Is Truth a Type of Good?

[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“)

What Does Science Explain? Part 5 – The Ghostly Forms of Physics

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work — that is, correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain esthetic criteria — that is, in relation to how much it describes, it must be rather simple. — John von Neumann (“Method in the Physical Sciences,” in The Unity of Knowledge, 1955)

Now we come to the final part of our series of posts, “What Does Science Explain?” (If you have not already, you can peruse parts 1, 2, 3, and 4 here). As I mentioned in my previous posts, the rise of modern science was accompanied by a change in humanity’s view of metaphysics, that is, our theory of existence. Medieval metaphysics, largely influenced by ancient philosophers, saw human beings as the center or summit of creation; furthermore, medieval metaphysics proposed a sophisticated, multifaceted view of causation. Modern scientists, however, rejected much of medieval metaphysics as subjective and saw reality as consisting mainly of objects impacting or influencing each other in mathematical patterns.  (See The Metaphysical Foundations of Modern Science by E.A. Burtt.)

I have already critically examined certain aspects of the metaphysics of modern science in parts 3 and 4. For part 5, I wish to look more closely at the role of Forms in causation — what Aristotle called “formal causation.” This theory of causation was strongly influenced by Aristotle’s predecessor Plato and his Theory of Forms. What is Plato’s “Theory of Forms”? In brief, Plato argued that the world we see around us — including all people, trees, and animals, stars, planets and other objects — is not the true reality. The world and the things in it are imperfect and perishable realizations of perfect forms that are eternal, and that continually give birth to the things we see. That is, forms are the eternal blueprints of perfection which the material world imperfectly represents. True philosophers do not focus on the material world as it is, but on the forms that material things imperfectly reflect. In order to judge a sculpture, painting, or natural setting, a person must have an inner sense of beauty. In order to evaluate the health of a particular human body, a doctor must have an idea of what a perfectly healthy human form is. In order to evaluate a government’s system of justice, a citizen must have an idea about what perfect justice would look like. In order to critically judge leaders, citizens must have a notion of the virtues that such a leader should have, such as wisdom, honesty, and courage.  Ultimately, according to Plato, a wise human being must learn and know the perfect forms behind the imperfect things we see: we must know the Form of Beauty, the Form of Justice, the Form of Wisdom, and the ultimate form, the Form of Goodness, from which all other forms flow.

Unsurprisingly, many intelligent people in the modern world regard Plato’s Theory of Forms as dubious or even outrageous. Modern science teaches us that sure knowledge can only be obtained by observation and testing of real things, but Plato tells us that our senses are deceptive, that the true reality is hidden behind what we sense. How can we possibly confirm that the forms are real? Even Plato’s student Aristotle had problems with the Theory of Forms and argued that while the forms were real, they did not really exist until they were manifested in material things.

However, there is one important sense in which modern science retained the notion of formal causation, and that is in mathematics. In other words, most scientists have rejected Plato’s Theory of Forms in all aspects except for Plato’s view of mathematics. “Mathematical Platonism,” as it is called, is the idea that mathematical forms are objectively real and are part of the intrinsic order of the universe. However, there are also sharp disagreements on this subject, with some mathematicians and scientists arguing that mathematical forms are actually creations of the human imagination.

The chief difference between Plato and modern scientists on the study of mathematics is this: According to Plato, the objects of geometry — perfect squares, perfect circles, perfect planes — existed nowhere in the material world; we only see imperfect realizations. But the truly wise studied the perfect, eternal forms of geometry rather than their imperfect realizations. Therefore, while astronomical observations indicated that planetary bodies orbited in imperfect circles, with some irregularities and errors, Plato argued that philosophers must study the perfect forms instead of the actual orbits! (The Republic, XXVI, 524D-530C) Modern science, on the other hand, is committed to observation and study of real orbits as well as the study of perfect mathematical forms.

