Science and Empiricism

In “The Assayer”, Galileo has belief that in order to understand the universe, one has to learn the language and the letters in which it is written. More specifically, he thinks that the language is written in mathematics, in geometry, and the letters are triangles, circles, and other geometric figures. Deeply believing in that both scientific and natural verity can be perceived through mathematics and geometry, Galileo thinks that “Without a background in mathematics, a reader can only wander in a dark maze…” (Galilei 18). Can we truly believe that mathematics and geometry are the eternal truth with respect to time? Pirsig does not think so. He states that geometry can only become more convenient as it is being developed, saying that “Geometry is not true, it is advantageous” (Pirsig 337). Similarly, Quine even furthered the disbelief of the absolutely scientific truth within geometry and mathematics by saying that the totality of pure mathematics and logic is a “man-made fabric” (Quine 26). How could Pirsig and Quine, two supposed apprentices of western scientific method, oppose the grandfather of science? I think that the main argument of those three authors is whether the truths of nature can be discovered by the scientific method and whether the scientific truths are absolutely unshakable. Obviously, on one hand, Galileo believes that mathematics and geometry are the absolutely scientific truths and they are necessary for one to grasp the truths in the nature. On the other hand, Pirsig and Quine think that mathematics and geometry fail to hold the absolute truth naturally or scientifically, for that mathematics and geometry are not eternal truth and nor will they remain unshakable as they develop. And thus the natural and scientific truths which are perceived by mathematics and geometry will be massively dwarfed and likely fail to be held within any mathematical and geometrical explanations. Even though they both disagree with Galileo’s belief to some extent, their reasons are apparently at odds.

The reason why Pirsig does not think that mathematics and geometry are eternally true is because he thinks that on one side the malfunction of scientific method shortens the life-span of the scientific truth and on the other side scientific axioms are made to be conventional for human convenience which makes the scientific truths fundamentally questionable. Then first of all, what is and causes the malfunction of scientific method? Pirsig believes that the malfunctions of scientific methods are caused by systematic flaws within the scientific method itself and the rapidly growing numbers of hypotheses which are generated by the systematic flaws of scientific method. In order to clarify the systematic flaws, Pirsig’s definition of scientific method should be discussed. Under Pirsig’s definition, scientific method is a mixture of deduction and induction where, induction is reasoning from particular experiences to general truths and deduction is the reverse (Pirsig 129). In a logic way of thinking, scientific method is broken down into six categories: (1) statement of the problem, (2) hypotheses as to the cause of the problem, (3) experiments designed to test each hypothesis, (4) predicted results of the experiments, (5) observed results of the experiments and (6) conclusions from the results of the experiments (130). From this we can clearly see two crucial factors which underdetermine the scientific truths—hypotheses and experiments. Theoretically, the more hypotheses are being tested by the experiments, the more likely we can get an absolutely scientific truth. But will it practically happen as our expectation?

For Pirsig, the answer is no. As more hypotheses are made and being tested, there will appear more hypotheses, for scientific method itself requires the falsifiability. If a well-established theory can always be falsified, according to scientific method, there will always be more questions. Then we refer back to the logic thinking of scientific method again, whenever the questions appear, we erect another hypothesis and test them to reach a brand new and better theory or hypotheses. Unfortunately, scientific truth will unlikely to occur in the process of the repetition of falsifying but end up with more and more repetition of falsifications. In this sense, Pirsig ironically mentions about the humor of Parkinson’s Law that ‘The number of rational hypotheses that can explain any given phenomenon is infinite” (Pirsig 139). So in essence, we assume that there are two variables which will give birth to hypotheses—time and the intensity of scientific activity (like experimentation). Then if time and the intensity of scientific activity are not fixed (obviously we know at least time cannot be a fixed in real life), infinitely many hypotheses are possible to be made. And if there are genuinely infinitely many hypotheses, they can never all be tested. Or we can say that scientific truths will reveal within a given period, accompanying with limitedly tested hypotheses. Thus Pirsig concludes “results of any experiment are inconclusive and the entire scientific method falls short of its goal of establishing proven knowledge” (Pirsig 140). Therefore, all scientific truths will not last eternally but are replaceable in the terms of time as if they have a life-span like all other living beings. If Pirsig is right, scientific truth can still be used to discover the truth of nature but only within a certain life-span, for scientific truth itself is more like a “temporal quantitative entity that could be studied like anything else” (Pirsig 140). For now, we only proved that scientific truth is not likely to be true for eternity from Pirsig’s perception. But it is still unclear that how and why does he make his statement of “Geometry is not true, it is advantageous”. Is there anything that can shake (or deny) the foundation of all science—mathematics and geometry?

