Saturday, November 4, 2017

The March of Progress

I wrote this in 2006 for my doctoral students at Syracuse University and just found it while unpacking after my move to Round Rock. I had not remembered having this basic thought so long ago.


What is it that makes possible the progressive development of knowledge and understanding? This is a complex question since it presumes that there indeed exists something legitimately called the progressive development of knowledge. I admit to starting out with such an assumption. I want to explore some principles or basic ideas that seem relevant to an account of the progressive development of knowledge. Without these ideas, it is not clear, at least to me, how to account for human knowledge and understanding. These seven basic ideas are:

1.     Humans are not born knowing everything that there is to know. As obvious as this might seem, there have been people who rejected this most basic idea (see Plato’s discussion of anamnesis in The Meno and The Phaedo, for example).
2.     Knowledge refers to widely held and exceptionally well-established beliefs to which people are generally warranted in attaching their very highest levels of confidence. Statements that are likely candidates in this category include: ‘there is a constant ratio between the circumference and the diameter of a circle’ and ‘the speed of sound varies depending on the medium through which it is traveling’.
3.     We hold many other beliefs that can also be formulated as statements. We might generally attach less confidence to these other beliefs, but these beliefs nevertheless help us build up our knowledge of our surroundings and experiences. Statements that are likely candidates in this category include: ‘experienced statisticians provide reliable statistical analyses’ and ‘historical documents reliably represent facts and events’. For a very nice discussion of how these beliefs are intertwined see The Web of Belief by Quine and Ullian.
4.     Asking a question involves formulating a particular grammatical structure that typically ends with a question mark if it happens to be formulated on paper or with a rising tone of voice when formulated orally in English. Questions might begin with a word that implies that a question follows (e.g., ‘how’, ‘what’, ‘who’, ‘when’, ‘where’, ‘why’, ‘whether’), or one can transform a declarative statement into a question without using a question word. A particular rule in English guides the transformation of a statement into a question: put the verb first and place a question mark at the end. For example, one can transform the statement ‘There is a constant ratio between the circumference and the diameter of a circle.’ into this question: ‘Is there a constant ratio between the circumference and the diameter of a circle?’ Moreover, one may ask that question without knowing the answer, although there is some evidence that this piece of knowledge dates back to biblical times (Kings I, 7, 23) and ancient Egypt (the Rhind Papyrus dated about 1650 BCE). What is old knowledge for some may become new knowledge for others. One can formulate a question without being concerned with the answer, however. For example, someone might reply in the course of a conversation, “Is that any business of yours?” The elements of a question are in place – verb comes first, question mark comes last. But there is no search for an answer in this case. Rather, this apparent question may be used to terminate any further inquiry. Beware rhetorical questions – they do not contribute to the progressive development of knowledge.
5.     Having a question involves a search for an answer. The person who asks about the ratio between the circumference and diameter might ask without knowing that there is in fact a constant ration. This person might then engage in some physical experiments and measurements and discover, much like the ancient Egyptians, that there did seem to be a constant ratio regardless of how large or how small the circle was. Such a person might then go on to prove, in the spirit of Archimedes, that the results obtained empirically were mathematically correct. Having arrived at the knowledge that the ratio between the circumference and diameter of a circle is constant, our budding mathematician might go on to wonder whether or not the sequence of numbers in the expansion of that constant ever repeated. One should set aside a fair amount of time for such an enterprise. In any case, having a question implies that one does not know the answer and is willing to engage in a search for an answer or for possible alternative answers. We ought to have more questions.
6.     The logic of having questions can be generally represented as follows:
a.      First, one admits to not knowing or understanding X but wanting to know or understand X, where X represents some apparently non-obvious state of affairs of phenomenon. This simply means that one does not engage in a search for the obvious or for what is already accepted as known. One starts from a position of humility (‘I do not know’) and optimism (‘I can understand this if I make an effort’).
