Jeremiah Hawkins Proportion in Philosophy Part I: Thales to Plato Ancient Philosophy 1. The long, stuttering conversation of philosophy renders little hope to the starry-eyed student of its history, that student who wishes to excavate a thread of progress. Picking with the axe of a sweat-drenched mind, the student cracks and chips away in the near hopeless attempt of coming out the other side of a dense block of books having learned something of humanity’s blossoming, some burgeoning of philosophical truth passed down the generations. But this is not the story of philosophy. It is not the snowball-gathering of knowledge along a fated path. The story of philosophy is one of plurality, views clashing with damning refutations and incompatibilities, leaving one unable to say whether we have come a long way or have merely gone about for centuries chasing the wind. If an ember of lasting truth is found amid the tomes, it must be held lightly in hand in the constant realization that the pages of another will someday come along, and in a Heraclitean flash demonstrate that all things comes-to-be just to pass-away. 2. The coming-to-be of the flux is the journey, the creative constant, the undulation of the breathing body. Alive, a beauty to invoke enchantment. So let my sympathetic pessimism end here. Let me step into this disjointed river of philosophic discussion and, in a sort of aphoristic dance, find a frayed thread, and with it held lightly in hand see if I can unravel something of interest. If I fail, I will take solace in my splash—in this fluff of words and plethora of analogies—and move on with a smile. But now let me be clear so as not to be misunderstood in my purpose. In the numbered spurts of this work, I will attempt to wade through and amongst a few main players in the history of philosophy with the hope of teasing out my thread. The players of Part I shall be of the ancient class: Thales, Pythagoras, Heraclitus, and Plato. (Aristotle will be mentioned in the concluding remarks, as he will lead us into Part II). In Part II, I shall move two thousand years into the future to Descartes, Hume, Kant, and Nietzsche. My purpose is to emphasize and explicate the great significance of proportion. This will be a history, but in my historicizing I am posing an argument, namely, that the emphasis of this soon to be demonstrated thread—proportion—is worthy of the pedestal upon which I raise it. In reading this history, it may be best to look upon the beginning through the lens of the end. This is to say, hindsight presents the clearest view, a panoramic that may (or may not) clarify particular ambiguities. 3. The mysterious in-between is proportion. Proportion is a comparative relation of things, both sensible and ideational. In Greek it is analogia and from this we get our word analogy. Analogies reveal the in-between that can be taken from one pair and applied to another. A is to B, and this is-to is the same is-to between C and D. But modify one’s angle of seeing the concept of proportion and one can see that it also serves as that which allows generalization. All chairs share an in-between—a proportion—that allows one to recognize a particular chair that looks exactly like no other chair one has ever seen. From this proportionality comes, within the mind, a unity. As to the chair’s attributes it might be utterly original, but the unity encapsulated within the word affords the recognition. This proportioning out a unity is the reduction of the many into one. This reduction that generates generalizations of sensible objects is also the method utilized in the creation of abstract concepts. By an identical way of gathering particulars and plastering them onto the canvas of the imagination, proportion is teased out as the common thread that ties the plurality together. The abstract concept becomes a word, and that word serves as a symbol for the extracted proportion between the particulars. For example, experiences A, B, C, D (and so on) may be grouped by a commonality that one may call experiences of love, despair, or epiphany. Through the following history, it is my hope that what has been said here becomes clear. And so, on to the first philosopher. 4. “Greek philosophy seems to begin with an absurd notion, with the proposition that water is the primal origin and the womb of all things” (Nietzsche 2003, p. 38). With Thales we have the wellspring of “all things are one.” With what magical method did he arrive at such a magnificent proclamation? Gazing out upon clouds, mountains, oceans, and animals, where did such an idea arise? What alchemy was employed, what chisel utilized? Upon what lofty viewpoint did Thales stand to see all as one, a singly unity hidden within the many? “Creative premonition will show the place; imagination guesses from afar that here it will find demonstrable resting place. But the special strength of imagination is its lightning-quick seizure and illumination of analogies” (Nietzsche 2003, p. 40). As the seas under the ship, as the blood beneath the skin, moisture is seen as the ground below the ground. The instances where moisture is taken to dominate earth and air are instances expanded by analogy unto all there is. Thales perceived a certain common ground amongst particulars, a thread throughout. From this thread, he weaves a sheet to spread out and blanket the cosmos. From his observed relation of things to water, he takes this relation, this proportion, and makes it the in-between and the inside and the underneath of everything, a universal link and foundation. Here we find the use of qualitative proportion. Qualitative proportion takes as its subject anything that is not a quantity. This is to say, it should be defined by juxtaposition to its opposite, namely, quantitative proportion. Quantitative proportion must be classed separately for no reason greater than its powerfully fixed precision. 5. The fixed precision of quantitative proportion (in relation to the less rigid qualitative proportion) holds the key to understanding not only Plato’s adherence to proportionality, but also the great rise of science in the modern era. Therefore, let this willfully jutting-out aphorism be seen as significant, and let it be placed safely in one’s pocket for future recollection. Quantitative proportion: The quantitative comparison of two magnitudes constitutes a ratio (e.g., 1:2), while the proportion is the equality of ratios between two pairs of quantities (e.g., 1:2=2:4). There must be at least three magnitudes in a true proportion—two extremes and a middle term, usually called the ‘mean’ (Wittkower 1960, p. 199-200). To lay hold of the difference in precision between qualitative and quantitative proportion, one merely needs to give the fourth term in these two analogies: 1) Tree is to Ground as Woman is to… 2) 2 is to 4 as 10 is to… The missing analogue in the latter, at least upon first glance, is 20. The analogue in the former, however, is far less obvious, and more vulnerable to a plurality of fitting answers, and thus less precise. The superimposition of the quantitative upon the qualitative will serve as a new chapter of humanity that will be like no other: the rise of modern science. But enough jutting-out. Let us not jump ahead in this history and forsake the sequence. 