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A Treatise on the Quine-Duhem Thesis in Relation to the Crucial Experiment and Popperian Falsification

Douglas Adams in his book Hitchhikers Guide to the Galaxy said "The answer to life, the universe and everything is 42." If only science and its inherent methodological principles were that simple. At first glance, the goal of science seems to be striving for just such an irrefutable answer. Biologists look for the answer to life, physicists look for the making of the universe and philosophers look for the meaning of everything. Scientists assume that the methodological principals that they use will point them towards reality. However, are we correct in assuming this? In assuming or maybe hoping that these methodological principals are true, the possibility exists that they may be fallible. The Quine-Duhem thesis, often seen as an attack on the aforementioned methods, claims that it is impossible for negative evidence to disprove a theory. A correct interpretation of the results of the Quine-Duhem thesis leads not to the apparent weakening of scientific methodology by actually helps to authenticate scientific method.

The methodology used in science attempts to give the scientist the best possible look at the reality that they are trying to measure. These methods include the crucial experiment, Popperian falsification and modus tollens. By using a crucial experiment or test, a scientist proposes that he can devise an experiment such that the two or more theories under test are contrary to each other. The crucial experiment simply represents the fact if one theory is true the others must false. For example suppose there are two contrary claims: The given glass contains only water or the given glass contains only sulfuric acid. The crucial test could a piece of litmus paper placed in both of them. The litmus papers will either turn a color or it will stay neutral. If the litmus paper turns blue then the first theory must me false. Notice though that this does not prove that the second is true. According to the crucial experiment, falsification of the first theory is true because it failed to pass the test. This is the first method of falsification contained within scientific methodology. Modus tollens is a simple logical principal that is used in many of the falsification methods. Modus tollens states that if (b) follows from (a), and (b) is shown to be false then it is allowable to infer that (a) is false. This logical situation never appears in such a simple form in nature though it is the base for many methodological principles. Popperian falsification attempts to determine the truth-value of a given theory by putting it through multiple tests. First a theory is determined as needed then is tested to try to prove the theory wrong. If the theory fails the test then it is determined to be false. If the theory passes the test, then it is not false. It is important to note that this does not show that a theory is true but only that it has passed all the tests thrown at it.

"Any seemingly disconfirming evidence can always be accommodated to any theory." The Quine-Duhem thesis as stated above seems to provide a method to deny falsification as proposed by the crucial experiment and by the Popperian method. The crucial experiment is vulnerable to the Quine-Duhem attack in part because of the crucial experiment's reliance on modus tollens. In the above example the experiment can represented in a first order language as: (A_{1 É} R) & (A_{2 É} B) & (A₁ v A₂) where A₁ = placing the litmus paper in acid and A₂ = placing the litmus paper in a non-acid (base or water). Since the paper can not be placed in an acid and a non-acid at the same time the (A₁ v A₂) term must be exclusive. In the crucial experiment the experiment gives either ~B or ~R (the paper turns red or blue). Then using modus tollens either ~A₁ or ~A₂ is found, implying falsification. Theoretically, the experiment would be set in such a way as to give us the last term (A₁ v A₂) but unfortunately, there are two places in this setup for an attack by a Quinean. First, a Quinean would argue that falsification is possible only if the following can shown to be true: that red must result from placing a strip of litmus paper in the acid, and that blue must result from placing a strip of litmus paper in a non-acid solution. But if any seemingly disconfirming evidence can be accommodated then it follows that even if a strip of litmus paper turns blue when placed in an acidic solution it is impossible and would even be foolhardy to conclude that the solution is non-acidic based solely on the litmus paper. The first and most obvious question would be about the quality of the litmus paper. The litmus paper would be tried again to verify or contradict the original result. Therefore, (A_{1 É} R) is not correct by itself, it must include qualifiers such as [(A₁ & W₁ & W₂ &...& W_n )É R] where W is a condition that must be met such as the litmus paper being absent of imperfection or that the solution under test be completely uniform. From that we see that if ~R is found then (A₁ & W₁ & W₂ &...&W_n ) as a whole is false. It is important to notice that A₁ is not necessarily false. Only if it can be shown that W₁ through W_n is true can A₁ be proven false. Notice also that this makes the (A₁ v A₂) almost meaningless, this is the second result of the Quine-Duhem attack.

For Popperian falsification, the Quinean attack almost completely destroys the method. Since Popperian falsification simply waits until a theory fails once to falsify it, it is easy to see how an application of the thesis forces the condition that to deny the theory it must be possible to unequivocally affirm the truth of all the auxiliary conditions. Given in a general form (T & W₁ &...& W_n) É P where T = theory under test, W = auxiliary conditions and P = predicted result. Therefore, since Popperian falsification relies on its use of modus tollens the whole thing falls apart.

Even though the Quine-Duhem thesis appears to have weakened the crucial experiment to point of triviality and has completely destroyed any hope of using Popperian falsification there must be some sort of reconciliation that allows at least the crucial experiment to function with some level of usefulness. With the crucial experiment, one possibility is to use Baye's theorem to assign a probability to each of the W_n terms. In this way, the probability of T can be found from the total probability of the W_n terms. Since this is only a probability it still does not allow for the falsification of theories but tells us which ones are more likely false than others. A second, more abstract, way to view the affects of the thesis is think of it as increasing the accuracy while decreasing the precision. In other words, since we can not completely falsify any theory, we know that we have not thrown out one that may have been correct. The lens through which we view reality, because of the Quine-Duhem thesis, is slightly less distinct but is impossible to be distorting. The scientific methodological principles, changed by the Quinean attack, are now more powerful than ever because it eliminates humans from introducing error and lets nature decide what is truly false.

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