“[T]ruth is one species of good, and not, as is usually supposed, a category distinct from good, and co-ordinate with it. The true is the name of whatever proves itself to be good in the way of belief. . . .” – William James,  “What Pragmatism Means”

“Truth is a static intellectual pattern within a larger entity called Quality.” – Robert Prisig, Lila

 

Does it make sense to think of truth as a type of good? The initial reaction of most people to this claim is negative, sometimes strongly so. Surely what we like and what is true are two different things. The reigning conception of truth is known as the “correspondence theory of truth,” which argues simply that in order for a statement to be true it must correspond to reality. In this view, the words or concepts or claims we state must match real things or events, and match them exactly, whether those things are good or not.

The American philosopher William James (1842-1910) acknowledged that our ideas must agree with reality in order to be true. But where he parted company with most of the rest of the world was in what it meant for an idea to “agree.” In most cases, he argued, ideas cannot directly copy reality. According to James, “of many realities our ideas can only be symbols and not copies. . . . Any idea that helps us to deal, whether practically or intellectually, with either the reality or its belongings, that doesn’t entangle our progress in frustrations, that fits, in fact, and adapts our life to the reality’s whole setting, will agree sufficiently to meet the requirement.” He also argued that “True ideas are those we can assimilate, validate, corroborate, and verify.” (“Pragmatism’s Conception of Truth“) Many years later, Robert Pirsig argued in Zen and the Art of Motorcycle Maintenance and Lila that the truths of human knowledge, including science, were developed out of an intuitive sense of good or “quality.”

But what does this mean in practice? Many truths are unpleasant, and reality often does not match our desires. Surely truth should correspond to reality, not what is good.

One way of understanding what James and Pirsig meant is to examine the origins and development of language and mathematics. We use written language and mathematics as tools to make statements about reality, but the tools themselves do not merely “copy” or even strictly correspond to reality. In fact, these tools should be understood as symbolic systems for communication and understanding. In the earliest stages of human civilization, these symbolic systems did try to copy or correspond to reality; but the strict limitations of “corresponding” to reality was in fact a hindrance to the truth, requiring new creative symbols that allowed knowledge to advance.

 

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The first written languages consisted of pictograms, that is, drawn depictions of actual things — human beings, stars, cats, fish, houses. Pictograms had one big advantage: by clearly depicting the actual appearance of things, everyone could quickly understand them. They were the closest thing to a universal language; anyone from any culture could understand pictograms with little instruction.

However, there were some pretty big disadvantages to the use of pictograms as a written language. Many of the things we all see in everyday life can be clearly communicated through drawings. But there are a lot of ideas, actions, abstract concepts, and details that are not so easily communicated through drawings. How does one depict activities such as running, hunting, fighting, and falling in love, while making it clear that one is communicating an activity and not just a person? How does one depict a tribe, kingdom, battle, or forest, without becoming bogged down in drawing pictograms of all the persons and objects involved? How does one depict attributes and distinguish between specific types of people and specific types of objects? How does one depict feelings, emotions, ideas, and categories? Go through a dictionary at random sometime and see how many words can be depicted in a clear pictogram. There are not many. There is also the problem of differences in artistic ability and the necessity of maintaining standards. Everyone may have a different idea of what a bird looks like and different abilities in drawing a bird.

These limitations led to an interesting development in written language: over hundreds or thousands of years, pictograms became increasingly abstract, to the point at which their form did not copy or correspond to what they represented at all. This development took place across civilizations, as seen is this graphic, in which the top pictograms represent the earliest forms and the bottom ones coming later:

(Source: Wikipedia, https://en.wikipedia.org/wiki/History_of_writing)

Eventually, pictograms were abandoned by most civilizations altogether in favor of alphabets. By using combinations of letters to represent objects and ideas, it became easier for people to learn how to read and write. Instead of having to memorize tens of thousands of pictograms, people simply needed to learn new combinations of letters/sounds. No artistic ability was required.

One could argue that this development in writing systems does not address the central point of the correspondence theory of truth, that a true statement must correspond to reality. In this theory, it is perfectly OK for an abstract symbol to represent something. If someone writes “I caught a fish,” it does not matter if the person draws a fish or uses abstract symbols for a fish, as long as this person, in reality, actually did catch a fish. From the pragmatic point of view, however, the evolution of human symbolic systems toward abstraction is a good illustration of pragmatism’s main point: by making our symbolic systems better, human civilizations were able to communicate more, understand more, educate more, and acquire more knowledge. Pictograms fell short in helping us “deal with reality,” and that’s why written language had to advance above and beyond pictograms.

 

Let us turn to mathematics. The earliest humans were aware of quantities, but tended to depicted quantities in a direct and literal manner. For small quantities, such as two, the ancient Egyptians would simply draw two pictograms of the object. Nothing could correspond to reality better than that. However, for larger quantities, it was hard, tedious work to draw the same pictogram over and over. So early humans used tally marks or hash marks to indicate quantities, with “four” represented as four distinct marks:  | | | | and then perhaps a symbol or pictogram of the object. Again, these earliest depictions of numbers were so simple and direct, the correspondence to reality so obvious, that they were easily understood by people from many different cultures.

In retrospect, tally marks appear to be very primitive and hardly a basis for a mathematical system. However, I argue that tally marks were actually a revolutionary advance in how human beings understood quantities — because for the first time, quantity became an abstraction disconnected from particular objects. One did not have to make distinctions between three cats, three kings, or three bushels of grain; the quantity “three” could be understood on its own, without reference to what it was representing. Rather than drawing three cats, three kings, or three bushels of grain, one could use | | |  to represent any group of three objects.