6. If the Age of Enlightenment cast backward a foreshadow it would fall coolly on the shoulders of Pythagoras. With Pythagoras and his school began the era of the mathematical approach to nature. Thus he opened the door to the specific Western view of the world. But such is the working of the human mind that, at the same time, two interpretive concepts of an entirely different character came into being, or rather acquired a new and long lease of life: number symbolism and number aesthetics. (Wittkower 1960, p. 200) What Galileo did through will and force, Pythagoras did through a stroll and a passive listening. What the former did with manipulation and experiment, the latter did with a squinted-eyed glare. As if the Divine had spoken in musical melody, Pythagoras heard what many now call the universal language. Without twisting arms or the subtlest manipulation of its march, Nature was heard and a great movement was born. Truth, undeniable truth seemed to be presented in the structured scales of harmonic proportion. Numbers were things unseen and unchanging, able to be the foundation of a philosophy and a lifestyle. It is here that the Greek notion of the Beautiful found either its inception or its greatest defense. Between Thales’ qualitative many-to-one reduction and Pythagoras’ discovery of quantitative harmony, we might say we have all we need to move forward to, whom I would call, the Father of Proportion. But, we would be missing an important element in this history if we breezed past the problem of coming-to-be on our way to Plato. And so, let us now turn to Heraclitus. 7. What if there is no such thing as definition? No boundaries to pinpoint, no borders to trace? What if reality rides like a river, and attempting to say “this is that” or “that is this” resembles pointing at a section of water within the body of a river and giving it a name just to watch it disappear before the enunciation can find an ear. Reality displays itself as a bumpy continuum from which reason pleases itself by turning bumps into borders, borders into definitions, definitions into words. You use names for things as though they rigidly, persistently endured; yet even the stream into which you step a second time is not the one you stepped into before. (Nietzsche 1962, p. 52) The flux is what Heraclitus saw. All comes-to-be and nothing is. If it is, it is as the now is, for all constantly shifts and flows. And who can capture the now before it passes into the past? It is—but as soon as you whisper it is—it is no more. Coming-to-be reveals itself as the paradoxical joining of being with not-being. If being and not-being interlock, then all that is is joined to its opposite in eternal embrace. Oppositions and enemies are inseparable, creating a raging fight through time. War reigns as the father of all coming-to-be with fire as its image. Within this burning battle there affords not a word to be said, but there exists a logos to be heard. Heraclitus did not presume to posit a chaos, unless one wishes, paradoxically, to call it an orderly chaos. Divine law guides the fiery flux of existence. 8. From Thales came the qualitative proportion of “all is one”; from Pythagoras, the spiritual and aesthetic numerical proportionality in nature; and from Heraclitus, the divine, otherworldly logos guiding all change. From here it is not a stretch to foresee the one who will latch onto proportion and, with it, create a heavenly realm of unities (eidos) that do not change but underlie all that does. 9. From the proposition that a circle has 360 degrees is derived the truths that each angle of a square is 90 degrees and those of a triangle must add up to 180 degrees. Are these Truths, or merely truths? Would I be sinking in falsity to say that the triangle has angles summing 600 degrees? I would say that there is no more falsity in my 600-degree triangle as there is in my theatre as opposed to your theater. The 180 arises half from the creative minds of humans and half from proportion. The 180 is derived from the 360 of the circle. But where is this 360 derived? It is assumed that this number comes from the amount of days from one summer or winter solstice to another, the estimated amount of days in a year. Thus, this number is just as arbitrary as going to the theater as opposed to the theatre—when in fact they are the same place. The number could have very well been 1,200. However, what is of interest is that no matter what that number is, the proportion between geometric shapes must hold true. If the circle is said to contain 1,200 degrees, then it is of necessity that the square has a set of angles each measuring 300 and the triangle’s angles must add up to 600. The in-between remains fixed, an unseen and unchanging proportion. It is an eye-popping sight that once the human mind creates symbols and pastes them smartly on objects, proportions once concealed reveal themselves. This, I believe is the spirit of Plato. 10. Many an intellectual will freely explicate a complex discourse by chattering out chains of abstract concepts, losing their listeners who have become entangled in the airy sentences. “Give us an example!” one might exclaim with boiling-over frustration. “Do not tell us what justice is by presenting us with equally abstract synonyms, but give us examples of justice so that we may understand by virtue of the commonality between your usage and the image.” This is what Glaucon and Adeimantus demanded of Socrates in Plato’s famous Republic. They wanted a “showing,” a sturdy example, not merely a logical stringing-together of terms un-tethered to anything familiar. In response Plato said: “The inquiry we’re setting ourselves to is no inconsiderable thing, but for someone sharp-sighted, as it appears to me. So since we aren’t clever…the sort of inquiry for us to make about it seems to be exactly like this: if someone had ordered people who were not very sharp-sighted to read small print from a distance, and then it occurred to someone that maybe the same letters are also somewhere else, both bigger and on something bigger, it would plainly be a godsend, I assume, to read those first and examine the smaller ones by that means, if they were exactly the same” (Plato 2007, p. 60/368d). And thus we have the beginning of the Polis from which the dialogue gets its name. Justice—and a sense of the Good—sought for in the soul will now be sought for in the much larger analogue of the city. I believe it is Plato’s hope that the proportions will remain true as they do between geometric shapes. 