The most important change that we need to make in talking about historiographical interpretation is that we know what is true. We do not know what is true, what really happened, and similar.
At the same time, we have to insist that some interpretations are false. As Umberto Eco pointed out long ago, if no interpretation is false, then every text is the same text, and there is only one text. The phone book of Vienna from 1973 is the same thing as Lenin's writings. If we cannot reject an interpretation, then there is no way to differentiate them, and it is all the same.
That combination of there being no true one answer but many wrong answers must strike many people as strange because most people know that not-true is false and not-false is true. Due to this symmetry that setup is then confusing.
The first point to make then is that this switch from true to false using negation only works in the case of a complete disjunction. We already said that we want to assume that not all texts are the same text, so we have at least two interpretations. So if the competing interpretations A and B are up for discussion, and we can show not-A, then the disjunction allows us to conclude B. So if two people Alice and Bea are locked in a room with a hard piece of candy, and the candy is gone, and we can prove that Alice did not eat it, then Bea must have eaten it.
For most historical events, however, this strategy fails because the disjunction of interpretations remains open. As David Hume pointed out in Dialogs concerning Natural Religion, some of these either-or arguments suffer from a lack of alternatives or become far from clear when other alternatives are considered (famously, that the world might be like a plant). The most obvious present day case is the restricted alternative between evolution and intelligent design, where the problems of evolution only can imply an affirmation of intelligent design if there are no competing interpretations.
So for the first measure of approximation, historiography cannot show what the true narrative is, only that there are false narratives because the disjunction of interpretations is not complete. Notice that psychologically, this may still be a problem, because a very large number of competing interpretations is almost an attack on conceptual resources, an interpretative denial-of-service strategy.
The next question then becomes however, how to show that an interpretation is false. Suppose that our hard candy contains a substance that some people have allergic reactions to. Suppose further that Alice has in the past shown allergic reactions. Then we can mount an argument that either Alice would have had an allergic reaction or that Alice did not eat the hard candy. Very quickly the devil shows itself in all the details as the tree of dependence and justification begins to extend downward into the minutiae of cellular biology, chemistry, and medicine of human food allergies. And that is just the natural science side of the problem. There are also other events that are historical in that chain, that have the same disjunction of interpretations intervening between the chemical processes, say, and the conclusions that we wish to draw for adjudicating between A and B. Perhaps Alice's prior episode was misdiagnosed; perhaps the reaction was caused by another allergenic substance; perhaps the evidence for that episode is suspect (Alice's grandmother told her, because Alice was too young at the time to remember herself).
However to resolve the conundrum of the interpretative process, what should be clear though is that we need to be ready to accommodate a shift in the truth value of our supports at any point in time. Precisely because the supports of the sub-theories might shift with any new piece of evidence; precisely because none of these matters are monotonic in the logical sense of the word---truth maintenance as part of the ongoing process of rejustification in the face of discovery becomes paramount.
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