Pirsig thinks there are. He believes that the crisis of scientific foundation is caused by the conventionalization and approximation of scientific axioms. For centuries, totality of scientific truth is consolidated and regarded as unshakable truth. Galileo was one of its preachers. If all scientific truths and logic of science are literally infallible, then the whole purpose of science will come down to, as Pirsig states, sheer refinements of past scientific truths with greater accuracy (Pirsig 333). Refinement, even this world itself indicates the true nature of so-called scientific development. Analogically, it is more like a process of amending than innovating, although innovations sometimes occur in the applications of scientific truth but not always within it. Yet, what if the fundamentals of the past scientific truths are not true? Surely if they are untrue, not only will the whole edifice of scientific truths be torn down to pieces, but also will all proved scientific truths turn into uncertainties. But for what reasons can they be untrue? Pirsig takes geometric axioms for an example. He thinks that geometric axioms are neither generated from synthetic consciousness of human nor by experimental verities because of their exogenous non-falsifiability (Pirsig 337). Hence he concludes that scientific truths are conventions that are generally adopted and only will be approximately convenient. And thus “One geometry cannot be more true than another; it can only be more convenient” (Pirsig 337). Inferably, I think that if the cornerstone of science—mathematics and geometry—is somehow a gerrymandered product of humanity, then the values of scientific truths will be conspicuously discounted. But it will only be true for geometry and mathematics but not totality of science that if they are not generated from synthetic consciousness or experimental verities. So the failure of scientific method is not yet fully proved. What if scientific truths (perceived through scientific method) are generated from another significant source—experience?

The entity of scientific method—mixture of induction and deduction—as previously mentioned, is greatly affected by experience. In this manner, Quine suggests that the scientific truth might fail as the liability of totality of science are dwarfed by the limited latitude of experience and because of the re-adjustments created by so-called logic laws which are actually folded by the experience (Quine 26). Substantially, we can consider the totality of science as a giant square which is formed by infinitely many small squares which fold the truths from individual experience. And I believe that scientific truths are only one small portion of natural truths. In the process of communicating experience, the truths must be passed by individual statements which we regard as logic laws and scientific method. Then the truth values of total science will be extremely underdetermined by the area of the intersecting parts from the individual experience. However, assume that the latitude of individual experience is extremely constrained (or self-contradictory in some cases); the sharing part will be extremely small. This means that no truths from individual experience can even reach the inner field of scientific truths. Thus the whole field of science will likely become indisputably inferior. Furthermore, Quine thinks that the way of communicating the truths contain re-adjustability (Quine 26). When individual statements are made to be conveniently ambivalent so that the truths can be certainly consisted, then there will exist, simultaneously, some hallucinations which enlarge the area of the sharing truths. Yet, when we somehow refer back to the totality of scientific truths, it will be consisting of huge chunk of supposed truths. And this is the fatal damage to all scientific truths. Therefore, if the total science is merely a gerrymandered product of internal human experience, it cannot be applied to discover the exogenous truths of nature.

In conclusion, we have proved that scientific truths are shakable and have a life-span from Pirsig’s perception; and we have proved that scientific truths cannot be used to discover the naturally truth since scientific truths are objective from Quine’s perception. However, we failed to prove that Galileo is wrong for two reasons: one, neither one of Pirsig and Quine denies that within scientific truths there exist partially natural truths; two, Pirsig and Quine both make the assumption about the origin of scientific truths to be a known source. However, there might be some unknown sources of scientific truths which are not yet discovered.