11. From here we may say that a city, such as Athens, goes by one name, and thus it is a unity not too unlike Thales’s water and Heraclitus’s fire. It is a many brought together into a unity. The diversity within Athens should work in a specific relational proportionality as to form and maintain the unity of “Athens.” —And this Plato calls justice. And this was meant to make it clear about the rest of the citizens as well, that they need to bring each one to one job, the one for which he’s naturally suited, so that each of them, by pursuing the one thing that belongs to him, will become one and not many, and in that way the city as a whole will grown to be one and not many (Plato 2007, p. 116/423d). And so goes the soul: Now, anything good is beautiful, and nothing beautiful lacks proportion, so we are bound to expect a healthy creature to be a well-proportioned creature. But although we discern and think rationally about trivial cases of proportion, we’re incapable of reasoning when it comes to the most important and significant cases. For instance, the factor that has the most bearing on health and sickness, and on moral goodness and badness, is whether or not there’s proportion between soul and body, but we don’t consider these things at all. (Plato 2008, p. 92/87c-d) Proportionality is the justice that binds together a city, maintains the balance, the harmony, the health, and of course its beauty. The soul must likewise achieve and maintain this proportionality. The charioteer of the Phaedrus must take tight the reins of the steeds—Spirit and Desire—to reach the heavenly realm of eidos. But what kind of charioteer can achieve this. A well-trained one, says Plato. Also, if proper nurture is supported by education, a person will become perfectly whole and healthy, once he has recovered from this serious of illnesses; but if he cares nothing for education, he will limp his way through life and return to Hades unfulfilled and stupid. (Plato 2008, p. 34/44c). 12. Education. Eidos, translated often as form, is the unity of a many, not the many, but a many. For instance, wolves have an eidos just as sheep do. Physical things are but shadows of the eidos, which is that which is most real, that which is unseen and unchanging underlying all that is experienced of the flux. Forms are the in-between, the is-to that links all shadows of wolves to the wolf in an analogous way the circle is-to the square is-to the triangle, a link that is unchanging regardless of what language is applied, what quantity given. The education of proportionality is what Plato seeks to inculcate. In Book III, Plato explains how those in his city should be initially educated. He begins with the proposition that the soul is imitative (Book III, 395d). Basically, as the cliché goes, we are what we eat. What the soul takes in, it becomes. As Nietzsche says: “If someone obstinately and for a long time wants to appear something it is in the end hard for him to be anything else” (Nietzsche 1996, p. 39/aphorism 51). Thus, one of the methods Plato wishes to employ is the education of Pythagoras—the proportionality of music—to instill a taste and an ear for proportion. Proportion, as the structure of the beautiful, will create between the students and proportion itself “a feeling of kinship” and attract and allure them for all their days (Plato 2007, p. 95/401d-402a). Thus, when the philosopher comes to them as they sit shackled in the dank cave, separated and alien to the Good warmth of the sun, the words of the philosopher will sound like familiar lullabies from childhood, a Pied Piper pleading to be followed. 13. Plato overflows and drips proportion. Proportion is the method, the content, the motive. Analogia is the Beautiful of which all Good partakes and presents. It lights up eidos to be perceived by the willing mind, but also, I argue, is eidos. Proportion is what Plato wishes to teach, to reveal, but also it is by Proportion that Plato must teach proportion. Teach us why the philosopher is useful, Adeimantus once demanded, teach us by what qualification he must rule the polis. “You’re asking a question…that needs an answer given by way of an image… Just listen to the image, then, so you can see even better how tenaciously I make images” (Plato 2007, p. 184/487e-488a). Among the images Socrates will make are the great analogies of the divided line, the sun, and the cave. Through analogia Socrates will teach analogia, the Beautiful proportion of the Good. Look upon the sun and learn how to see it, is the teaching of Socrates. Look to learn to see. In looking you may not at first see, but continue to look, listen to the musical proportions and behold the bright sun until the ears pick-up, the eyes adjust, the palate develops. And the soul becomes. 14. The how-to-look from Plato did not become an idle teaching but was snatched up and utilized quickly by a great follower of his. As music is-to the young guardians, Plato is-to Aristotle. Plato’s proportion set Aristotle on a path of seeing the world as few have before him. In Plato, there were still remnants of a divine realm, a place of eidos and spirits. As for Aristotle, however, he took Plato’s reified Forms and saw something a bit more local: generalizations based on what is common (or essential) to the labeled group. Even beyond the Forms (and that which illuminates the Forms) Aristotle questions Plato’s reification. “But then in what way is good meant? For these things certainly do not seem to have the same name by chance. But do they have the same name by being derived from one thing, or by all adding up together into one thing, or rather by analogy” (Aristotle 2002, p. 8/ 1096b-20)? Aristotle seemed to understand with greater clarity the freedom with which thinkers before him dealt with the plurality of existence. One may say that thinkers before Aristotle were artists in the modern sense, creating philosophies to a greater degree on the canvas of their imagination. Those before Plato looked upon the world and saw all as water, fire, air, birthed from war, products of love and strife, combinations of roots and elements, and so on. With Plato, we have a heavenly realm of eidos and a world of images unified and lighted by the Good. It is all quite artistic and aesthetically appealing. With Aristotle, however, we get categories and causes, a methodological approach that distinguishes and defines, a complex philosophy that lacks the dreamy broad strokes that often disregard consistency in detail, but creates a portrait that invites one to judge it as much for its beauty as for its truth. Aristotle painted no such portrait. He converted Plato’s paintbrushes into chisels, and with an increasingly refined use of proportion, Aristotle carved joints into Nature where none had been seen before. And it is here with Aristotle’s attempts to carve with precision the categories and causes of the plurality of experience that I wish to leap ahead into the modern age, an age where the categories and causes will find greater precision by being enwrapped in number; an age of the superimposition of qualitative and quantitative proportion, namely, the age of science. Jeremiah Hawkins Proportion in Philosophy Part II: Descartes to Nietzsche Modern Philosophy 15. Who can overestimate the effect the rise of modern science has had on humanity and this planet? Only a chuckle can I give to the one who thinks one can. To recount the changes this world has undergone (for better or worse!) in a mere 400 years is staggering, like counting the stars in the sky. What is the particular power of science? Some may say it is the scientific method of hypothesis and experimentation. But could we not find examples in the ancient world where some hypothesized and experimented? Maybe this particular power finds its source in numerical measurement or prediction? But, how could such wonders as the Great Pyramid of Giza or Stonehenge be constructed without numerical measurement and the ability to predict the movement of the celestial bodies? It could be the discipline of strict observation and a pulling away from imaginative metaphysics. But this would only account for things that can be seen, whereas much of what science discovers cannot. In this part, I intend to demonstrate that the combining (or superimposition) of qualitative and quantitative proportion forms the foundation of the Age of Enlightenment’s great scientific advance. As stated in Part I, I will achieve this by spotlighting proportion within the texts of a few of the main philosophers of the age: Descartes, Hume, Kant, and Nietzsche. 