From The Significance and Basic Postulates of Economic Theory by T. W. Hutchison (1938, 1960), pp. 40-46:
As an example of the use of the ceteris paribus assumption we may take the proposition "If the price at which a good is sold rises, ceteris paribus the amount of the good demanded declines." Is this an empirical generalisation which can conceivably be false without any contradiction, or is it an analytical-tautological proposition?
This, usually, is not made clear, and perhaps such propositions are sometimes meant in one way, sometimes in another. One can only ask in each particular case whether the validity of the ceteris paribus proposition in question depends on facts, or whether, on the other hand, the denial of it simply shows that one does not understand by the terms "rise in price" and "amount demanded" what the language of economists understands.
If the proposition "If the price at which a good is sold rises, ceteris paribus the amount of the good demanded declines" is an empirical generalisation, so it can only have a clear scientific meaning if it is indicated under what conditions it would be true, or under what false. Further, it is desirable that the difference be shown between this empirical generalisation (with ceteris paribus) and the other empirical generalisation, "If the price at which a good is sold rises the amount of the good demanded declines" (without ceteris paribus).
Ceteris paribus propositions can be interpreted in this way. But if they are to be so interpreted—as empirical generalisations—then they are usually very vaguely and unclearly formulated. For no attempt is made, usually, to indicate under what conditions they are true and under what false, and the meaning of the vital qualification "ceteris paribus" is left hopelessly imprecise. The ceteris paribus assumption, just as much as any other, must be precisely formulated if the propositions it qualifies are to have any clear meaning. The intention of the assumption obviously is to lessen the falsifiability of the too often falsified generalisation "If the price of a good rises, the amount sold declines." But exactly how far is its falsifiability thus lessened, and if it remains an empirical proposition, what conceivable possibilities of falsification remain?
On the other hand, it seems more probable that ceteris paribus propositions are frequently treated as analytical-tautological propositions, the example taken in this case explaining a relation between the definitions of "rise in price" and "amount demanded" at different points on a demand curve of a particular shape—a purely logical or geometrical relation. Then it is inconceivable that its truth or falsity (as against its applicability) can be established by any facts, since it is without factual content. In this case one simply determines whether, in fact, the ceteris paribus assumption is true or false, by observing whether or not the price has risen appropriately or not—a circular procedure. This appears to be the interpretation favoured by Menger, though it involves a very elastic conception of "cetera." For example, if the well-known case of poor people buying more bread when the price of it rises in no way falsifies our proposition, this involves a considerable stretching of the assumption "ceteris paribus."
Thus interpreted the ceteris paribus clause is an accessory assumption of pure theory, and ceteris paribus propositions may be analysed in the same way as the propositions of pure theory have been. The ceteris paribus assumption makes out of an empirical proposition that is concerned with facts, and therefore conceivably can be false, a necessary analytical-tautological proposition. For a mathematical solution (by tautological transformations) the number of equations must be equal to the number of unknowns. The ceteris paribus assumption sweeps all the unknowns together under one portmanteau assumption for a logical "solution."
In Physics and Chemistry, where there are far more discovered empirical regularities, the ceteris paribus assumption is not used in the same way. For if the assumption is broadly true, or if, as is rather the case, the "cetera" in the natural sciences themselves act in accordance with known laws, then the ceteris paribus assumption is more or less a given one, and a true premise can always be dropped. For in a certain sense it is only necessary to make an assumption when one does not know it is true, or knows that it is untrue. This is the peculiar dilemma—apparently unique throughout science—of the "isolating," "assumption-making" procedure of economic theory where there are few empirical generalisations known to be true
In the natural sciences certain fundamental propositions can be taken either to be analytical-tautological or to be empirical generalisations, exactly as the ceteris paribus propositions may be so taken. For example, originally the proposition "All gases expand on warming" was probably arrived at by empirical experiments. But if to-day an experiment was made with something which as regards the other ways in which it was tested behaved like a "gas" but did not expand on warming, one would at first be inclined to suggest that some mistake had been made in the experiment. But if after repeated experiments this "gas" did not expand, scientists would be faced with a choice. Either they must say "Our law that all gases expand on warming is destroyed, and we must find a new law," or they could say "This stuff which does not expand on warming is no 'gas ', for by definition a 'gas 'must expand on warming; we must find some other name for this." The choice of this second course on all conceivable occasions would mean that the proposition "All gases expand on warming" was not an empirical law at all, but an analytical-tautological definition which was always true because it was not allowed to be false. From the mere wording and form of the proposition one cannot say whether it is the one or the other. One can only find out by a test case when scientists are forced to choose one alternative or the other.
