Tag Archives: quality

The Dynamic Quality of Henri Bergson

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Robert Pirsig writes in Lila that Quality contains a dynamic good in addition to a static good. This dynamic good consists of a search for “betterness” that is unplanned and has no specific destination, but is nevertheless responsible for all progress. Once a dynamic good solidifies into a concept, practice, or tradition in a culture, it becomes a static good. Creativity, mysticism, dreams, and even good guesses or luck are examples of dynamic good in action. Religious traditions, laws, and science textbooks are examples of static goods.

Pirsig describes dynamic quality as the “pre-intellectual cutting edge of reality.” By this, he means that before concepts, logic, laws, and mathematical formulas are discovered, there is process of searching and grasping that has not yet settled into a pattern or solution. For example, invention and discovery is often not an outcome of calculation or logical deduction, but of a “free association of ideas” that tends to occur when one is not mentally concentrating at all. Many creative people, from writers to mathematicians, have noted that they came up with their best ideas while resting, engaging in everyday activities, or dreaming.

Dynamic quality is not just responsible for human creation — it is fundamental to all evolution, from the physical level of atoms and molecules, to the biological level of life forms, to the social level of human civilization, to the intellectual level of human thought. Dynamic quality exists everywhere, but it has no specific goals or plans — it always consists of spur-of-the-moment actions, decisions, and guesses about how to overcome obstacles to “betterness.”

It is difficult to conceive of dynamic quality — by its very nature, it is resistant to conceptualization and definition, because it has no stable form or structure. If it did have a stable form or structure, it would not be dynamic.

However the French philosopher Henri Bergson (1859-1941) provided a way to think about dynamic quality, by positing change as the fundamental nature of reality. (See Beyond the “Mechanism” Metaphor in Physics.) In Bergson’s view, traditional reason, science, and philosophy created static, eternal forms and posited these forms as the foundation of reality — but in fact these forms were tools for understanding reality and not reality itself. Reality always flowed and was impossible to fully capture in any static conceptual form. This flow could best be understood through perception rather than conception. Unfortunately, as philosophy created larger and larger conceptual categories, philosophy tended to become dominated by empty abstractions such as “substance,” “numbers,” and “ideas.” Bergson proposed that only an intuitive approach that enlarged perceptual knowledge through feeling and imagination could advance philosophy out of the dead end of static abstractions.

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The Flow of Time

Bergson argued that we miss the flow of time when we use the traditional tools of science, mathematics, and philosophy. Science conceives of time as simply one coordinate in a deterministic space-time block ruled by eternal laws; mathematics conceives of time as consisting of equal segments on a graph; and philosophers since Plato have conceptualized the world as consisting of the passing shadows of eternal forms.

These may be useful conceptualizations, argues Bergson, but they do not truly grasp time. Whether it is an eternal law, a graph, or an eternal form, such depictions are snapshots of reality; they do not and cannot represent the indivisible flow of time that we experience. The laws of science in particular neglected the elements of indeterminism and freedom in the universe. (Henri Bergson once debated Einstein on this topic). The neglect of real change by science was the result of science’s ambition to foresee all things, which motivated scientists to focus on the repeatable and calculable elements of nature, rather than the genuinely new. (The Creative Mind, Mineola, New York: Dover, 2007, p. 3) Those events that could not be predicted were tossed aside as being merely random or unknowable. As for philosophy, Bergson complained that the eternal forms of the philosophers were empty abstractions — the categories of beauty and justice and truth were insufficient to serve as representations of real experience.

Actual reality, according to Bergson, consisted of “unceasing creation, the uninterrupted upsurge of novelty.” (The Creative Mind, p. 7) Time was not merely a coordinate for recording motion in a determinist universe; time was “a vehicle of creation and choice.” (p. 75) The reality of change could not be captured in static concepts, but could only be grasped intuitively. While scientists saw evolution as a combination of mechanism and random change, Bergson saw evolution as a result of a vital impulse (élan vital) that pervaded the universe. Although this vital impetus possessed an original unity, individual life forms used this vital impetus for their own ends, creating conflict between life forms. (Creative Evolution, pp. 50-51)

Biologists attacked Bergson on the grounds that there was no “vital impulse” that they could detect and measure. But biologists argued from the reductionist premise that everything could be explained by reference to smaller parts, and since there was no single detectable force animating life, there was no “vital impetus.” But Bergson’s premise was holistic, referring to the broader action of organic development from lower orders to higher orders, culminating in human beings. There was no separate force — rather entities organized, survived, and reproduced by absorbing and processing energy, in multiple forms. In the words of one eminent biologist, organisms are “resilient patterns . . . in an energy flow.” There is no separate or unique energy of life – just energy.