16. It may be helpful now to return to Part I with a quick glance. With Thales and Heraclitus (and some other Pre-Socratics), the reduction of the many-to-one by analogy begins the story of western philosophy. It was a poetic flourishing where all of reality was encapsulated in metaphors, such as “all is water.” With Pythagoras, a sort of numerical spacing evidenced itself to undergird the great art form of music. This discovery of the embrace between order and beauty sufficed to inspire a religious movement, as well as much of the philosophy of Plato. Plato intuitively perceived the great breadth of the concept of proportion and constructed an entire philosophy around it. But all of these discoveries and uses of proportion have one thing in common: they mostly deal solely with naming. They attempt to define and distinguish. Very few of them invite temporal elements such as motion, change, and coming-to-be. More often, however, they attempt to filter out temporality as a pesky impurity. Like a stubborn splinter, the concept of time pestered the ancient world. The wide-spread application of proportion to temporal considerations would have to wait for the modern age and its superimposition. And so, now on to Descartes and modernity. 17. More so than Descartes’ cogito or his radical doubt, his adherence and development of method ought to be recollected. A contemporary of Gallileo, who was one of the first to dress up the processes of nature in the garb of mathematical formulae, Descartes recognized, as well as Plato, the power of number and the significance of proportion. He exhibits this in his early work, Rules for the Direction of the Mind. There will be three steps to my explication of Descartes. The first will be his method of achieving precise knowledge worthy of science, called enumeration. Second will be the claim that when all blurry notions are stripped away from a subject, what remains is magnitude. And the third is that the certainty in enumeration consists of reducing proportions to equalities. These three comprise the superimposition, and thus need to be remembered through the rest of this history. 18. Enumeration. Let us begin with displaying just how important this method of enumeration is: “We say here, further, that enumeration is required for the complete attainment of scientific knowledge” (Descartes 2000, p. 15/388). Enumeration, to Descartes, basically means a chain of inference that is continuous and lacks holes or gaps. This method may find use in both a definition of a thing, as well as giving a causal account of a thing. As his guide and analogue, Descartes considers a chain of numbers in a scale of proportion, such as the observation that “the numbers 3, 6, 12, 24, etc. form a continuous proportion” (Descartes 2000, p. 13/385). Another way of presenting this proportion is 3 is-to 6 as 6 is-to 12, and so on. But why would such an illustrious mathematical thinker tinker with such basic ideas? Although all these things are so clear as to appear almost childish, I understand, on attentive reflection, in what way all questions are involved which can be posed about proportions or the relations of things, and in what order they should be investigated: and this alone embraces the whole of the science of pure mathematics. (Descartes 2000, p. 13/385) Following the above statement, Descartes continues with his child play for roughly the length of a page, and does so for the sole purpose of inculcating this process of numerical proportion. He spends this amount of time in child play in order to burrow and engrave this process inside the reader for the purpose of breeding discernment of the deeper truth of proportion. Here it may be helpful to recall Plato’s wish to educate by means of music. Descartes recognizes the in-between, the is-to proportionality, and claims that “in all ratiocination it is only comparison that we know the truth with precision” (Descartes 2000, p. 26/439). Comparison seeks the relations—the in-between—of multiple subjects. However, knowledge is thwarted when comparisons are not clear and distinct, but blurred by interpretive ambiguity. To arrive at the greatest clarity, it might be best to stick with magnitudes, as their precision is of the highest degree. 19. Magnitude. When gazing upon a red silk curtain, what can we say we know of the curtain? What is red? What is silk? We have names for such things, which act as placeholders for distinctions the mind has made. It is “red” and “silk.” But, if all we have is the word based on experience, the clarity is at best blurred. For although one thing can be called more or less white than another, or again one sound more or less acute, and so of other things, still we cannot define exactly whether this more or less is in double or triple proportion, except by a certain analogy with the extension of a figured body. (Descartes 2000, p. 27/441) Descartes desires a more precise proportion, and analogy signifies an unclear proportion, a mere feeling or sentiment of the in-between, not something useful, and definitely not scientific. All fuzzy attributes of a subject must be brushed away in a rigorous attempt to excavate the absolute structure, to bring us to a view of a thing that affords certainty. Thus when the terms of the difficulty have been abstracted from every subject, according to the preceding rule, we understand that we have nothing further to occupy us except magnitudes in general. (Descartes, p. 26/440) Thus, colors must be transformed into frequencies and materials reduced to compositions that can be expressed in percentages, even as precise as percentages of atomic numbers. This is what satisfies Descartes’ appetite for clarity, for it can raise our proportions to a state of perfection: equality. 