Ceteris paribus

Cēterīs pāribus is a Latin phrase, literally translated as "with other things [being] the same," and usually rendered in English as "all other things being equal." A prediction, or a statement about causal or logical connections between two states of affairs, is qualified by ceteris paribus in order to acknowledge, and to rule out, the possibility of other factors which could override the relationship between the antecedent and the consequent.

A ceteris paribus assumption is often fundamental to the predictive purpose of scientific inquiry. In order to formulate scientific laws, it is usually necessary to rule out factors which interfere with examining a specific causal relationship. Experimentally, the ceteris paribus assumption is realized when a scientist controls for all of the independent variables other than the one under study, so that the effect of a single independent variable on the dependent variable can be isolated. By holding all the other relevant factors constant, a scientist is able to focus on the unique effects of a given factor in a complex causal situation.

Such assumptions are also relevant to the descriptive purpose of modeling a theory. In such circumstances, analysts such as physicists, economists, and behavioral psychologists apply simplifying assumptions in order to devise or explain an analytical framework that does not necessarily prove cause and effect but is still useful for describing fundamental concepts within a realm of inquiry.

The clause
One of the disciplines in which ceteris paribus clauses are most widely used is economics, in which they are employed to simplify the formulation and description of economic outcomes. For example, it can be predicted that if the price of beef decreases &mdash; ceteris paribus &mdash; the quantity of beef demanded by buyers will increase. In this example, the clause is used to operationally describe the relationship between both the price and the quantity demanded of an ordinary good.

This operational description intentionally ignores both known and unknown factors that may also influence the relationship between price and quantity demanded. Such factors include: the relative change in price of substitute goods, (e.g., the price of beef vs pork or lamb); the level of risk aversion among buyers (e.g., fear of mad cow disease); or the level of overall demand for a good regardless of its current price level (e.g., a societal shift toward vegetarianism).

The clause is often loosely translated as "holding all else constant."

Characterization given by Alfred Marshall
The clause is used to consider the effect of some causes in isolation, by assuming that other influences are absent. Alfred Marshall expressed the use of the clause as follows:


 * The element of time is a chief cause of those difficulties in economic investigations which make it necessary for man with his limited powers to go step by step; breaking up a complex question, studying one bit at a time, and at last combining his partial solutions into a more or less complete solution of the whole riddle. In breaking it up, he segregates those disturbing causes, whose wanderings happen to be inconvenient, for the time in a pound called Ceteris Paribus. The study of some group of tendencies is isolated by the assumption other things being equal: the existence of other tendencies is not denied, but their disturbing effect is neglected for a time. The more the issue is thus narrowed, the more exactly can it be handled: but also the less closely does it correspond to real life. Each exact and firm handling of a narrow issue, however, helps towards treating broader issues, in which that narrow issue is contained, more exactly than would otherwise have been possible. With each step more things can be let out of the pound; exact discussions can be made less abstract, realistic discussions can be made less inexact than was possible at an earlier stage. (Principles of Economics, Bk.V,Ch.V in paragraph V.V.10).

Two Uses
The above passage by Marshall highlights two ways in which the ceteris paribus clause may be used: The one is hypothetical, in the sense that some factor is assumed fixed in order to analyse the influence of another factor in isolation. This would be hypothetical isolation. An example would be the hypothetical separation of the income effect and the substitution effect of a price change, which actually go together. The other use of the ceteris paribus clause is to see it as a means for obtaining an approximate solution. Here it would yield a substantive isolation.

Substantive isolation has two aspects: Temporal and causal. Temporal isolation requires the factors fixed under the cetreris paribus clause to actually move so slowly relative to the other influence, that they can be taken as practically constant at any point in time. So if Vegetarianism spreads very slowly, inducing a slow decline in the demand for beef, and the market for beef clears comparatively quickly, we can determine the price of beef at any instant by the intersection of supply and demand, and the changing demand for beef will account for the price changes over time (→Temporary Equilibrium Method).

The other aspect of substantive isolation is causal isolation: Those factors frozen under a ceteris paribus clause should not significantly be affected by the processes under study. If a change in government policies induces changes in consumers' behavior on the same time scale, the assumption that consumer behavior remains unchanged while policy changes is inadmissible as a substantive isolation (→Lucas critique).

Ceteris paribus in philosophy
So-called ceteris paribus clauses are also important in philosophy, particularly in ethics and moral psychology (where they are often used in the analysis of the relation between mental states and behavior), as well as in the philosophy of science (where they are often used in the analysis of laws of nature, causation, and related topics).