b.     Next, one begins to generate explanations and gathers evidence. This may be difficult in those cases where one has very little idea as to the nature of what one is seeking. A search, after all, is a search for what one does not have – in this case we are talking about looking for knowledge and understanding. There is a paradox of sorts connected with the fact that one is searching for an unknown X – if the item being sought is totally unknown in every respect, it is difficult to imagine how the search could be successfully resolved. The way around this apparent paradox is to simply acknowledge the situation that gave rise to the search, which presumably involved some things that one accepted, other things that required explanation, and some notion of what an adequate explanation would be like. For example, suppose that I am seeking to understand why sound seems to travel faster in water than in air. I might gather some evidence first to confirm my point of departure – that sound does indeed travel faster in water than in air. I might gather additional data points, at differing depths and altitudes and formulate an initial hypothesis that density appears to play a role (water being more dense than air, air being less dense at higher altitudes, and salt water being more dense than fresh water). I might even be sufficiently clever to test this initial hypothesis that the density of the medium is relevant to the speed of sound by checking to see if sounds travels even faster through a solid object such as a piece of metal or how fast sound travels in a vacuum (not very fast). While these further tests and observations may confirm the initial hypothesis, one ought not abandon one’s initial humility too readily – the hypothesis that the speed of sound through a medium is directly and closely correlated with the density of that medium could still be mistaken. Indeed, one might happen to observe that sound does not seem to travel very fast through hydrogen in comparison with nitrogen, even though nitrogen is more dense than hydrogen. Factors other than density must be added to the hypothesis to account for such additional observations – for example, the elasticity of the medium may well be relevant to the propagation of sound waves through that medium.
c.      Having a question, then, is often a process of iterative refinement and often involves a search for a satisfactory answer – one that may serve a short-term purpose (explain a difference between the observed speed of sound in air and water) – but the process may continue. This is how a body of knowledge is built up. Maintaining a sense of humility (‘I do not fully understand this phenomenon yet’) is just as important as maintaining a sense of optimism (‘I can understand this phenomenon better if I continue my investigations’).
7.     Not all beliefs are like this. Some beliefs are withheld from the scrutiny of such investigative cycles for various reasons. It is perhaps worthwhile to distinguish those beliefs that we are willing to subject to further investigation – and by implication willing to admit may be false or misleading or in need for refinement – from those that we wish to exclude, for whatever reasons, from such inquiry and refinement. What beliefs do we withhold from scrutiny and why? This may be a question worth investigating. It is likely that different people will admit to withholding different beliefs and for different reasons. Consider the statement ‘there is intelligent life outside our solar system’ as a candidate. One person may decide to withhold it from scrutiny because it is simply too difficult to investigate. Another may decide to withhold it because it conflicts with other beliefs that person has accepted, some of which might also be withheld from the process of iterative scrutiny. Still others may decide that it is worth investigating and not withhold it from scrutiny (see Carl Sagan’s Cosmos, for example).

As an additional example, imagine that you are backpacking with a friend in the Rocky Mountains and happen across a rock which appears to contain a fossil of a creature you do not recognize (see Gould’s Wonderful Life). You happen to be very knowledgeable about geology, paleontology, and zoology. Neither you nor your friend can explain the fossil. You speculate that the fossil may represent a species that no longer exists, one that died out millions of years ago. Your friend may object, perhaps on religious grounds. In this case, one of you may decide to investigate further, and one may decide to abandon any search for an explanation. At this point, the dialogue may end in amicable disengagement – hopefully it does not degenerate into brow and breast beating or worse. It is important in such cases to distinguish a search for an explanation, which involves gathering additional evidence and a willingness to abandon initial hypotheses explaining the phenomenon in question, from a search for reasons to adopt one explanation or another. Gathering reasons, constructing arguments, and developing positions of advocacy for one position or another should not be confused with conducting searches and making empirically grounded inquiries (see Sextus Empiricus’ Against the Logicians). Yes, I admit to having been trained as a logician. People do engage in both kinds of enterprises – inquiry and rationalization. This seventh idea is about why and how we ought to avoid confusing these two different kinds of cognitive enterprise. And on this seventh point, I shall rest … until I trip over a butterfly or find another interesting question.

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