Is it tenable to hold the belief that Plato and Aristotle’s view of eternal forms is mostly subjective nonsense, but they were absolutely right about mathematical forms being real? I argue that this selective borrowing of the ancient Greeks doesn’t quite work, that some of the questions and difficulties with proving the reality of Platonic forms also afflicts mathematical forms.

The main argument for mathematical Platonism is that mathematics is absolutely necessary for science: mathematics is the basis for the most important and valuable physical laws (which are usually in the form of equations), and everyone who accepts science must agree that the laws of nature or the laws of physics exist. However, the counterargument to this claim is that while mathematics is necessary for human beings to conduct science and understand reality, that does not mean that mathematical objects or even the laws of nature exist objectively, that is, outside of human minds.

I have discussed some of the mysterious qualities of the “laws of nature” in previous posts (here and here). It is worth pointing out that there remains a serious debate among philosophers as to whether the laws of nature are (a) descriptions of causal regularities which help us to predict or (b) causal forces in themselves. This is an important distinction that most people, including scientists, don’t notice, although the theoretical consequences are enormous. Physicist Kip Thorne writes that laws “force the Universe to behave the way it does.” But if laws have that kind of power, they must be ubiquitous (exist everywhere), eternal (exist prior to the universe), and have enormous powers although they have no detectable energy or mass — in other words, the laws of nature constitute some kind of supernatural spirit. On the other hand, if laws are summary descriptions of causation, these difficulties can be avoided — but then the issue arises: do the laws of nature or of physics really exist objectively, outside of human minds, or are they simply human-constructed statements about patterns of causation? There are good reasons to believe the latter is true.

The first thing that needs to be said is that nearly all these so-called laws of nature are actually approximations of what really happens in nature, approximations that work only under certain restrictive conditions. Both of these considerations must be taken into account, because even the approximations fall apart outside of certain pre-specified conditions. Newton’s law of universal gravitation, for example, is not really universal. It becomes increasingly inaccurate under conditions of high gravity and very high velocities, and at the atomic level, gravity is completely swamped by other forces. Whether one uses Newton’s law depends on the specific conditions and the level of accuracy one requires. Kepler’s laws of planetary motion are an approximation based on the simplifying assumption of a planetary system consisting of one planet. The ideal gas law is an approximation which becomes inaccurate under conditions of low temperature and/or high pressure. The law of multiple proportions works for simple molecular compounds, but often fails for complex molecular compounds. Biologists have discovered so many exceptions to Mendel’s laws of genetics that some believe that Mendel’s laws should not even be considered laws.

The fact of the matter is that even with the best laws that science has come up with, we still can’t predict the motions of more than two interacting astronomical bodies without making unrealistic simplifying assumptions. Michael Scriven, a mathematician and philosopher at Claremont Graduate University, has concluded that the laws of nature or physics are actually cobbled together by scientists based on multiple criteria:

Briefly we may say that typical physical laws express a relationship between quantities or a property of systems which is the simplest useful approximation to the true physical behavior and which appears to be theoretically tractable. “Simplest” is vague in many cases, but clear for the extreme cases which provide its only use. “Useful” is a function of accuracy and range and purpose. (Michael Scriven, “The Key Property of Physical Laws — Inaccuracy,” in Current Issues in the Philosophy of Science, ed. Herbert Feigl)

The response to this argument is that it doesn’t disprove the objective existence of physical laws — it simply means that the laws that scientists come up with are approximations to real, objectively existing underlying laws. But if that is the case, why don’t scientists simply state what the true laws are? Because the “laws” would actually end up being extremely long and complex statements of causation, with so many conditions and exceptions that they would not really be considered laws.

