Descartes vs. Kant — What is Transcendental Philosophy?

The significant breakthroughs made by Immanuel Kant are often gathered together under the title of ‘transcendental philosophy.’ Indeed, Kant himself used that word, Transzendentalphilosophie, to describe his own thought.

But what is meant by the phrase ‘transcendental philosophy’? The reader will be aware that, in the history of philosophy, the simple paradigm is common in which Rene DesCartes is the representative of ‘rationalist’ philosophy, while John Locke is the icon for ‘empiricist’ philosophy. Each of those two was joined by teammates. Alongside DesCartes were, e.g., Jacques du Roure, Geraud de Cordemoy, Francois Bayle, and Jacques Rohault. Locke’s fellow empiricists included, among others, David Hume and Thomas Reid.

The rationalist team distrusted empirical knowledge, arguing that sense-data was unreliable. The rationalists found certain knowledge in a priori reasoning.

The empiricists discounted a priori knowledge as largely vacuous, consisting mostly of tautologies like “a = a” and “all triangles have three sides.” They argued that meaningful content came from sensations.

A sort of stalemate between these two teams had emerged by Kant’s time. Kant hoped to find a third option in philosophy: his Transzendentalphilosophie.

Webster’s dictionary defines ‘transcendental’ as “of or relating to experience as determined by the mind’s makeup” or “transcending experience but not human knowledge.” Webster offers an important contrast between ‘transcendental’ and ‘transcendent’ — the latter being “beyond the limits of all possible experience and knowledge.”

Random House offers a similar distinction: ‘transcendent’ is “transcending experience, not realizable in human experience,” while ‘transcendental’ is “of, pertaining to, based on, or concerned with the a priori elements in experience that condition human knowledge.” Random House adds that ‘transcendental philosophy’ is “based upon the doctrine that the principles of reality are to be discovered by the study of the processes of thought.”

Likewise, the dictionary of Funk and Wagnalls defines ‘transcendent’ as “lying beyond the bounds of all possible human knowledge,” and explains ‘transcendental’ as “having an a priori character; transcending experience.” According to Funk and Wagnalls,

Intuitive truths are those which are in the mind independently of all experience, not being derived from experience nor limited by it, as that the whole is greater than the part, or that things which are equal to the same thing are equal to one another. All intuitive truths or beliefs are transcendental. But transcendental is a wider term than intuitive, including all within the limits of thought that is not derived from experience, as the ideas of space and time.

Significantly, Funk and Wagnalls directed the reader to a reference work by Charles Krauth and William Fleming. This book went through several editions, with slight variations in the book’s title. Henry Calderwood seems to have been involved in one of earliest editions. It is usually cited as Vocabulary of the Philosophical Sciences. Fleming and Krauth give extensive discussions of the word ‘transcendental.’

Eric Kandel offers a glimpse into Kant’s philosophy of mind, and into Kant’s epistemology:

The view of the brain as a creativity machine that constantly uses inference and guesses to reconstruct the external world — the view advocated by Ernst Kris and Ernst Gombrich — was a dramatic shift from the naive philosophical realism of the seventeenth-century British philosopher John Locke that dominated thinking about mind at that time. Locke conceived of mind as receiving all the information capable of being gathered by the senses, a view in which mind simply mirrors the reality of the external world. Kris and Gombrich’s view of the brain was a modern version of Kant’s theory that sensory information allows reality to be invented by the mind.

Kant perhaps would not have phrased it as Kandel does, but the point is made: Kantian epistemology sees the mind as active. The mind doesn’t passively receive sense-data and then process them into perceptions. Even at the earlier stage of sensation, before perception, the mind is shaping the sense-data by placing it into space and time — or rather, by creating space and time around the sense-data.

Without using the word ‘transcendental,’ Eric Kandel describes the Kantian epistemological process:

The biological study of learning raises some familiar philosophical questions: What aspects of the organization of the human mind are innate? How does our mind acquire knowledge of the world?

Serious thinkers in every generation have struggled with these questions. By the end of the seventeenth century, two opposing views had emerged. The British empiricists John Locke, George Berkeley, and David Hume argued that our mind does not possess innate ideas; rather, all knowledge derives from sensory experience and is therefore learned. By contrast, the continental philosophers Rene Descartes, Gottfried Leibniz, and particularly Immanuel Kant argued that we are born with a priori knowledge; our mind receives and interprets sensory experience in an innately determined framework.

The definitions offered by Webster, Random House, and Funk and Wagnalls are compressed, intended for laymen, and somewhat simplified. They are not written by philosophers for philosophers. Eric Kandel is a brilliant and recognized neuroscientist, but his descriptions of Kant’s thought are not from the viewpoint of Kantian specialist and are not for an audience of Kant scholars.