20. Reducing Proportions to Equalities. The perfect analogy, the proper proportion consists in an equality between subjects, an equality that can never be affirmed when speaking of qualities. Like beauty, qualities differ ever so slightly depending on the eye that casts its judging glance. But as for quantity, the eye has no power of persuasion. …and that the principle part of human contriving consists only in reducing these proportions in such a way as to see clearly an equality between what is sought and something known. It must be noted, further, that nothing can be reduced to this equality except what admits of more and less, and that all this is comprised under the name magnitude. (Descartes 2000, p. 26/440) And thus, the beginning of the superimposition: the act of covering over qualitative proportions—such as unities ranging from “chair” to “electricity”—by quantitative proportions in order to achieve a high degree of precision. Thus, we have entered the modern age of science. Now, let us spend time reflecting on these three steps as a whole. 21. What this superimposition brought about was the reduction of qualities to magnitudes, which allowed a further reduction of proportions to equalities. This superimposition produced the unique power to describe temporal happenings in tight little equalities, called formulae (or equations). Descartes’ enumeration (chain of inferences) fleshes out to encompass such enumerations as inferring causal chains of events. Inferences regarding cause and effect stand as the beginning of the wide-spread application of proportion to temporal considerations. Descartes’ method of reducing proportions to equalities, which can only be achieved through magnitudes, sets the stage for such symbols of proportion as E=MC2. This is to say that the proportion between mass and energy—the conversion ratio—is the square of the speed of light. It is an analogy that is an equality. Now, the measurement of speed applied within the formula adds a temporal element (speed is distance over time, such as miles per hour), and provides a way to describe causal relations in mathematical terms. Other formulae, such as Newton’s F=MA (force equals mass times acceleration), also do this. Formulae are Descartes’ perfect proportions; quantities superimposed onto qualities and the proportions reduced to equations. An inherent gift of the equation is the invocation of the Law of Identity. Where we can utilize a=a as a criterion of truth, we appear to be no longer riding the river of flux, but standing firm upon stable ground. Again, the “equals” sign is vital. We are no longer talking of ‘this is-to this as that is-to that,’ but instead we say ‘this equals that.’ Contradiction sits as the presiding judge of all propositions. But that is not all. This judge can also legislate. Laws of Nature form from cracks of its gavel, laws that sentence causal relations of the future to act as they did in the past. However, when equalities cannot be achieved, Descartes recognizes that proportion is prevented from being lifted to the status of formulae, but must remain a lowly analogy, and open to interpretation. The language of science may at times conceal the truth that all laws of nature are a species of analogy. How easy it is to forget that all formulae are perfect proportions, and all proportions are analogy. It will take David Hume to remind us of this. 22. Modesty and humility so often grants a sense of beauty. Our world, our universe invokes awe and deep feelings of the sublime within the mind of the one willing to become lost in its vast abyss of mysteries. Having these mysteries explained away as machinery often strips the paint from the canvas, blurs the poetry off the page, and darkens the sensitive soul. I believe there are some in the history of philosophy who stood up to defend the aesthetic sentiment. Maybe I am wrong about Hume, but I wish to see him as a guardian of the mysterious unknown. His skepticism urges us not to fool ourselves into thinking we know, but just to revel in the knowledge that we feel. Keep open the curtains to the artistry of nature, base all our convictions on sentiment and brush-stroked impressions, and, of course, always remember that “[a]ll our reasoning’s concerning matter of fact are founded on a species of ANALOGY, which leads us to expect from any cause the same events, which we have observed to result from similar causes” (Hume 1993, p. 69). For Hume, all that we can say of nature consists in matters of fact, and all matters of fact remain under the heading of causality, and all causality is a certain constant conjunction, which is produced by customary experience. When he calls causality a species of analogy, he refers to the reduction of the many-to-one in causal relations similar to the reduction of the relations between chairs. For example, cause1 is-to effect1 AS cause2 is-to effect2 AS cause3 is-to effect3, and so on, even into the future. The predictive power of science is nothing more than a very sophisticated and precise power of analogy—an is-to and as—the very same power that Thales used in order to say “all is water.” Laws of nature are proportions, which we call formulae, derived from constant conjunctions of experience. “Thus, it is a law of motion, discovered by experience, that the moment or force of any body in motion is in the compound ratio or proportion of its solid contents and it velocity” (Hume 1993, p. 20.). Hume does seem to attribute a degree of authority to natural laws, but he makes it clear that these so-called truths heralded by many rationalist philosophers of his day are merely probabilistic. In those probabilities of chance and causes above-explain’d, ‘tis the constancy of the union, which is diminish’d; and in the probability deriv’d from analogy, ‘tis the resemblance only, which is affected. Without some degree of resemblance, as well as union, ‘tis impossible there can be any reasoning’s: but as this resemblance admits of many different degrees, the reasoning becomes proportionably more or less firm and certain. An experiment loses of its force, when transferr’d to instances, which are not exactly resembling; tho’ ‘tis evident it may still retain as much as may be the foundation of probability, as long as there is any resemblance remaining. (Hume 1992, p. 142) Here we can discern Descartes’ reduction of proportions to equalities. Hume sets up a gradient where certainty is the goal if the resemblance is identical. Reducing resemblances to identicals is the same as the reduction of proportions to equalities. A proportion is an analogy, which deals with resemblance. Also, those things and events that are identical convey a sense of equality. But there is nothing in a number of instances, different from every single instance, which is supposed to be exactly similar; except only, that after repetition of similar instances, the mind is carried by habit, upon the appearance of one event, to expect its usual attendant, and to believe, that it will exist. This connexion, therefore, which we feel in the mind, this customary transition of the imagination from one object to its usual attendant, is the sentiment or impression, from which we form the idea of power or necessary connexion. (Hume 1993, p. 50) Hume saying that there is no instance exactly similar to any other is saying that we cannot reduce our proportions to equalities, that there will always be some degree of difference between analogues. The precision between everyday analogy and scientific formulae is a distinction not of kind, but of mere degree. In science, the resemblances are more precise, and the probability approaches closer to certainty, though