Scientia Propter Quid: Method for Disconfirmation
Consider some theory/hypothesis, T, and an observation consequence, O, entailed or predicted by T. Given T, our expectation is to observe or experience O. A method for disconfirming T goes as follows:
1. If T, then O.
2. Not-O.
_________________
3. Therefore, not T.
This method for disconfirmation is deductively valid. If O is entailed by T and we find that O does not obtain when we expect that it should, T cannot be true. T is sufficient for O. O is necessary for T. Hence, if O is not the case, T cannot be the case, either. Here's a simple example. Hypothesis: Tony just spilled orange juice on the kitchen floor. Observation consequence: orange juice will be observable on the kitchen floor. When I immediately rush to the kitchen, however, I find no orange juice on the kitchen floor. Therefore, the above hypothesis is false.
AUXILIARY HYPOTHESES
Most of the time, disconfirmation reasoning is not as simple as the above syllogism suggests. This is due, in part, to the presence of auxiliary hypotheses -- "further statements about the conditions under which the hypothesis is tested" [1]. Thus, if T is true and the relevant conditions obtain, O will result. Let 'A1 & A2...& An' represent auxiliary hypotheses. With these auxiliary hypotheses in mind, disconfirmation reasoning usually goes as follows:
1. If T & A1 & A2...& An, then O.
2. Not-O.
____________________
3. Therefore, either not T, or not A1, or not A2...or not An.
Notice that any one of the auxiliary hypotheses -- or a combination of them -- could be the reason for O's not obtaining. The whole theory cannot be thrown out until it is known, with a good degree of probability, that none of the auxiliary hypotheses themselves are responsible for O's not obtaining [2]. In many cases (perhaps in all such cases) where an expected consequence or observation does not obtain, it is reasonable to first consider whether one or more of the auxiliary hypotheses is problematic before throwing out one's theory.
AN HISTORICAL CASE STUDY: MARS AND TELESCOPES
Consider Galileo's (and, earlier, Copernicus') hypothesis that the solar system is helio-centric (Sun-centered), H. A consequence of Galileo's helio-centric model is that the distance between Earth and Mars will get larger and then closer again as their orbits carry them around the sun. This is a result of Earth having a faster orbit than Mars (which is a consequence of Earth being closer to the Sun). The following observation consequence was predicted even before Galileo's time:
S: for observer's on Earth, there should be a significant change in the appearance of the size of Mars as Earth gets further and then closer to it.
S was not the case, though. The apparent change in the size of Mars was negligible and didn't fit precisely with the calculations made by scientists. Therefore, the following argument, among others, was endorsed against helio-centricism:
1. If the solar system is helio-centric (H), then S.
2. Not-S.
__________________
3. Therefore, the solar system is not helio-centric (~H).
However, the following auxiliary hypothesis was being assumed:
V: either plain sight or the most advanced visual apparatus (or both) is capable of detecting the expected change in the appearance of Mars.
Thus, the argument should have been
1`. If H and V, then S.
2`. ~S
__________________
3`. ∴ ~H or ~V
Before throwing out H, the auxiliary hypothesis, V, needed to be considered. As it turned out, neither plain sight nor the best telescopes of the time were capable of detecting the shift in the apparent size of Mars predicted by the helio-centric model. The problem was not with H, but with V. With Galileo's new and improved telescopes, however, the shifts became apparent. H could be salvaged from disconfirmation when it was understood that the auxiliary hypothesis was the source of error. Again, it is always best to check the sustainability or possible faults with one's auxiliary hypotheses before rejecting a general theory all together [3].
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Footnotes:
[1] Rosenberg, Alex. Philosophy of Science: A Contemporary Introduction. 3rd ed. New York: Routledge, 2012. Print
[2] Richard DeWitt writes, "[W]hen one is faced with evidence that seems to disconfirm a theory, it is not only an option, but indeed it is often more reasonable, to maintain one's belief in the theory and instead reject one of auxiliary hypotheses." Dewitt, Richard. Worldviews: An Introduction to the History and Philosophy of Science. 2nd ed. N.p.: Blackwell Publishing Ltd, 2003. Print.