A text coauthored by Julius Maria Roth and Paul Schulmeister points out that epistemology in general — and especially Kant’s epistemology in particular — is concerned not about what we know, but about how we know it, and the conditions which make knowledge possible:

Die Wende, die mit Immanuel Kants (1724-1804) Transzendentalphilosophie eingeläutet wurde, lässt sich am prägnantesten durch den Vergleich von Rene Descartes (1596-1650) und Kant nachvollziehen. Es handelt sich um den Unterschied zwischen Wissen und den Bedingungen von Wissen.

Roth and Schulmeister argue that DesCartes sought certain knowledge which can’t be doubted, while Kant sought the prerequisite which made knowledge attainable. Both Kant and DesCartes were concerned with the formal mechanisms of epistemology, but under the interpretation of Roth and Schulmeister, DesCartes was driving toward specific contents of knowledge as well as the form of knowledge:

Descartes ging es darum, sicheres Wissen zu erlangen, das nicht mehr bezweifelt werden kann. Kant hingegen fragte nach der Bedingung der Möglichkeit von Wissen.

DesCartes proceeded from the assumption that knowledge was possible, and so his questions were “What can we know? What do we know? Do we know what we think we know?”

Descartes setzte die Möglichkeit von Erfahrung als gegeben heraus. Ihn interessierte deshalb die Wirklichkeit von Erfahrung. Seine Frage lautete: Sind die Dinge wirklich so, wie sie uns erscheinen?

Kant, in contrast to DesCartes, focused on this question: “Can we know? How can we know? What are the mechanisms which would, or which do, make experience possible?” Understanding how experience is structured, or constructed, also points to the centrality of space and time in Kantian thought. Without space and time, there would be and could be no experience, and accordingly, early in the Kritik der Reinen Vernunft, Kant explores space and time.

Kant rückte jedoch genau jenen Aspekt in den Vordergrund, den Descartes als gegeben hingenommen hatte, nämlich die Möglichkeit von Erfahrung. Seine Frage lautete: Wie ist die Erfahrung überhaupt möglich?

The questions “How do I perceive objects? How do my experiences arise?” is closely related to the question “Why is it that my experiences and perceptions happen necessarily in a certain way?” The observer will note that it is not possible to have an idea of a physical object without having an idea of it in space. The mind finds it impossible to conceive of a physical object which is not in space. Likewise with time.

Kant’s exploration begins, not by asking about the objects in the world, but rather by asking about the mind which perceives them.

Bevor man wie Descartes danach fragt, ob die Dinge, wirklich so sind, wie sie uns erscheinen, lautet Kants Vorschlag, dass wir zunächst klären sollten, wie es überhaupt dazu kommt, dass die Dinge auf eine bestimmte Weise erscheinen. Mit Kant lernen die Philosophen, nicht gleich nach der Wirklichkeit und Wahrheit zu fragen, sondern zunächst das eigene Denken zu untersuchen. Genau das ist der Clou der Transzendentalphilosophie, die sich nicht vorschnell in metaphysische Gefilde vorwagen will, bevor nicht die Frage nach den Bedingungen der Möglichkeit von etwas geklärt ist.

The above summary of one part of Kant’s thought relies on Julius Maria Roth and Paul Schulmeister. The reader will ask, to which extent have those two authors accurately understood and expressed this part of the Kantian system?

Perhaps one of the main interpreters and advocates of Kant’s work is Carl Christian Erhard Schmid. Schmid is perhaps most responsible for explaining, and drawing attention to, Kant’s writings. Kant would have been much less well-known if Schmid hadn’t lectured and written about him.

Not only did C.C.E. Schmid offer a clear and influential exposition of Kant’s thought, but he is one of the few Kantian scholars to have published and lectured extensively during Kant’s lifetime. Schmid’s Kritik der Reinen Vernunft im Grundrisse nebst einem Wörterbuche zum leichteren Gebrauch der kantischen Schriften appeared in 1786, one year prior to the second edition of Kant’s Kritik der Reinen Vernunft. Schmid’s book about Kant went through several editions, the exact title changing slightly.

Schmid was writing and teaching about Kant, not only while Kant was still alive, but during Kant’s most productive years. It is left as an exercise to the reader to find primary source documents to answer questions about the extent to which Kant was aware of, and familiar with, Schmid’s writings — and questions about whether or not there was any direct communication between Kant and Schmid.

What is clear is that there was no objection from Kant about Schmid’s explanations of the Kantian system. In a hierarchy of reliability, therefore, Schmid would be near the top. To cite Schmid is arguably to cite one of the most dependable secondary sources on Kant.

Schmid’s Wörterbuch articulates a similar distinction between ‘transcendent’ and ‘transcendental’ and offers a lengthy entry on the latter word. The entry includes:

Transzendental bedeutet überhaupt eine Vorstellung (Anschauung oder Begriff), Urteil, Wissenschaft a priori, so fern sie sich doch auf Gegenstände bezieht, und darauf anwenden läßt; die Erkenntnis von dem objektiven Gebrauche, der rein a priori entsprungenen Vorstellungen und ihrer Vermögen.