never quite achieving it. Descartes would have us believe that the as can become an equals, and therefore we can call it a law and send it into the future. The equals sets up a possibility for contradiction and binds the relations, supposed to be identical, under the Law of Identity. The as does no such thing. Hume wishes to restore modesty, humility and mystery by reminding us that the equals is actually nothing more than an as, that there is no contradiction if future causal relations do not equal those of the past. Truth is like Zeno’s Tortoise. We can continually draw closer to it, but we can never catch it. 23. And so the pendulum swings once again, the revolving door of history continues its revolutions. But unlike Sisyphus’ monotonous back-and-forth, this revolution will change philosophy forever. First, Hume’s challenge: When it is asked, What is the nature of all our reasonings concerning matter of fact? the proper answer seems to be, that they are founded on the relation of cause and effect. When again it is asked, What is the foundation of all our reasonings and conclusions concerning that relation? it may be replied in one word, EXPERIENCE. But if we still carry on our sifting humour, and ask, What is the foundation of all conclusions from experience? this implies a new question, which may be of more difficult solution and explication. Philosophers, that give themselves airs of superior wisdom and sufficiency, have a hard task, when they encounter persons of inquisitive dispositions, who push them from every corner, to which they retreat, and who are sure at last to bring them to some dangerous dilemma. (Hume 1993, p. 20). And so, the Kantian revolution: Experience has therefore a foundation, a priori principles of its form, that is to say, general rules of unity in the synthesis of phenomena, the objective reality of which rules, as necessary conditions—even of the possibility of experience—can always be shown in experience. (Kant 2003, p. 111) Kant comes onto the scene desiring to explain the derivation of Hume’s many sentiments and feelings. Like a physician telling her patient that kidney stones are what he feels, Kant, the metaphysician, tells Hume that it is a general rule in his pure understanding that he feels when he predicts that a stone will fall when dropped. What Hume deems a conjunction derived from repetitious experience, Kant calls a synthesis derived from the innermost workings of the human mind, a synthesis that precedes experience and organizes it so that it can even be called experience. Now experience depends on the synthetic unity of phenomena, that is, upon a synthesis according to conceptions of the object of phenomena in general, without which experience could never become knowledge, but would merely be a rhapsody of perceptions, never fitting together into any connected text… (Kant 2003, p. 111) This synthesis stands as the gem of Kant’s tome. The possibility of synthetic a priori judgments sits as the cornerstone of a critique that could be said to be one of the most important works in western philosophy. To get at this gem and excavate the superimposition, I will begin with billiard balls and a piece simple arithmetic. 24. Hume argues that the connection of cause and effect derives from experience. Kant wishes to refute this, saying that even though knowledge of this connection begins with the experience, this knowledge comes from the mind. Before Kant gets to the question of how this is possible, he demonstrates that it is. He does so by showing that the very same synthesis that subsumes causation is the one that also subsumes arithmetic. Hume, in his famous billiard balls example, says: The mind can never possibly find the effect in the supposed cause, by the most accurate scrutiny and examination. For the effect is totally different from the cause, and consequently can never be discovered in it. Motion in the second Billiard-ball is a quite distinct event from motion in the first… (Hume 1993, p. 18) And now compare this with Kant’s statements concerning 5 + 7 = 12: The conception of twelve is by no means obtained by merely cogitating the union of seven and five; and we may analyze our conception of such a possible sum as long as we will, still we shall never discover in it the notion of twelve… Arithmetical propositions are therefore always synthetical, of which we may become more clearly convinced by trying large numbers. (Kant 2003, p. 10) Just as Kant suggested that we might be convinced by trying large numbers—which would subject us to a mathematical problem that we must take time to calculate rather then knowing by rote—Hume asks us to consider causal relations that “we remember to have once been altogether unknown to us” (Hume 1993, p. 17). Thus, Kant uses Hume’s reasoning with arithmetic in order to demonstrate the similarity between billiard balls and 5 + 7 = 12. Categorizing causality and arithmetic under one heading—a priori synthetic judgment—is Kant’s first step in his defense of the superimposition of modern science. 25. Kant’s next move consists in positing his two pure intuitions: space and time. These two intuitions act as the stage upon which the rhapsody of perceptions are organized. These intuitions are inflicted upon the rhapsody by the mind, or one may say that the intuitions are superimposed onto the manifold, the flux, the plurality of existence. The intuitions of space and time cannot themselves be experienced, for they are analogous to light: though not able to be seen itself, allows objects to be seen. But what can be said at all in regards to space and time? What can we say about that which allows all things to be experienced? Quantity, only quantity. Nothing qualitative can be said. Time has duration, space has distance, all are magnitudes. Thus, the light that affords vision does so quantitatively. All phenomena contain, as regards their form, an intuition in space and time, which lies a priori at the foundation of all without exception. Phenomena, therefore, cannot be apprehended, that is, received into empirical consciousness otherwise than through the synthesis of a manifold, through which the representations of a determined space or time are generated; that is to say, through the composition of the homogeneous, and the consciousness of the synthetical unity of this manifold (homogeneous). Now the consciousness of a homogeneous manifold in intuition, in so far as thereby the representation of an object is rendered possible, is the conception of quantity (quanti). Consequently, even the perception of an object as phenomenon is possible only through the same synthetical unity of the manifold of the given sensuous intuition, through which the unity of the composition of the homogeneous manifold in the conception of a quantity is cogitated; that is to say, all phenomena are quantities, and extensive quantities, because as intuitions in space or time, they must be represented by means of the same synthesis, through which space and time are determined. (Kant 2003, p. 115) To sum, all that can be said of space and time is quantity, therefore all that appears in space and time can be quantified. And thus, Kant has argued for the justification of Descartes’ pivotal step of turning all that is qualitative into quantities. As for his talk of the homogeneous manifold, the benefit of converting all qualities into quantities is the production of identical units (unities) of measure that can be used in formulae. Space and time are measured in distance and duration. Therefore, to translate, everything in space can be represented in meters, just as all time can be represented in seconds. And thus, Kant has also paved the way for the justification of the reduction of proportions to equalities (formulae). 