The problem with tally marks, of course, was that this system could not easily handle large quantities or permit complex calculations. So, numerals were invented. The ancient Egyptian numeral system used tally marks for numbers below ten, but then used other symbols for larger quantities: ten, hundred, thousand, and so forth.

The ancient Roman numeral system also evolved out of tally marks, with | | | or III representing “three,” but with different symbols for five (V), ten (X), fifty (L), hundred (C), five hundred (D), and thousand (M). Numbers were depicted by writing the largest numerical symbols on the left and the smallest to the right, adding the symbols together to get the quantity (example: 1350 = MCCCL); a smaller numerical symbol to the left of a larger numerical symbol required subtraction (example: IX = 9). As with the Egyptian system, Roman numerals were able to cope with large numbers, but rather than the more literal depiction offered by tally marks, the symbols were a more creative interpretation of quantity, with implicit calculations required for proper interpretation of the number.

The use of numerals by ancient civilizations represented a further increase in the abstraction of quantities. With numerals, one could make calculations of almost any quantity of any objects, even imaginary objects or no objects. Teachers instructed children how to use numerals and how to make calculations, usually without any reference to real-world objects. A minority of intellectuals studied numbers and calculations for many years, developing general theorems about the relationships between quantities. And before long, the power and benefits of mathematics became such that mathematicians became convinced that mathematics were the ultimate reality of the universe, and not the actual objects we once attached to numbers. (On the theory of “mathematical Platonism,” see this post.)

For thousands of years, Roman numerals continued to be used. Rome was able to build and administer a great empire, while using these numerals for accounting, commerce, and engineering. In fact, the Romans were famous for their accomplishments in engineering. It was not until the 14th century that Europe began to discover the virtues of the Hindu-Arabic numeral system. And although it took centuries more, today the Hindu-Arabic system is the most widely-used system of numerals in the world.

Why is this?

The Hindu-Arabic system is noted for two major accomplishments: its positional decimal system and the number zero. The “positional decimal system” simply refers to a base 10 system in which the value of a digit is based upon it’s position. A single numeral may be multiplied by ten or one hundred or one thousand, depending on its position in the number. For example, the number 832 is:  8×100 + 3×10 + 2. We generally don’t notice this, because we spent years in school learning this system, and it comes to us automatically that the first digit “8” in 832 means 8 x 100. Roman numerals never worked this way. The Romans grouped quantities in symbols representing ones, fives, tens, fifties, one hundreds, etc. and added the symbols together. So the Roman version of 832 is DCCCXXXII (500 + 100 + 100 + 100 + 10+ 10 + 10 + 1 + 1).

Because the Roman numeral system is additive, adding Roman numbers is easy — you just combine all the symbols. But multiplication is harder, and division is even harder, because it’s not so easy to take apart the different symbols. In fact, for many calculations, the Romans used an abacus, rather than trying to write everything down. The Hindu-Arabic system makes multiplication and division easy, because every digit, depending on its placement, is a multiple of 1, 10, 100, 1000, etc.

The invention of the positional decimal system took thousands of years, not because ancient humans were stupid, but because symbolizing quantities and their relationships in a way that is useful is actually hard work and requires creative interpretation. You just don’t look at nature and say, “Ah, there’s the number 12, from the positional decimal system!”

In fact, even many of the simplest numbers took thousands of years to become accepted. The number zero was not introduced to Europe until the 11th century and it took several more centuries for zero to become widely used. Negative numbers did not appear in the west until the 15th century, and even then, they were controversial among the best mathematicians until the 18th century.

The shortcomings of seeing mathematical truths as a simple literal copying of reality become even clearer when one examines the origins and development of weights and measures. Here too, early human beings started out by picking out real objects as standards of measurement, only to find them unsuitable in the long run. One of the most well-known units of measurement in ancient times was the cubit, defined as the length of a man’s forearm from elbow to the tip of the middle finger. The foot was defined as the length of a man’s foot. The inch was the width of a man’s thumb. A basic unit of weight was the grain, that is, a single grain of barley or wheat. All of these measures corresponded to something real, but the problem, of course, was that there was a wide variation in people’s body parts, and grains could also vary in weight. What was needed was standardization; and it was not too long before governing authorities began to establish common standards. In many places throughout the world, authorities agreed that a single definition of each unit, based on a single object kept in storage, would be the standard throughout the land. The objects chosen were a matter of social convention, based upon convenience and usefulness. Nature or reality did not simply provide useful standards of measurement; there was too much variation even among the same types of objects provided by nature.

 

At this point, advocates of the correspondence theory of truth may argue, “Yes, human beings can use a variety of symbolic systems, and some are better than others. But the point is that symbolic systems should all represent the same reality. No matter what mathematical system you use, two plus two should still equal four.”

In response, I would argue that for very simple questions (2+2=4), the type of symbolic system you use will not make a big difference — you can use tally marks, Roman numerals, or Hindu-Arabic numerals. But the type of symbolic system you use will definitely make a difference in how many truths you can uncover and particularly how many complicated truths you can grasp. Without good symbolic systems, many truths will remain forever hidden from us.  As it was, the Roman numeral system was probably responsible for the lack of mathematical accomplishments of the Romans, even if their engineering was impressive for the time. And in any case, the pragmatic theory of truth already acknowledges that truth must agree with reality — it just cannot be a copy of reality. In the words of William James, an ideal symbolic system “helps us to deal, whether practically or intellectually, with either the reality or its belongings . . . doesn’t entangle our progress in frustrations, that fits, in fact, and adapts our life to the reality’s whole setting.”(“Pragmatism’s Conception of Truth“)