Ceteris paribus or caeteris paribus is a Latin phrase meaning "with other things the same" or "all or other things being equal or held constant" or "all other things being equal" or "all else being equal". A prediction or a statement about a causal, empirical, or logical relation between two states of affairs is ceteris paribus if it is acknowledged that the prediction, although usually accurate in expected conditions, can fail or the relation can be abolished by intervening factors.
A ceteris paribus assumption is often key to scientific inquiry, as scientists seek to screen out factors that perturb a relation of interest. Thus, epidemiologists for example may seek to control independent variables as factors that may influence dependent variables—the outcomes or effects of interest. Likewise, in scientific modeling, simplifying assumptions permit illustration or elucidation of concepts thought relevant within the sphere of inquiry.
Whereas fundamental physics tends to state universal laws, other sciences, such as biology, psychology, and economics, tend to state laws that hold true in normal conditions but have exceptions, ceteris paribus laws (cp laws). The focus on universal laws is a criterion distinguishing fundamental physics as fundamental science, whereas ceteris paribus laws are predominant in most other sciences as special sciences, whose laws hold in special cases. This distinction assumes a logical empiricist view of science. It does not readily apply in a mechanistic understanding of scientific discovery. There is reasonable disagreement as to whether mechanisms or laws are the appropriate model, though mechanisms are the favored method. 
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. When using ceteris paribus in economics, one assumes that all other variables except those under immediate consideration are held constant. For example, it can be predicted that if the price of beef increases—ceteris paribus—the quantity of beef demanded by buyers will decrease. In this example, the clause is used to operationally describe everything surrounding 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, and thus to assume ceteris paribus is to assume away any interference with the given example. Such factors that would be intentionally ignored include: a change in the price of substitute goods, (e.g., the price of pork or lamb); a change in the level of risk aversion among buyers (e.g., due to an increase in the fear of mad cow disease); and a change in the level of overall demand for a good regardless of its current price (e.g., a societal shift toward vegetarianism).
The clause is often loosely translated as "holding all else constant." It does not imply that no other things will in fact change; rather, it isolates the effect of one particular change. Holding all other things constant is directly analogous to using a partial derivative in calculus rather than a total derivative, and to running a regression containing multiple variables rather than just one in order to isolate the individual effect of one of the variables.
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).
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 ceteris 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' behaviour on the same time scale, the assumption that consumer behaviour remains unchanged while policy changes is inadmissible as a substantive isolation (Lucas critique).
- Schlicht, E. (1985). Isolation and Aggregation in Economics. Springer Verlag. ISBN 0-387-15254-7. chapter 2
- Alexander Reutlinger, Gerhard Schurz & Andreas Hüttemann, "Ceteris paribus laws", in Edward N Zalta, ed, The Stanford Encyclopedia of Philosophy, Spring 2014 edn.
- Glennan, S. (2014). Mechanisms. In M. Curd & S. Psillos (Eds.), The Routledge companion to philosophy of science (2nd ed., pp. 420–428). New York: Routledge.
- Persky, Joseph (1990). "Retroperspectives: Ceteris Paribus". The Journal of Economic Perspectives 4 (2): 187–193. doi:10.1257/jep.4.2.187. JSTOR 1942898.
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