An Illustration of the Truncation Principle

3 June 2012


Science often (though not always or exclusively) involves a quantitative approach to phenomena. As the phenomena of the world are often (though not always or exclusively) continuous, the continuum of phenomena must be broken up into discrete chunks of experience, however imperfect the division. If we are to quantify knowledge, we must have distinctions, and distinctions must be interpolated at some particular point in a continuum.

The truncation principle is the principled justification of this practice, and the truncation fallacy is the claim that distinctions in the name of quantification are illegitimate. The claim of the illegitimacy of a given distinction is usually based on an ideal standard of distinctions having to be based on a sharply-bounded concept that marks an exhaustive division that admits of no exceptions. This is an unreasonable standard for human experience or its systematization in scientific knowledge.

One of my motivations (though not my only motivation) for formulating the truncation principle was the obvious application to historical periodization. Historians have always been forced to confront the truncation fallacy, though I am not aware that there has previously been any name for the conceptual problems involved in historical periodization, though it has been ever-present in the background of historical thought.

Here is an implicit exposition of the problems of the truncation principle by Marc Bloch, one of the most eminent members of the Annales school of historians (which also included Fernand Braudel, of whom I have written on many occasions), and who was killed by the Gestapo while working for the French resistance during the Second World War:

“…it is difficult to imagine that any of the sciences could treat time as a mere abstraction. Yet, for a great number of those who, for their own purposes, chop it up into arbitrary homogenous segments, time is nothing more than a measurement. In contrast, historical time is a concrete and living reality with an irreversible onward rush… this real time is, in essence, a continuum. It is also perpetual change. The great problems of historical inquiry derive from the antithesis of these two attributes. There is one problem especially, which raises the very raison d’être of our studies. Let us assume two consecutive periods taken out of the uninterrupted sequence of the ages. To what extent does the connection which the flow of time sets between them predominate, or fail to predominate, over the differences born out of the same flow?”

Marc Bloch, The Historian’s Craft, translated by Peter Putnam, New York: Vintage, 1953, Chapter I, sec. 3, “Historical Time,” pp. 27-29

Bloch, then, sees times itself, the structure of time, as the source both of historical continuity and historical discontinuity. For Bloch the historian, time is the truncation principle, as for some metaphysicians space (or time, for that matter) simply is the principle of individuation.

The truncation principle and the principle of individuation are closely related. What makes an individual an individual? When it is cut off from the rest of the world and designated as an individual. I haven’t thought about this yet, so I will reserve further remarks until I’ve made an effort to review the history of the principium individuationis.

The “two attributes” of continuity and change are both functions of time; both the connection and the differences between any two “arbitrary homogenous segments” are due to the action of time, according to Bloch.

The truncation principle, however, has a wider application than time. To express the truncation principle in terms of time invites a formulation (or an example) in terms of space, and there is an excellent example ready to hand: that of the color spectrum of visible light. There is a convention of dividing the color spectrum into red, orange, yellow, green, blue, indigo, and violet. But this is not the only convention. Because the word “indigo” is becoming almost archaic, one now sees the color spectrum decomposed into red, orange, yellow, green, blue, and purple.

Both decompositions of the color spectrum, and any others that might be proposed, constitute something like, “arbitrary homogenous segments.” The decomposition of the color spectrum is justified by the truncation principle, but the principle does not privilege any one decomposition over any other. All distinctions are equal, and if any one distinction is taken to be more equal than others, it is only because this distinction has the sanction of tradition.

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Grand Strategy Annex

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