One of the key pillars of the Scientific Method is the ascendancy of observation and measurement in the pursuit of knowledge. Science is an empirical endeavor, and observation is the first and most important step in the scientific process. It is the emphasis on observation over “pure thought” that separates modern science from early and medieval science. Science’s grounding in evidence based methods also explains it’s great success over the last few centuries.
Approaching “Pure Reason” With Caution
For a very large part of human history, people believed that it was possible to derive the fundamental truths of the Universe from abstract reason alone. Chief among these thinkers was Plato, but the thread was strong among the Greeks and carried through to a lot of medieval thinkers .
There is a certain attraction to the purest, most abstract forms of reason, like mathematical logic. However, one should be careful to distinguish between inevitability of mathematical conclusions within mathematical systems and the ability of those mathematical systems to draw absolute conclusions about the “outside world”.
For one thing, there are many possible mathematical systems one can construct by choosing different sets of starting assumptions (axioms). Each system can lead to conclusions which are inevitable within that particular system. Yet, the inevitable conclusions drawn from one set of axioms can contradict the logical conclusions of a slightly different set of axioms! For example, in Euclidean geometry the sum of the angles of a triangle has to add up to 180 degrees. But, there are equally logical, “non-euclidean” formulations of geometry where this does not have to be the case . As it turns out, some physical phenomena are well described by euclidean geometry. Other systems are best described by non-euclidean models. The necessary/inevitable conclusions of each system do not apply equally well to all cases .
To scientists, arguments made without grounding in externally observable phenomena are suspect. Observation “keeps it real”. Observation ties us to something external, outside of ourselves. As such, the combination of observation with sound research methodologies can place a check against our cognitive biases. I would argue that the scientific approach is one of realism compared with the idealism often characteristic of proponents of pure thought. To a scientist, “proofs” only exist in the very circumscribed world of math. Outside of math, proofs do not carry weight. We value ideas based on their ability to predict and explain things which can be observed, not on whether we find them to adhere to our limited sense of what is or is not logical.
Hiding Behind A Proof of Smoke
The above thoughts may seem self-evident, but there are many people for whom this isn’t so clear. I often encounter individuals who claim to have logical, purely deductive “proofs” that support their beliefs. I would like to highlight 2 ways in which these “proofs” fail to achieve the rigor or certitude that they are sold as having: (1) they shift the burden of the proof to axioms which are not sufficiently demonstrated and (2) they artificially restrict the allowable outcomes of the system in a way that leads to their desired conclusion, but does not fully reflect the full richness of reality. Let me elaborate:
Shifting the Burden of Proof to the Axioms:
You can prove anything if you start with the right axioms. But, the important question is: are your axioms right? One trick used in phony proofs is to shift some of the burden of proof into the axioms. The presenter hopes that his audience will view the axioms as untouchable, or at least he hopes they will be less skeptical of the axioms. But, it is a mistake to think that the axioms must be accepted without question.
Mathematics is the only field where you take an axiom to be true “just because…”. When we make statements about the real world, scientists still insist that our “first-principles” be rigorously tested. So, how do you validate a postulate?
1) Often, it is possible to test your assumptions directly. For example, the Theory of Relativity takes as a postulate that nothing can go faster than the speed of light. That’s just how the Universe seems to be. But, we don’t have to accept it blindly or even because it “seems to make sense”. We can test it. And, indeed, the speed of light has been tested and observed unfathomably many times, with no exceptions observed. It is a well-supported postulate of the theory.
2) Even if the postulate cannot be directly tested, the implications of the postulate can always be tested. If the consequences of an assumption cannot be tested, we say that the theory is not well defined. The point of a theory is to start with a minimal set of postulates and to work out the consequences of the postulates. If the consequences of those postulates agree with observation and if none of the consequences of those postulates contradict observation, then we feel that the postulates are good at explaining reality. Only then do we place trust and weight on new predictions made by that theory. The value of axioms in science lies only in how well they describe reality. But, as soon as the conclusions of an axiom contradict observations, that axiom is questioned or even thrown away. Unlike the “proofs” offered by opinionated and belief-driven people, the assumptions of science are not sacred or immutable.
A scientist will typically say something like :
Axioms A and B lead to hundreds of inevitable conclusions that are all confirmed by external observation. Therefore I consider proposition C (which hasn’t yet been observed) to be highly likely, since it follows from the same assumptions.