According to Edgeworth, "The treating as constant what is variable [e.g., supply, margin, wages-fund] is the source of most of the fallacies in political economy," and it is the danger of the ceteris paribus assumption that it particularly facilitates such fallacies. It is quite probably true that in more cases than not a rise in price is in fact followed by a decrease in demand, but this of course might not be so; and whether it is so or not can only be decided by statistical investigation. Our proposition with ceteris paribus does not tell us this. In fact the ceteris paribus clause seems sometimes so to be used that one might equally significantly and correctly advance the proposition that ceteris paribus a rise in price is followed by an increase in demand, as the proposition that ceteris paribus it is followed by a decrease. "Ceteris paribus this follows that" seems to come to mean simply "In many cases this follows that," and however often it may not, the reply is that the proposition only said "in many cases" (or ceteris paribus), and this was simply one of the other cases (or "ceteris paribus" did not hold).
In the recent developments of the "dynamic" pure theory of employment the ceteris paribus assumption appears sometimes to have been applied to propositions which standing alone (without "ceteris paribus") are quite probably more often empirically false than true, but when it is added are meant to get away with some kind of exact and significant empirical content.
Mr. Keynes gives an example of the use of the ceteris paribus clause on these lines. He contrasts the two propositions: (1) "A decreased readiness to spend... will ceteris paribus increase investment," and (2) "A decreased readiness to spend... will ceteris paribus diminish employment." Are these empirical or analytical propositions—that is, what is the precise content of "ceteris paribus"? If they are empirical, then it is difficult to see what the qualification "ceteris paribus" can mean other than "usually." Then we have two propositions: "A decreased readiness to spend will usually" either (1) "increase investment" or (2) "diminish employment"—two rather vague impressionist generalisations; and though one may be more often true than the other, neither is of much scientific value compared with statistical investigations as to what, in fact, does follow a decreased readiness to spend in. different cases, pending the results of which it seems difficult to justify an exclusive insistence on one as against the other.
If, on the other hand, these propositions are analytical, there is of course no question of one being "true" and the other "false," and no particular reason for contrasting them, since neither says anything about what in fact follows a decreased readiness to spend. "Ceteris paribus" is simply used differently for the two equations. In the first total outlay is included among the "ceteris" that remain the same, so that a decrease in one division of it (consumption spending) mathematically implies an increase in the other division (investment). In the second equation employment on capital goods is assumed to remain the same, so that a decrease in employment on consumption goods mathematically implies a decrease in total employment.
Either of these interpretations is possible and there may be others. In the first place such a use of the "ceteris paribus" clause leaves it quite ambiguous as to what kind of proposition is being put forward. In the second place it appears to give to what is either simply an empirically empty analytical proposition, or a very vague and statistically unsupported empirical generalisation, an air of some kind of precise and widely valid empirical content.
We suggest that the ceteris paribus assumption can only be safely and significantly used in conjunction with an empirical generalisation verified as true in a large percentage of cases but occasionally liable to exceptions of a clearly describable type.Conclusion (p. 163):
That ceteris paribus propositions are frequently hopelessly ambiguous and that the ceteris paribus assumption should be used less often and more cautiously.