An additional counterargument to mathematical Platonism is that while mathematics is necessary for science, it is not necessary for the universe. This is another important distinction that many people overlook. Understanding how things work often requires mathematics, but that doesn’t mean the things in themselves require mathematics. The study of geometry has given us pi and the Pythagorean theorem, but a child does not need to know these things in order to draw a circle or a right triangle. Circles and right triangles can exist without anyone, including the universe, knowing the value of pi or the Pythagorean theorem. Calculus was invented in order to understand change and acceleration; but an asteroid, a bird, or a cheetah is perfectly capable of changing direction or accelerating without needing to know calculus.

Even among mathematicians and scientists, there is a significant minority who have argued that mathematical objects are actually creations of the human imagination, that math may be used to model aspects of reality, but it does not necessarily do so. Mathematicians Philip J. Davis and Reuben Hersh argue that mathematics is the study of “true facts about imaginary objects.” Derek Abbot, a professor of engineering, writes that engineers tend to reject mathematical Platonism: “the engineer is well acquainted with the art of approximation. An engineer is trained to be aware of the frailty of each model and its limits when it breaks down. . . . An engineer . . . has no difficulty in seeing that there is no such a thing as a perfect circle anywhere in the physical universe, and thus pi is merely a useful mental construct.” (“The Reasonable Ineffectiveness of Mathematics“) Einstein himself, making a distinction between mathematical objects used as models and pure mathematics, wrote that “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” Hartry Field, a philosopher at New York University, has argued that mathematics is a useful fiction that may not even be necessary for science. Field goes to show that it is possible to reconstruct Newton’s theory of gravity without using mathematics. (There is more discussion on this subject here and here.)

So what can we conclude about the existence of forms? I have to admit that although I’m skeptical, I have no sure conclusions. It seems unlikely that forms exist outside the mind . . . but I can’t prove they don’t exist either. Forms do seem to be necessary for human reasoning — no thinking human can do without them. And forms seem to be rooted in reality: perfect circles, perfect squares, and perfect human forms can be thought of as imaginative projections of things we see, unlike Sherlock Holmes or fire-breathing dragons or flying spaghetti monsters, which are more creatively fictitious. Perhaps one could reconcile these opposing views on forms by positing that the human mind and imagination is part of the universe itself, and that the universe is becoming increasingly consciously aware.

Another way to think about this issue was offered by Robert Pirsig in Zen and the Art of Motorcycle Maintenance. According to Pirsig, Plato made a mistake by positing Goodness as a form. Even considered as the highest form, Goodness (or “Quality,” in Pirsig’s terminology) can’t really be thought of as a static thing floating around in space or some otherworldly realm. Forms are conceptual creations of humans who are responding to Goodness (Quality). Goodness itself is not a form, because it is not an unchanging thing — it is not static or even definable. It is “reality itself, ever changing, ultimately unknowable in any kind of fixed, rigid way.” (p. 342) Once we let go of the idea that Goodness or Quality is a form, we can realize that not only is Goodness part of reality, it is reality.

As conceptual creations, ideal forms are found in both science and religion. So why, then, does there seem to be such a sharp split between science and religion as modes of knowledge? I think it comes down to this: science creates ideal forms in order to model and predict physical phenomena, while religion creates ideal forms in order to provide guidance on how we should live.

Scientists like to see how things work — they study the parts in order to understand how the wholes work. To increase their understanding, scientists may break down certain parts into smaller parts, and those parts into even smaller parts, until they come to the most fundamental, indivisible parts. Mathematics has been extremely useful in modeling and understanding these parts of nature, so scientists create and appreciate mathematical forms.

Religion, on the other hand, tends to focus on larger wholes. The imaginative element of religion envisions perfect states of being, whether it be the Garden of Eden or the Kingdom of Heaven, as well as perfect (or near perfect) humans who serve as prophets or guides to a better life. Religion is less concerned with how things work than with how things ought to work, how things ought to be. So religion will tend to focus on subjects not covered by science, including the nature and meaning of beauty, love, and justice. There will always be debates about the appropriateness of particular forms in particular circumstances, but the use of forms in both science and religion is essential to understanding the universe and our place in it.