Indeterminacy problem
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The argument is as follows:
- Given an infinite number of possible theories,
- And given a finite amount of experimental evidence,
- It is impossible to disambiguate between all viable theories.
The logic here is simple; with an infinite number of theories, it is always possible to take one viable theory which is supported by evidence, and change it to add some complexity, and the result is yet another perfectly viable theory. Often it is even possible to invoke totally different forces with the same result.
For example, it could be that the Earth revolves around the sun due to the effects of inertia and gravity, or it could be simply that the Earth enjoys revolving around the sun and so chooses to do so. Experimentally these two theories cannot be differentiated.
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[edit] Solutions
But since science certainly does select and develop theories, a paradox arises here; the question becomes, if evidence is not enough to select a theory, then how are theories selected?
Several methods have been suggested of dealing with this paradox:
[edit] Social forces
The first is to say that experimental evidence is not the only deciding factor, and that social and historical forces direct the selection between competing theories. This seems to undermine the value of scientific thought in many ways.
In the above example, it might be possible to say that the theory using inertia and gravity is more accepted because modern science is founded on determinism, and animism has fallen out of favor. It is socially more acceptable in the scientific community to apply natural rather than conscious forces.
Upon careful analysis, however, this argument seems an incomplete answer; given that there is a finite amount of experimental evidence, it also makes sense that there should be a finite amount of social forces as well, and still the problem persists.
[edit] False premise
A second method of dealing with this problem says that in fact there is not an infinite number of possible theories, since the available theories are limited by the ideas which have actually been imagined by scientists.
This argument undermines the first premise of the paradox, but still it is possible to envision situations (such as that above) when even a finite number of theories is indistinguishable by experiment. It is unclear what this idea says about the value of scientific thought.
[edit] Occam's Razor
The third solution is based upon Occam's Razor, which forms much of the basis of modern scientific thought. Given that one seeks the simplest explanation, a theory which accounts best for all observed phenomena, does not predict disproven phenomena, and does not introduce unobserved phenomena is to be preferred. This solution only serves to strengthen scientific thought rather than undermine it.
In the above example, it is quite clear that the simpler explanation is to apply inertia and gravity, since this theory involves attributing no consciousness to the Earth, uses a relatively small number of forces, and also has applications to other experiements in physics.
However, this solution has flaws as well, if it is possible for two theories to be equal in complexity and account for all observations while still remaining fundamentally different. In this case, Occam's Razor would not be able to disambiguate.
[edit] Conclusions
In truth, it is likely that all of these solutions, and perhaps others, play a part in dealing with this problem. Occam's Razor is certainly important, the limits of what has been imagined are definitely play a role, and even social forces may have some effect on scientific development.
