Partial Truth Versus Verisimilitude
Return to the Ptolemy-Copernicus case. So far we have assumed that Ptolemaic astronomy was empirically adequate, and Copernican astronomy true. Of course, neither assumption is strictly correct.
What is really the case is that Ptolemy’s explanation of retrograde motions shared a true part with Copernican theory. That true part, common to both theories, sets out the relative motions of earth, sun and superior planets.Partial truth is not the same as verisimilitude. Verisimilitude is closeness to the truth—the ‘whole truth'—of a false theory taken as a whole. Partial truth is just truth of parts. A simple example will make the difference clear. “All swans are white” is false, because of the black swans in Australasia. (I had to get this baby example in—as some uncharitable soul once joked, having black swans in it is Australasia's chief contribution to the philosophy of science!) Despite its falsity, “All swans are white” is predictively successful in Europe, and bird-watchers find it useful to employ it there. I do not know how close to the (whole) truth “All swans are white” is, and none of the captains of the verisimilitude industry can tell me in less than 100 pages of complicated formulas. I do know that “All swans are white” has a true part (a true consequence) “All European swans are white”, whose simple truth explains the success European bird-watchers have.
The simple example with the swans can be generalised. A false theory T might be successful (issue nothing but true predictions) in a certain domain D. Explain this, not by saying that T is close to the truth, but by saying that “In domain D, T” is true. A false theory T might be successful (issue nothing but true predictions) when certain special conditions C are satisfied. Explain this, not by saying that T is close to the truth, but by saying that “Under conditions C, T” is true.
A false theory T might be successful as a limiting case. Explain this, not by saying that T is close to the truth, but by saying that “In the limit, T” is true. Notice that “In domain D, T” and “Under conditions C, T” and “In the limit, T” are all logical parts of T, that is, logical consequences of T. Of course, the conjunction S of the successes of T is also a logical consequence of T. But while S does not (satisfactorily) explain S itself, “In domain D, T” or “Under conditions C, T” or “In the limit, T” might explain S perfectly well. These restricted versions of T are not the same as its surrealist transform—restricted versions of T may be explanatory while its surrealist transform is not.Of course, if we accept such an explanation, it immediately raises the question of why the restricted version of T is true while T is false. Typically, it is the successor theory to T that tells us that T is true in a certain domain, or under certain special conditions, or as a limiting case. Still, that this further question can be asked and answered does not alter the fact that a true restricted version of T can explain T's partial success while T's surrealist transform does not.
It is the same with approximate truth, as when we say that “It is 4 o'clock” or “John is 6 feet tall” are only approximately true. What we mean is that “It is approximately 4 o'clock” or “John is approximately 6 feet tall” are true. And if we want to be more precise, we can say that “It is 4 o'clock give or take 5 min” or “John is 6 feet tall give or take an inch” are true. Approximate truth is not to be explained by trying to measure the distance of a sentence from the (whole) truth. Approximate truth is truth of an approximation. Approximate truth is a species of partial truth, since the approximations in question are logical parts of what we began with. “It is 4 o'clock” logically implies “It is approximately 4 o'clock” as well as “It is 4 o'clock give or take 5 min”, and “John is 6 feet tall” logically implies “John is approximately 6 feet tall” as well as “John is 6 feet tall give or take an inch”.
I have come to believe that the entire verisimilitude project was a bad and unnecessary idea. Popper's definition of the notion of ‘closeness to the (whole) truth' did not work. The plethora of alternative definitions of ‘distance from the (whole) truth' that have taken its place are problematic in all kinds of ways. And what was the point of the verisimilitude project? Precisely to explain how a false theory can have partial success. Now it is obvious that a true theory will be successful—after all, true premises yield true conclusions. But it is not obvious that a theory which is close to the truth will be successful, since near-truths yield falsehoods as well as truths. We should eschew the near-truth of false wholes, in favour of the simple truth of their parts. We should explain partial success in terms of truth of parts. Whole truths are wholly successful, partial truths partially successful. Either way, it is simple truth, not verisimilitude, that is doing the explaining.
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