Science and the fallacy of induction

Yesterday was the date of submission for my 2 papers (one research, one exegetical), which by God's grace I have managed to complete. My research paper was on the philosophy of science. More specifically, it was on Thomas Kuhn's idea of 'normal science'. Without reproducing the paper until after it is being graded, here is a small excurses into one of the problems of science as related to its supposed gathering of truth. (which incidentally is not on my paper, which is more philosophical in nature)

The issue is the problem of induction. Scientific arguments are almost always inductive arguments with the argument form as follows:

If p, then q; q, therefore p.

Logicians will immediately see this as committing the fallacy of affirming the antecedent. p is the hypothesized scientific theory of which we desire to know its truth value. Scientists come up with hypotheses of how nature works and tests them (at least in the classical idea of scientific methodology). Experiments are then set up to get a data set of measured values. If the values from the experiments match the anticipated values (q), then the conclusion is made that the theory p is right.

Scientists of course are not that stupid to stay with such fallacious arguments. Typically, they try through the use of double-blind experiments and other such procedures to confirm their theory. What they are attempting is to construct the argument to be as follows:

If and only if p, then q; q, therefore p.

While I am sure some instances the auxiliary experiments may be able to help construe the research project to form a logically valid argument (especially if the researcher is rigorous and meticulous in his experiment), nevertheless at a deeper level, are there assumptions built into the scientific enterprise of which scientists in general are blind to?

We would like to look at an elementary problem with science dealing with the fallacy of induction. Consider three data points from an experiment

Fig.1

How should we construe the relation between these two quantities x and y? This looks like a simple linear correlation, so we draw a black line through these three points.

Fig.2

The equation of that straight line is y=3x-1. Now, we have a problem. We can see in Fig. 2 a red curve that intersects the same data points and thus is a valid interpretation of the actual relationship between the two quantities. The equation of that red curve is the equation y=(4x²-4x+2)/x. The question before us therefore is this: Upon what basis do we discount one equation for the other? If you say that we should opt for the simpler equation, in an application of Occam's razor, then the next question is this: Why must the truth be simple? Why is Occam's razor a valid rule to be applied in this case?

Perhaps it is said that we should be more rigorous in our experiments and get a larger data set. Indeed, that helps. The best scientific research is backed up with lots of experimental data and attempts to cover every loophole imaginable. That is after all what being a good scientist is about. But even with all these extra research done and data possessed, can it still differentiate between two different equations?

Fig. 3

In Fig. 3, we once again see our proposed equation in black, and the alternate equation in red. Now however, we have a competing equation of the form y=3x-1+ 1/(1000-100x). Now, it can be seen that no matter how much data we have from 0<x<9 thereabouts, there is simply no way to differentiate between the two equations. If all our data points are within that range of x values, then we simply have no way to choose between them.

What does this tell us about science therefore? Science is limited. Science cannot give us the truth of anything. What science does is to give us a working description of reality (which is of course immensely practical in application), but it does not explain it. And the working description of scientifically derived laws are circumscribed by the limitations of the experiments, but we can cannot go beyond it. As I am sure it is still taught in classes on scientific methodology, scientists are not allowed to extrapolate their equations beyond the range of their data. For instance, in the initial data set of 3 points given, nothing should be said of anything with an x value of 4 or 5. If the data set has a highest x value of 7, nothing should be said of what the case would be if x=9.

This has implications especially for what is called 'historical science', which is the investigation of the past using scientific methodology. Since scientists are not and cannot be in the past, all of such historical science investigations are inherently fallacious. Most of them of course are done within the framework of naturalistic uniformitarianism, which as a philosophy is not science and is not testable. Translated into data interpretation, it is a hopelessly naive methodology which assumes that the simplest interpretation of existing data points must hold true in the past too. Thus, if we have the data set above, uniformitarianism simply assumes that the equation must be a linear one. If another data set seems to follow a quadratic or simple logarithmic equation, then that must be the right type of equation.

All of such historical science is therefore fallacious. Evolution is therefore not scientific, although evolutionary science is a scientific explication of the evolutionary metanarrative. The Big Bang theory, the theory of abiogenesis and others such are simply metanarratives that are scientifically explicated as to how the metanarratives may have played out in history. All of these commit the most blatant form of the induction fallacy, and their truthfulness can be legitimately disputed.

Christians therefore do not have to be intimidated by the evolutionists. Their science is done as an attempted deductive validation of their metanarrative, which we have no reason to buy into. If we reject their metanarratives of how things are and come to be, we can have confidence that the so-called entity called "science" is not on their side. As Paul Feyerabend says,

…the people who say that it is science that determines the nature of reality assume that the sciences speak with a single voice. They think that there is this monster, SCIENCE, and when it speaks it utters and repeats and repeats and repeats again a single coherent message. Nothing could be further from the truth. Different sciences have vastly different ideologies
—Paul Feyerabend, The Tyranny of Science (Malden, MA: Polity Press, 2011), 55

Science is merely an instrument and a tool. It is dumb and deaf and blind. Those who make science into their idol will be as dumb as the idol they worship. Amen.