Definitions are dogmas; only the conclusions drawn from them can afford us any new insight - Karl Menger

There is a clear understanding in this world about things we know and things we do not. Yet there are those things that we don’t even know that we don’t know. Here, I am not indulging in circumlocution, but pointing out that human knowledge is only a projection of a few years of experience, passed on with the advent of civilization, which has made us who we are from the time when we were about as influential in this world as an ape.

Say there is a lady, Ms. B. Now, I may believe that B is a selfless person but I don’t quite know it, and I know (or am aware) that I don’t know it. However, in another case, Mr. M, whom I always considered and knew to be a selfless man, turns out to be a selfish man. Here, I didn’t know that M was selfish but I also didn’t know that I didn’t know. Just like my dispositions about people dictated this case of knowledge, there are other such factors that affect every case of knowledge in a similar fashion. The problem that comes up is how to distinguish from real cases of knowledge and those that just seem to be cases of knowledge. At a personal level, it can get extremely hard to know whether the items of knowledge that we possess are, indeed, genuine. Besides, even though all our arguments may seem to have a general strategy, they rely on some preconceived ‘knowledge’ assuming it to be the most reliable way we have at establishing beliefs or drawing conclusions.

Therefore, our ideas of what we know are based on our assumptions. But these assumptions themselves must be questioned. I intend to come back to this later in the discussion.

William of Ockham, a 14^th century English logician and a prominent herald of modern philosophy, came up with a principle popularly known as Occam’s razor - Entia non sunt multiplicanda praeter necessitatem. The adage translates to “Entities should not be multiplied unnecessarily” or in ’simpler’ words, “All other things being equal, the simplest solution is the best”. Thus, his ‘razor’ suggests that minimum assumptions should be made when attempting to explain any phenomenon. For most scientific and practical purposes, Occam’s razor works beautifully. The desirability of a theory or a even a hypothesis is often directly related to the number of independent parameters involved. One with an excess of such parameters is always less desirable.

The maxim found great use in fields of science, medicine, philosophy and so on. However, the razor proved to be too austere a statement, as it often happens that the best explanation is much more complicated than the simplest possible explanation because its assumptions amount to less of an improbability. ”The simplest explanation is the best one” fuses a rigorous notion of simplicity and ease of human comprehension. The two are not equivalent.

Here, I feel I should talk a little about the word that seeped into my last paragraph and is the subject matter of Whitehead’s ‘advice’ – simplicity; something of central importance when considering something like the epistemology of natural sciences. The word itself can be, and is, used in many different senses. We can easily say for a particular problem that the solution to it is not simple but difficult, but then there are others, like many a theory, that are of great methodological simplicity but ‘complex’ in another sense.  Simplicity and complexity (in other words, order and disorder) are antonyms, yet related in a sense that behind every apparently smooth and unruffled surface lies an ocean of complexity. So it is seen that even though the two are inseparable, we would like things to be simple.

In his popular work, Logic of Scientific discovery, Karl Popper argues that our preference for simplicity is explained by his falsifiability criterion wherein we prefer simpler theories to complex ones “because their empirical content is greater; and because they are better testable”. This makes some sense since a simple theory applies to more cases and is more easily falsifiable. At the same time, Alfred N. Whitehead (British mathematician and philosopher) suggests that one should always question the solution because things are not usually as simple.

In effect, it initially seems as if ’seek simplicity, and distrust it’ is an overlay of scientific skepticism over Occam’s razor rather than a separate philosophical suggestion or advice. However, a little pondering makes one remember instances and details back from school and suddenly Alfred Whitehead’s words seem to bear some truth. There are various things that we were taught or picked up in school that might have been simple but aren’t correct. For instance, theories of classical physics helped us understand electric current in a conductor as a flow of positive charge and this worked well for many a circuit problem. However, we can now thank J.J. Thompson for making us aware now that it isn’t really protons that flow to produce current but much smaller units called electrons. For a long time, we considered the atom to be the smallest fundamental unit. However, now we know that there can be further break down of this atom into protons, neutrons and electrons. The first two can further be divided into quarks and gluons. Thus, we are able to conclude that atoms aren’t really the smallest building blocks of matter. Similarly, there was many an assumption that didn’t hold true in reality. Thus, it can be seen that certain assumptions or cases of knowledge may work for certain purposes but don’t hold true any more, since relevant discoveries regarding respective complexities were made.

The more one thinks, the more he or she realizes that Whitehead’s words are, in fact, full of inherent wisdom and they may soon become of extreme importance to all of us. They nowadays resonate with every practicing scientist seeking out simple, useful descriptions of reality and then distrusting them for their simplicity. It is here that the point I made in the beginning comes in. As we know that our descriptions are only approximations, there is the constant need to refine our understanding. Yet there are some obvious obstacles to this. Firstly, the process is hardly ever straightforward or predictable. Secondly, there needs to be a continual assessment of our knowledge. Without a regular critical assessment of knowledge, one runs the risk of jeopardizing his or her knowledge. If we do not keep asking ourselves new questions, we would remain in an erroneous comfort zone.

Albert Einstein wrote in 1933 that “Theories should be as simple as possible, but no simpler”. I think that is as sweet a piece of advice as we can get.

Bibliography

Logic of Scientific Discovery, K. Popper (1934)
Dimensionstheorie, K. Menger (1928)
Ockham, S. C. Tornay (1938)
The Development of Logic, W. Kneale & M. Kneale (1962)
Editorial: Too complex to comprehend?, F. Gannon, The EMBO Journal (Aug 22, 2007)
Epistemology, Michael Huemer (2002)

Photo Courtesy: Mykl Roventine

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