1. If T, then O.
2. Not-O.
_________________
3. Therefore, not T.
This method for disconfirmation is deductively valid. If O is entailed by T and we find that O does not obtain when we expect that it should, T cannot be true. T is sufficient for O. O is necessary for T. Hence, if O is not the case, T cannot be the case, either. Here's a simple example. Hypothesis: Tony just spilled orange juice on the kitchen floor. Observation consequence: orange juice will be observable on the kitchen floor. When I immediately rush to the kitchen, however, I find no orange juice on the kitchen floor. Therefore, the above hypothesis is false.
AUXILIARY HYPOTHESES
Most of the time, disconfirmation reasoning is not as simple as the above syllogism suggests. This is due, in part, to the presence of auxiliary hypotheses -- "further statements about the conditions under which the hypothesis is tested" [1]. Thus, if T is true and the relevant conditions obtain, O will result. Let 'A1 & A2...& An' represent auxiliary hypotheses. With these auxiliary hypotheses in mind, disconfirmation reasoning usually goes as follows:
1. If T & A1 & A2...& An, then O.
2. Not-O.
____________________
3. Therefore, either not T, or not A1, or not A2...or not An.
Notice that any one of the auxiliary hypotheses -- or a combination of them -- could be the reason for O's not obtaining. The whole theory cannot be thrown out until it is known, with a good degree of probability, that none of the auxiliary hypotheses themselves are responsible for O's not obtaining [2]. In many cases (perhaps in all such cases) where an expected consequence or observation does not obtain, it is reasonable to first consider whether one or more of the auxiliary hypotheses is problematic before throwing out one's theory.
AN HISTORICAL CASE STUDY: MARS AND TELESCOPES
Consider Galileo's (and, earlier, Copernicus') hypothesis that the solar system is helio-centric (Sun-centered), H. A consequence of Galileo's helio-centric model is that the distance between Earth and Mars will get larger and then closer again as their orbits carry them around the sun. This is a result of Earth having a faster orbit than Mars (which is a consequence of Earth being closer to the Sun). The following observation consequence was predicted even before Galileo's time:
S: for observer's on Earth, there should be a significant change in the appearance of the size of Mars as Earth gets further and then closer to it.
S was not the case, though. The apparent change in the size of Mars was negligible and didn't fit precisely with the calculations made by scientists. Therefore, the following argument, among others, was endorsed against helio-centricism:
1. If the solar system is helio-centric (H), then S.
2. Not-S.
__________________
3. Therefore, the solar system is not helio-centric (~H).
However, the following auxiliary hypothesis was being assumed:
V: either plain sight or the most advanced visual apparatus (or both) is capable of detecting the expected change in the appearance of Mars.
Thus, the argument should have been
1`. If H and V, then S.
2`. ~S
__________________
3`. ∴ ~H or ~V
Before throwing out H, the auxiliary hypothesis, V, needed to be considered. As it turned out, neither plain sight nor the best telescopes of the time were capable of detecting the shift in the apparent size of Mars predicted by the helio-centric model. The problem was not with H, but with V. With Galileo's new and improved telescopes, however, the shifts became apparent. H could be salvaged from disconfirmation when it was understood that the auxiliary hypothesis was the source of error. Again, it is always best to check the sustainability or possible faults with one's auxiliary hypotheses before rejecting a general theory all together [3].
___________________________________________________________________
Footnotes:
[1] Rosenberg, Alex. Philosophy of Science: A Contemporary Introduction. 3rd ed. New York: Routledge, 2012. Print
[2] Richard DeWitt writes, "[W]hen one is faced with evidence that seems to disconfirm a theory, it is not only an option, but indeed it is often more reasonable, to maintain one's belief in the theory and instead reject one of auxiliary hypotheses." Dewitt, Richard. Worldviews: An Introduction to the History and Philosophy of Science. 2nd ed. N.p.: Blackwell Publishing Ltd, 2003. Print.
[3] In many cases, it is not clear where the error lies. An observation or experiment may yield conclusions that contradict a theory (or are really unlikely, given the theory), but may not point out where exactly the problem exists. The 20th century philosopher of science, Pierre Duhem, wrote that "...the physicist can never subject an isolated hypothesis to experimental test, but only a whole group of hypotheses; when the experiment is in disagreement with his predictions, what he learns is that at least one of the hypotheses constituting this group is unacceptable and ought to be modified; but the experiment does not designate which one should be changed" (see his essay "Against Crucial Experiments" found in McGrew et. all, Philosophy of Science: An Historical Anthology).
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