26. Now, as for the many-to-one reduction, we come to Kant’s Analogies of Experience. The analogies of experience are the synthesis of perceptions that amounts to experience itself. The analogies tame the rhapsody and dam the flowing flux into bordered unities. Kant provides three analogies: permanence, succession, and co-existence. (I will only deal with the first two here.) The general principle of all three analogies rests on the necessary unity of apperception in relation to all possible empirical consciousness (perception) at every time, consequently, as this unity lies a priori at the foundation of all mental operations, the principle rests on the synthetical unity of all phenomena according to their relation in time. (Kant 2003, p. 122) Before Kant delivers these fundamental analogies, he draws the important distinction between what I have simply termed qualitative and quantitative proportion. The former he will say is regulative, and the latter constitutive. My reading of the two interprets these terms in light of aphorism 5, where I attempt to distinguish the precision of quantitative proportion over qualitative. I give this example: 1) Tree is to Ground as Woman is to… 2) 2 is to 4 as 10 is to… The first is an analogy where the fourth term can only be found with an appeal to experience, and thus, in my opinion (for I do not speak for Kant here), renders it interpretive. Kant will say that it is regulative because we have a rule to guide us as we make our appeal to experience. The fourth term of the latter analogy can be said to be constituted within the relation of the first and second terms. Analogies in philosophy mean something very different from that which they represent in mathematics. In the latter they are formulae, which enounce the equality of two relations of quantity, and are always constitutive, so that if two terms of the proportion are given, the third is also given, that is, can be constructed by the aid of these formulae. But in philosophy, analogy is not the equality of two quantitative but of two qualitative relations. In this case, from three given terms, I can give a priori and cognize the relation to a fourth term, but not this fourth term itself, although I certainly possess a rule to guide me in the search for this fourth term in experience, and a mark to assist me in discovering it. (Kant 2003, p. 123). Here we see the “all is water” of Thales, in which he connected the entire rhapsody of perceptions into a single unity. Could we say it was a misuse of the rule that Kant argues lies a priori within our understanding? That is up to the reader to decide. 27. The first analogy is permanence and deals with coming-to-be and change. Kant draws from Aristotle here and posits the notion of substance, which is permanent. “Substances (in the world of phenomena) are the substratum of all determinations of time” (Kant 2003, p. 127). Without positing something permanent, such as substance, change is not possible. That is to say that only that which is can change, can become. If the thing that changes is not a unity of some sort, than what keeps us from seeing with every change an entirely new object? If it is true that every single cell of my body is replaced every seven years, then what makes me still me, and not something entirely new? Is the river that Heraclitus steps into a second time a different river? Something permanent must be there to underlie the change if we are to think of it as the same. As Kant says, “upon this notion of permanence rests the proper notion of the conception of change” (Kant 2003, p. 127). Thus, this analogy is the reduction of a plurality into a unity. 28. The second analogy deals with the infamous character of causality. The connection of cause and effect links occurrences into events and lies at the foundation of experience itself. In opposition to Hume, Kant argues that causality does not arise from experience, but experience from causality. Hume was only able to analyze causation because his understanding already organized his perceptions in such a way. Also, we can only speak of space and time because we were born with an understanding that intuited space and time. In Kant’s words, But the same is the case with this law [causality] as with other pure a priori representations (e.g. space and time), which we draw in perfect clearness and completeness from experience, only because we had already placed them therein, and by that means, and by that alone, had rendered experience possible. (Kant 2003, p. 131-2) By this, we do not have a complete refutation of Hume’s attacks. The general notion of causality is a rule of the pure understanding that renders experience possible. But as for individual causal events, we do need experience and we do draw off the past. The superimposition, however, allows us to turn qualitative analogy (which is merely regulative, as the fourth term has to be sought in experience) into quantitative. Reducing the plurality of experience into unities that are quantified, such as reducing objects to a measurement of “mass,” creates the opportunity to draw up theories of mathematics—blueprints of the universe in numerical terms—and make astounding predictions, such as Einstein’s Special Theory of Relativity that predicted that gravity curves space. However, science has proven over the course of its brief history to be fallible. Its greatest defense appears to be technology, as the more abstract theories of science are overturned with every new generation. Thus, maybe as Hume tempered Descartes, it is time to bring one to the stage who can temper Kant. 29. Like a flamethrower, Friedrich Nietzsche enters the world of philosophy. He comes armed with a keen eye for literature and history, and a frenzied pen for poetry. Wading into Nietzschean waters is wading into a raging flux. A fiery fan of Heraclitus, Nietzsche seemed to embody Heraclitean views, as Nietzsche’s works flow like a river that may not be the same upon a second dip. Though, those who have ridden the entire river seem able to reduce the plurality, by analogy between all the works, into a single feeling of what Nietzsche said on a whole. For example, is his “will to power” a claim that underlies all of existence, or merely a pragmatic claim applicable only to human beings? Is it a psychology or a metaphysics—an “all is water” reduction? What exactly did he mean when he said “God is dead?” Debates continue to flare concerning the intricacies. With this said, I mean to speak of Nietzsche’s philosophy with humility, recognizing that I am a mere tadpole in the pool