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The Justification and Description of Induction are Not Really Problems

by David M. Petersen


"Scientific laws and theories are universal generalizations that far outstrip the finite number of observations and experiments on which they are based" (Curd and Cover 409). This is very true, and the idea that fills in the gap between observation and support for a law for us (as humans trying to discover the natural laws on which the universe is based) is inductive reasoning. However, according to Peter Lipton, a big problem is the fact that inductive reasoning cannot be logically justified. Also, he believes that the problem of describing inductive inferences is very difficult. The various models that he gives to do this will be listed. I believe that the model that does the best job is all four of them put together, and that the problems of justifying and describing induction are not really very pressing problems.


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According to Peter Lipton, Inductive reasoning cannot be justified for two main reasons, underdetermination and circularity. The former is illustrated well by an example Lipton gives in his essay "Induction". "A finite number of points on a curve underdetermine the curve, since there are many curves that would pass through those points" (412). In other words, we may have a theory that we believe corresponds quite well with observations we make in reality, but the fact is that hypothetically there are many possible theories that could explain the same observations. This to me seems like a somewhat minor problem; our scientific theories seem to do quite well and are getting better all the time as evidenced by technologies based on them that are very effective. Our knowledge of quantum mechanics is being used in computer circuitry, for example. As our theories get more and more effective, they get closer and closer to true objective reality (but of course, they may never actually reach it). The other aspect of the problem with logically validating induction according to Lipton is circularity. Simply stated, circularity is the fact that if one tries to justify induction logically, one is forced to use an inductive argument, and this makes it logically invalid. This is of course true. Lipton says, "The argument that conservative inductions will work because they have worked is itself an induction"(416). I agree with Lipton that induction cannot be validated logically; I just don't think that it really matters in the grand scheme of things, since we are using induction (loosely defined) and moving forward in science all the time.

The problem of the description of inductive inference that Lipton espouses seems to me to be not much of a problem either, really. Essentially, the problem can be stated as the difficulty of stating logically what it is that is actually going on when we are practicing what we call inductive inference. The limited options that Lipton gives us are four in number. The first, the "more of the same" model, is the idea that because something has happened in the past, we can infer that it will happen again in the future. Secondly, we have the instantial model, which in Lipton's words is the idea that "a hypothesis of the form 'all A's are B' is supported by its positive instances, by observed A's that are also B" (Lipton 420). Then we have the hypothetico-deductive model, which is simply the idea that "a theory is supported by its successful predictions" (422). Lastly, there is the causal inference model, commonly known as Mill's methods, or the method of agreement and the method of difference. The method of agreement is as follows: if there is only one thing in common between all the instances of an event, this thing is a cause. The method of difference is as follows: if there is only one difference between two situations, one where an event occurs and one where it does not, that difference is a cause (424). Lipton describes the pros and cons of all of these models in much detail.

The reason I don't believe that the description of inductive inference is much of a problem is due to the fact that I believe that the universe and everything in it, including the pursuit of science, transcends mere logic. I think that these models are all valid to an extent, and the real "problem" is trying to understand the phenomenon of science in this manner. The idea is that everything in the universe, including the pursuit of science, is organic or very complex and not mechanical or simple enough to be described with mere logic. Logic is simple. For example, take the argument, "If it rains, the sidewalks will be wet. It is raining, therefore: the sidewalks are wet." This is a valid logical argument. The problem is that it has no real correspondence to actual life. In real life, the sidewalks being referred to could be in another city were it isn't raining, or there could be an overhang over the sidewalks in question, keeping them from getting wet. One can think of any number of situations that would invalidate this simple argument. This perfectly logical statement approach completely breaks down when trying to perfectly describe actual "entities" or situations that exist in our universe, because things in our universe have evolved over billions of years and are extremely complex. The emerging theory that illustrates this quality of things existing in our universe is called complexity theory. In complexity theory, evolving systems reach a "critical mass" of complexity and then spontaneously self organize into larger entities that can be named, like mankind's individual natural curiosity morphing into what we now call science. A good book on the subject is Complexity, the Emerging Science at the Edge of Order and Chaos, by M. Mitchell Waldrop. If this paradigm is just accepted, this problem of logically describing inductive inference becomes a waste of time (although previous work wasn't), because we would realize that it is too complex of a process to ever be summed up in a "logical" manner, but it is still a highly useful entity that we are using to further our success as a species. This is why I don't believe that the description of inductive inference is much of a problem.

In my view the "model" that does the best job of describing inductive inference is the fact that all of these models (and others probably) can be kind of superimposed together to achieve an imperfect version of the actual process. They all work to some extent, it seems to me, and one will work better in one situation better than another depending on the situation. The "more of the same" model would definitely work better at predicting whether the sun will rise tomorrow than the method of difference would! I think that it is a fairly pointless undertaking to try to declare one of these the winner or to try to come up with another logical model that will perfectly describe what is happening with inductive inference.

As discussed, inductive reasoning cannot be justified for two main reasons according to Peter Lipton, underdetermination and circularity, and the problem of describing inductive inferences as shown can be made difficult! It is my opinion that these philosophers of science get a little too caught up in a kind of hairsplitting overly analytical approach to understanding why science works that will always fail (although I suppose it is possible that more valuable insight could be gained from trying). Science works, and the fact that it does, and we have a rough understanding of it, is good enough. A better question to explore would be: what function is science performing in our evolution as a species? I think that the above stated problems of justifying and describing induction are related to the fact that the universe and everything in it is organic or very complex, not mechanical or simple, and that these philosophers hold logic, which is simple, in too high esteem. In other words, you will never be able to reduce the pursuit of science down to some completely understood simple picture, which is what these guys have been trying to do. Science is far too complex of an undertaking for that. It would be best to just try to grasp it holistically and then focus on larger questions, like: what is its place in the universe? Perhaps this view is eventually reached in the field of philosophy of science, I don't know. Logic is a very powerful tool, but it will always break down when trying to describe very complex systems.


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Work Cited

Curd, Martin and J. A. Cover. Philosophy of Science: The Central Issues. New York: W.W. Norton & Company, 1998.


Waldrop, M. Mitchell. Complexity - The Emerging Science at the Edge of Order and Chaos. New York: Touchstone, 1992.


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