As an example: it seems that we can say that if a person wants to get her hat off of the roof, and she knows that the easiest way to do this is by putting a ladder up against the wall and climbing it, then she will place the ladder up against the wall and climb it &mdash; and if she does not act in that way, then that seems to be as good a reason as any to say that she did not really want to get her hat back, or did not believe that climbing up the ladder was the easiest way to do it, after all. But a little consideration shows that we can assert this as an analytic truth only if it is qualified by a "ceteris paribus clause" &mdash; since there are myriad other factors which might prevent her from climbing up the ladder, without making us retract the claim that she did want her hat &mdash; for example, she might have a crippling fear of heights, or she might want to get to work on time much more than she wants to get her hat back. Nevertheless, it seems that when we do add the ceteris paribus qualification, there is at least a good case to be made that the principle so qualified is an a priori principle of moral psychology.

However, there is some meta-philosophical debate on analyses of this sort. Although many philosophers have relied on them (either explicitly or implicitly), some philosophers allege that any analysis that depends on a ceteris paribus clause is philosophically suspect.

In order to understand the worry, a distinction should be made between two different ways for a statement to be qualified by a ceteris paribus clause: some ceteris paribus clauses are in principle eliminable by further analysis, whereas other clauses are ineliminable. So, for example, if I say "If the current month is February &mdash; ceteris paribus &mdash; then it will last only 28 days," then the ceteris paribus clause is added in order to exclude the possibility that it is a leap year. Since there is a fixed set of rules that define whether or not the present year is a leap year, one could (in principle) eliminate the ceteris paribus clause from the analysis by rephrasing the sentence to "If the current month is February, and the current year is not evenly divisible by 4, then it will last only 28 days." (Actually the rules for determining a leap year are more complex than that; but there is a finite number of rules, and you could in principle include them all in the sentence.)

Philosophers who worry about ceteris paribus analyses do not worry about this sort; their worries are focused on ceteris paribus clauses that are not even eliminable in principle. For example, in the philosophy of science it is common to say that there is a natural law that events of kind A cause events of kind B if and only if an event of type A, ceteris paribus, is always followed by an event of kind B &mdash; in order to rule out the possibility of other causal phenomena overriding the ordinary effect of the event of type A. But in order to eliminate the ceteris paribus clause in this analysis, a philosopher would need to know every sort of causal event that could possibly override any other sort of causal event &mdash; and even if there is in principle some finite list that exhausts all of these possibilities (a philosophically controversial claim), that list is certainly not known to the person who is claiming to be giving a definition of causality. So there is no-one who can say just what all is being ruled out by the ceteris paribus clause in this analysis. (Even if an omniscient physicist could spell it all out in a finite period of time, we are the ones who are purporting to understand how to use the words, and we only see these things as through a glass, darkly.)

But if it is not even possible in principle to say just what all is being ruled out by the ceteris paribus clause in these examples, then (these philosophers worry) it is no longer clear that the analysis is philosophically informative. The suspicion of ceteris paribus arises because it seems sometimes to be used to conceal a sort of conceptual "blank spot" in the analysis, and (these philosophers allege) the existence of such a "blank spot" is as good a reason as any to think that an analysis which depends on it is not the right direction to take in analyzing a particular concept. This is not to say that such ceteris paribus statements are not analytically true. The argument is, instead, that the clause shows that their truth depends on a proper analysis of the concept, which has yet to be done. For example, consider the analysis of causation as B following A ceteris paribus. If the analyst is asked to pin down just what condition the ceteris paribus is imposing, and the ceteris paribus clause is genuinely ineliminable, then it looks as though all that can be said is something like, "A causes B if and only if A is followed by B in a cause-like pattern". And that is certainly true, but it would be hard to give it as an analysis of causation with a straight face. The charge, then, is that ineliminable ceteris paribus clauses in an analysis conceal a conceptual circularity.

On the other hand, it might be argued that the objections to ceteris paribus analyses depend on problematic expectations about the methods and results of conceptual analysis. Some philosophers, in particular, worry that the arguments against ceteris paribus analyses depend on a tacit reductionism about analysis: the assumption seems to be that in order to give a conceptual analysis of a concept C, you must be able to explain C entirely in terms that have nothing to do with C. For these philosophers, a ceteris paribus clause may be indicative of virtuous circularity in an analysis rather than vicious circularity: that is, that we cannot ultimately explain (say) causation in terms that do not tacitly or explicitly have causal implications; but rather than indicating the need for further analysis, they argue, the ineliminable dependence on ceteris paribus clauses or further causal talk may just show that causality cannot be explained in non-causal terms, but rather that terms like "natural law" and "cause" and "accident" can only be explained in terms of one another, by elucidating the connections between them.