of many interpretations, and I wish simply to pull out statements that, I feel, have great bearing and truth in regards to this growing thread I am teasing out of the history of philosophy. So, without further adieu, the last philosopher… 30. My thread has proven to be of a subject that is quite basic to human understanding, nature, and epistemology. It has wide implications for metaphysics and science. Thus, let me step into a single part of the Nietzschean river and wade lightly into his attack on metaphysics in the section titled, “Of First and Last Things,” in Human, All Too Human. And, therefore, with only my thread in mind to prevent from being overcome by the current, I will let Nietzsche speak for himself. Logic too depends on presuppositions with which nothing in the real world corresponds, for example on the presupposition that there are identical things, that the same thing is identical at different points of time: but this science came through the opposite belief (that such conditions do obtain in the real world). (Nietzsche 1996, p. 16/aphorism 11). Thus there comes to be constructed habitual rapid connections between feelings and thoughts which, if they succeed one another with lightning speed, are in the end no longer experienced as complexes but as unities. It is in this sense of the moral feelings, of the religious feelings, as though these were simple unities: in truth, however, they are rivers with a hundred tributaries and sources. Here too, as so often, the unity of the word is no guarantee of the unity of the thing. (Nietzsche 1996, p. 19/aphorism 14). The invention of the laws of numbers was made on the basis of error, dominant even from the earliest times, that there are identical things (but in fact nothing is identical with anything else); at least that there are things (but there is no ‘thing’). The assumption of plurality always presupposes the existence of something that occurs more than once: but precisely here error already holds sway, here already we are fabricating beings, unities which do not exist. –Our sensations of space and time are false, for tested consistently they lead to logical contradictions. The establishment of conclusions in science always unavoidably involves us in calculating with certain false magnitudes: but because these magnitudes are at least constant, as for example are our sensations of time and space, the conclusions of science acquire a complete rigorousness and certainty in their coherence with one another; one can build on them—up to that final stage at which our erroneous basic assumptions, those constant errors, come to be incompatible with our conclusions, for example in the theory of atoms. (Nietzsche 1996, p. 22/aphorism 19) Here we have the reason for the fallibility of science. Every generalization inevitably covers over details that will, in some future time, make themselves known. Like the intricacies of a woman’s body beneath her dress, generalizations conceal great secrets lying beneath, secrets of uniqueness. Reality can be forced into formulae only to a certain degree before the missed or discarded details rally up to be heard. Science does not deliver Truth. No, it delivers technology. Beyond this, science is merely philosophy, bearing many-to-one and proportion-to-equality reductions. All is not water, nor is it magnitude. All is analogy. 31. And so I conclude this aphoristic gallop through history. It is my abundant hope that my thread has been received with squinting of eyes and tilting of heads, as maybe I am right in saying that this thread warrants the pedestal. But, of course, it seems that maybe I should conclude with more than just a reaffirmation of my thesis. Maybe I should give a moral to this story, try my hand at asserting something further, and say what may be extracted from this history, at least in my eyes. What have I learned? Well, if I am to do this, let me do it with some bombast and flare, while at the same time give care to brevity, as this history has gone on long enough. And hopefully the history I have presented will be enough to back my claims and justify my brevity. Epistemology, how we form knowledge, takes place through analogy. How we learn language itself takes place through analogy. Words are unities that represent a plurality. For us to make the associations between a grouping of things and to classify them under the category of a word is to make the comparisons and mentally sense the proportions. When we say we know something, there are analogies that underlie this claim that generally go beyond our consciousness. However, Knowledge and Truth are teleological terms, a distant bull’s-eye to be forever aimed at, but never hit. Our analogies are more or less perfect, equalities never actually achieved, because all things are unique. We draw closer to Knowledge and Truth, but we can never reach it and we have no criterion to judge if we have. Mystery will forever be with humanity, and with it the beautiful, the sublime, the unknown, the scary, the surprising. The journey is infinite and, thus, must be enjoyed for its own sake. Every new generation may think they have come to something true about this existence, but at best they came to a more or less precise view. Epistemology consists in a precision of proportion. It is a degree of resemblance of analogues, a more or less, but void of a beginning or an end, void of the existence of the finish line, of the perfect resemblance, the equality. It is true that we must posit the possibility of Truth and Knowledge—the bulls-eye must be there for the teleology—but let our modesty assent to the necessary mirage gracing the horizon, the unattainable goal that nevertheless beckons us to come. We should not frown upon the mirage, but look back upon humanity’s journey toward sharpening the knife of knowledge, and feel a deep sense of nostalgia. But now, in our present age, is it possible that the degree of precision reached is possibly too sharp for the clumsy hands of humanity? Many feel technology may have passed far beyond our understanding of its long-term implications… This, however, takes us into the arena of ethics, possibly an ethics of proportion. And, that might be another paper for another time. Works Cited Aristotle. 2002. Nichomachean Ethics. Trans. Joe Sachs. Newburyport: Focus. Descartes, René. 2000. Philosophical Essays and Correspondence. Ed. Roger Ariew. Indianapolis: Hackett. Hume, David. 1993. An Enquiry Concerning Human Understanding. 2nd ed. Ed. Eric Steinberg. Indianapolis: Hackett. Hume, David. 1992. Treatise of Human Nature. Buffalo: Prometheus. Kant, Immanuel. 2003. Critique of Pure Reason. Trans. J.M.D. Meiklejohn. Mineola: Dover. Nietzsche, Friedrich. 1996. Human, All Too Human. Trans. R.J. Hollingdale. New York: Cambridge University Press. Nietzsche, Friedrich. 1962. Philosophy in the Tragic Age of the Greeks. Trans. Marianne Cowan. Washington D.C.: Regnery. Plato. 2007. Republic. Trans. Joe Sachs. Newburyport: Focus. Plato. 2008. Timaeus and Critias. Trans. Robin Waterfield. New York: Oxford University Press. Wittkower, Rudolf. 1960. “The Changing Concept of Proportion.” Daedalus Vol. 89, No. 1: 199-215.