The Superiority of Perception over Conception

Bergson believed with William James that all knowledge originated in perception and feeling; as human mental powers increased, conceptual categories were created to organize and generalize what we (and others) discovered through our senses. Concepts were necessary to advance human knowledge, of course. But over time, abstract concepts came to dominate human thought to the point at which pure ideas were conceived as the ultimate reality — hence Platonism in philosophy, mathematical Platonism in mathematics, and eternal laws in science. Bergson believed that although we needed concepts, we also needed to rediscover the roots of concepts in perception and feeling:

If the senses and the consciousness had an unlimited scope, if in the double direction of matter and mind the faculty of perceiving was indefinite, one would not need to conceive any more than to reason. Conceiving is a make-shift when perception is not granted to us, and reasoning is done in order to fill up the gaps of perception or to extend its scope. I do not deny the utility of abstract and general ideas, — any more than I question the value of bank-notes. But just as the note is only a promise of gold, so a conception has value only through the eventual perceptions it represents. . . . the most ingeniously assembled conceptions and the most learnedly constructed reasonings collapse like a house of cards the moment the fact — a single fact rarely seen — collides with these conceptions and these reasonings. There is not a single metaphysician, moreover, not one theologian, who is not ready to affirm that a perfect being is one who knows all things intuitively without having to go through reasoning, abstraction and generalisation. (The Creative Mind, pp. 108-9)

In the end, despite their obvious utility, the conceptions of philosophy and science tend “to weaken our concrete vision of the universe.” (p. 111) But we clearly do not have God-like powers to perceive everything, and we are not likely to get such powers. So what do we do? Bergson argues that instead of “trying to rise above our perception of things” through concepts, we “plunge into [perception] for the purpose of deepening it and widening it.” (p. 111) But how exactly are we to do this?

Enlarging Perception

There is one group of people, argues Bergson, that have mastered the ability to deepen and widen perception: artists. From paintings to poetry to novels and musical compositions, artists are able to show us things and events that we do not directly perceive and evoke a mood within us that we can understand even if the particular form that the artist presents may never have been seen or heard by us before. Bergson writes that artists are idealists who are often absent-mindedly detached from “reality.” But it is precisely because artists are detached from everyday living that they are able to see things that ordinary, practical people do not:

[Our] perception . . . isolates that part of reality as a whole that interests us; it shows us less the things themselves than the use we can make of them. It classifies, it labels them beforehand; we scarcely look at the object, it is enough for us to know which category it belongs to. But now and then, by a lucky accident, men arise whose senses or whose consciousness are less adherent to life. Nature has forgotten to attach their faculty of perceiving to their faculty of acting. When they look at a thing, they see it for itself, and not for themselves. They do not perceive simply with a view to action; they perceive in order to perceive — for nothing, for the pleasure of doing so. In regard to a certain aspect of their nature, whether it be their consciousness or one of their senses, they are born detached; and according to whether this detachment is that of a particular sense, or of consciousness, they are painters or sculptors, musicians or poets. It is therefore a much more direct vision of reality that we find in the different arts; and it is because the artist is less intent on utilizing his perception that he perceives a greater number of things. (The Creative Mind, p. 114)

The Method of Intuition

Bergson argued that the indivisible flow of time and the holistic nature of reality required an intuitive approach, that is “the sympathy by which one is transported into the interior of an object in order to coincide with what there is unique and consequently inexpressible in it.” (The Creative Mind, p. 135) Analysis, as in the scientific disciplines, breaks down objects into elements, but this method of understanding is a translation, an insight that is less direct and holistic than intuition. The intuition comes first, and one can pass from intuition to analysis but not from analysis to intuition.

In his essay on the French philosopher Ravaisson, Bergson underscored the benefits and necessity of an intuitive approach:

[Ravaisson] distinguished two different ways of philosophizing. The first proceeds by analysis; it resolves things into their inert elements; from simplification to simplification it passes to what is most abstract and empty. Furthermore, it matters little whether this work of abstraction is effected by a physicist that we may call a mechanist or by a logician who professes to be an idealist: in either case it is materialism. The other method not only takes into account the elements but their order, their mutual agreement and their common direction. It no longer explains the living by the dead, but, seeing life everywhere, it defines the most elementary forms by their aspiration toward a higher form of life. It no longer brings the higher down to the lower, but on the contrary, the lower to the higher. It is, in the real sense of the word, spiritualism. (p. 202)

