swim in the deep waters of reality, or if, worse, we deny any reality to test our theories and ideas against, we have no one but ourselves to blame for the ridicule which falls on those who talk a big game but refuse a difficult challenge. Let us, therefore, go on boldly, but humbly, while we tilt against windmills and struggle to deal with the complicated world around us. All other things being the same, I'd rather face as much of the reality this world confronts us with as possible.