On the contrary, belief driven people tend to say things like
Let us start with assumptions A and B which make sense and therefore we accept as true. Conclusion C is inevitable, therefore C absolutely must be true!
Note that their “purely deductive” proof is no different from the scientific statement, except that the scientific statement is based on axioms which are rigorously tested and shown to agree with observation.
To summarize: don’t take the axioms of a so-called “proof” for granted. Apply scientific skepticism. Can they be rigorously tested, either directly or systematically through their theoretical consequences? If not, one should be very skeptical of the grounds upon which the proof is made. Finally, one should be aware that a proof, based on “pure” deductive reason is not really so “pure” if the axioms are observations about the real world. If the axioms make claims which should be testable, then those claims need to be tested. And if the axioms are untestable, then the proof is incomplete.
Restricting the Freedom of the System:
So-called “logical proofs” are often constructed in such a way that limits the number of possibilities available to the system. A skilled rhetorician will present a series of yes-no questions that limit the possible conclusions in a way that forces a person to their conclusion. But, nature often operates on a continuum; not necessarily a finite number of yes-no questions. Let us say that I have a glass marble. I present its color in a way that makes it seem as if the marble can either be red or blue. If I can demonstrate that the marble is not red, then my audience is led to the inevitable conclusion that the marble must be blue. In reality, the marble could well have been green or pink. My argument was logically correct. And, if the audience is focused on my logic, they will miss the bigger picture: that I have limited framework in which that logic exists. My logic is correct and the conclusion follows from the premises, but the logical model I’ve constructed does not completely describe the full richness of reality. A complete system would need to include the possibility of green marbles.
Pure though has value. Just don’t oversell it.
I am not saying that the inner dictates of our pure minds or intuitions are necessarily wrong. My issue is with calling them proofs. They are arguments that cannot be corroborated experimentally, but rather appeal to our inner senses. As a religious scientist I believe that these inner voices do indeed have a value to them.
But, it is important for us to realize that what may seem so compelling to our inner voices cannot be conveyed in the form of “proofs”. We cannot oversell how “obvious” our intuited or derived views of the world are. And, we need to balance our world of pure thought with experience gained from real-life interaction. I do not buy into scientism: the view that the only meaningful things we can say about the world are those that can be determined through science. But, I urge my readers to challenge themselves to take empirical findings seriously. As a matter of realism and pragmatism, it is important to check our beliefs against what we can observe and see.
From my experiences in the religious world, I am extremely frustrated by people who try to sell their beliefs by arguments that I term: “it’s obvious, stupid!”. I’ve been to religious talks where very skilled and educated rhetoricians resort to very intellectually aggressive tactics that cross a serious line for me.
Science “starts” with observation…but it does not end there
Earlier in this post I suggested that observations can place a check on our cognitive biases. But, I must be careful. Observations do not (at all) guarantee objectivity or correctness, as I discussed in my post on “jumping to conclusions”. Even very dogmatic and opinionated people can identify factual observations that support their views. In fact, one of the most insidious forms of bias is confirmation bias, wherein people selectively identify only those facts which support the conclusions they already choose to believe.
Science starts with observation but is does not end there. It is the first mile marker on a very long road. Science does not just ask for evidence, it demands that said evidence be placed in the context of a careful methodology. This road is fraught with peril. Even the best research falls fall short of attaining this ideal. And there is plenty of shoddy work in science that fails on a more rudimentary level.
In my next post I will talk about some of the methodological steps that scientists take in order to avoid the effects of bias. I will also take the opportunity to indulge in describing some of my own research. Stay tuned!
Aristotelian “physics” is different from what we mean today by this word, not only to the extent that it belongs to antiquity whereas the modern physical sciences belong to modernity, rather above all it is different by virtue of the fact that Aristotle’s “physics” is philosophy, whereas modern physics is a positive science that presupposes a philosophy…. This book determines the warp and woof of the whole of Western thinking, even at that place where it, as modern thinking, appears to think at odds with ancient thinking. But opposition is invariably comprised of a decisive, and often even perilous, dependence. Without Aristotle’s Physics there would have been no Galileo.
Martin Heidegger, The Principle of Reason, trans. Reginald Lilly, (Indiana University Press, 1991), 62-63 by way of wikipedia
 Applicability of non-Euclidean geometry: http://www.pbs.org/wgbh/nova/physics/blog/tag/non-euclidean/