From Philosophy to Religion

A religious tendency is apparent in Bergson’s philosophical writings, and this tendency grew more pronounced as Bergson grew older. It is likely that Bergson saw religion as a form of perceptual knowledge of the Good, widened by imagination. Bergson’s final major work, The Two Sources of Morality and Religion (Notre Dame, IN: University of Notre Dame Press, 1977) was both a philosophical critique of religion and a religious critique of philosophy, while acknowledging the contributions of both forms of knowledge. Bergson drew a distinction between “static religion,” which he believed originated in social obligations to society, and “dynamic religion,” which he argued originated in mysticism and put humans “in the stream of the creative impetus.” (The Two Sources of Morality and Religion, p. 179)

Bergson was a harsh critic of the superstitions of “static religion,” which he called a “farrago of error and folly.” These superstitions were common in all cultures, and originated in human imagination, which created myths to explain natural events and human history. However, Bergson noted, static religion did play a role in unifying primitive societies and creating a common culture within which individuals would subordinate their interests to the common good of society. Static religion created and enforced social obligations, without which societies could not endure. Religion also provided comfort against the depressing reality of death. (The Two Source of Morality and Religion, pp. 102-22)

In addition, it would be a mistake, Bergson argued, to suppose that one could obtain dynamic religion without the foundation of static religion. Even the superstitions of static religion originated in the human perception of a beneficent virtue that became elaborated into myths. Perhaps thinking that a cool running spring or a warm fire on the hearth as the actions of spirits or gods were a case of imagination run rampant, but these were still real goods, as were the other goods provided by the pagan gods.

Dynamic religion originated in static religion, but also moved above and beyond it, with a small number of exceptional human beings who were able to reach the divine source: “In our eyes, the ultimate end of mysticism is the establishment of a contact . . . with the creative effort which life itself manifests. This effort is of God, if it is not God himself. The great mystic is to be conceived as an individual being, capable of transcending the limitations imposed on the species by its material nature, thus continuing and extending the divine action.” (pp. 220-21)

In Bergson’s view, mysticism is intuition turned inward, to the “roots of our being , and thus to the very principle of life in general.” (p. 250) Rational philosophy cannot fully capture the nature of mysticism, because the insights of mysticism cannot be captured in words or symbols, except perhaps in the word “love”:

God is love, and the object of love: herein lies the whole contribution of mysticism. About this twofold love the mystic will never have done talking. His description is interminable, because what he wants to describe is ineffable. But what he does state clearly is that divine love is not a thing of God: it is God Himself. (p. 252)

Even so, just as the dynamic religion bases its advanced moral insights in part on the social obligations of static religion, dynamic religion also must be propagated through the images and symbols supplied by the myths of static religion. (One can see this interplay of static and dynamic religion in Jesus and Gandhi, both of whom were rooted in their traditional religions, but offered original teachings and insights that went beyond their traditions.)

Toward the end of his life, Henri Bergson strongly considered converting to Catholicism (although the Church had already placed three of Bergson’s works on its Index of Prohibited Books). Bergson saw Catholicism as best representing his philosophical inclinations for knowing through perception and intuition, and for joining the vital impetus responsible for creation. However, Bergson was Jewish, and the anti-Semitism of 1930s and 1940s Europe made him reluctant to officially break with the Jewish people. When the Nazis conquered France in 1940 and the Vichy puppet government of France decided to persecute Jews, Bergson registered with the authorities as a Jew and accepted the persecutions of the Vichy regime with stoicism. Bergson died in 1941 at the age of 81.

Once among the most celebrated intellectuals in the world, today Bergson is largely forgotten. Even among French philosophers, Bergson is much less known than Descartes, Sartre, Comte, and Foucault. It is widely believed that Bergson lost his debate with Einstein in 1922 on the nature of time. (See Jimena Canales, The Physicist and the Philosopher: Einstein, Bergson, and the Debate that Changed Our Understanding of Time, p. 6) But it is recognized today even among physicists that while Einstein’s conception of spacetime in relativity theory is an excellent theory for predicting the motion of objects, it does not disprove the existence of time and real change. It is also true that Bergson’s writings are extraordinarily difficult to understand at times. One can go through pages of dense, complex text trying to understand what Bergson is saying, get suddenly hit with a colorful metaphor that seems to explain everything — and then have a dozen more questions about the meaning of the metaphor. Nevertheless, Bergson remains one of the very few philosophers who looked beyond eternal forms to the reality of a dynamic universe, a universe moved by a vital impetus always creating, always changing, never resting.

Is Truth a Type of Good?

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“[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

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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.