Schmid’s detailed entry defining ‘transcendental’ merits detailed study, and is perhaps a powerful instrument for gaining insight in what is meant by the word Transzendentalphilosophie.

John Locke’s Epistemology: What Is Supernatural Knowledge?

In the long history of epistemology, many philosophers have asserted some form of a distinction between the knowledge humans gain through the five physical senses and the knowledge they gain through the exercise of reason. This distinction is drawn slightly differently from one philosopher to the next, and described in slightly different vocabulary, but the dichotomy is perennial one.

As an empiricist, John Locke looked to experience as the source of much or most of knowledge, and in some way, perhaps, the foundation of all knowledge. Yet Locke was aware of the complexities which arise when one uses this distinction in the careful analysis of knowledge.

There are relatively clear cut cases: The sense of vision may tell us that before us is a blueness; rational reflection may tell us that a = a. But between those extremes are a variety of borderline cases which are more complicated and do not always fall neatly into or or the other of those two categories.

One example is a perception which is the result of raw a posteriori sense-data which have been processed by a priori rational concepts, as J.L. Mackie explains:

The empiricist may, and Locke does, recognize that even the reception of ideas in perception is not wholly passive, but includes a considerable element of (unconscious) interpretation.

Locke shows how raw sense-data, which is a sensation and not yet a perception, needs to be processed by concepts in order to become a perception and eventually to become knowledge. A drawing on a two-dimensional paper of a three-dimensional object furnishes an example:

We are further to consider concerning perception, that the ideas we receive by sensation are often, in grown people, altered by the judgment, without our taking notice of it. When we set before our eyes a round globe of any uniform color, v.g. gold, alabaster, or jet, it is certain that the idea thereby imprinted on our mind is of a flat circle, variously shadowed, with several degrees of light and brightness coming to our eyes. But we having, by use, been accustomed to perceive what kind of appearance convex bodies are wont to make in us; what alterations are made in the reflections of light by the difference of the sensible figures of bodies; — the judgment presently, by an habitual custom, alters the appearances into their causes. So that from that which is truly variety of shadow or color, collecting the figure, it makes it pass for a mark of figure, and frames to itself the perception of a convex figure and an uniform color; when the idea we receive from thence is only a plane variously coloured, as is evident in painting.

There is a long series of thinkers in the history of philosophy who have written about this matter. Routinely, it is framed by some type of dichotomies: experience vs. reason, a priori vs. a posteriori, analytic vs. synthetic, etc.

As with any dichotomy, one may ask whether there are other alternatives in addition to the two given.

As William Uzgalis writes, “Locke claims that ideas are the materials of knowledge and all ideas come from experience.” Uzgalis is expressing the more-or-less standard understanding of Locke. It is worth noting that Locke, in most of his texts, hesitates to write that all knowledge comes from experience, but rather writes that all ideas come from experience: this nuance is worth noting.

In any case, however, another question presents itself: when Locke writes ‘experience,’ does he mean ‘sensory experience,’ i.e., from our five physical senses? Or does he leave room for some other types of experience?

Locke wrote about Paul, the author of several New Testament epistles, that Paul obtained something — ideas or knowledge — directly. Would Paul’s reception of propositions from God count as ‘experience’ for Locke? Locke writes:

Paul was miraculously called to the ministry of the gospel, and declared to be a chosen vessel; that he had the whole doctrine of the gospel from God, by immediate revelation; and was appointed to be the apostle of the Gentiles.

Even more direct, Locke uses the word ‘knowledge’ to refer to the content of Paul’s experience:

For his information in Christian knowledge, and the mysteries and depths of the dispensation of grace by Jesus Christ, God himself had condescended to be his instructor and teacher.

One could, then, begin to construct a paradigm with two categories of experience: first, the experience which arrives by means of the five physical senses; second, experience which arrives otherwise.

If there is such a thing as some type of experience distinct from physical experience, then what could it be? There might be more than one answer. Such non-sensory experiences could be emotional: experiencing happiness or sadness. They could be rational: the experience of calculating, for example. Locke speaks of ‘dictation’ to describe Paul’s experience: Locke says that Paul was “under the Spirit of God, that dictated these sacred writings.” Was this an audible dictation, i.e., the ordinary physical sense of hearing? Or was it somehow an experience of ideas: ideas arising without the five physical senses?

Rene DesCartes is often seen as the opposite of Locke, especially in terms of their respective epistemological systems. Locke however uses one of DesCartes’ more notorious vocabulary items when speaking of Paul’s experience. Cartesian scholars have long wrestled with how DesCartes uses the word ‘light,’ especially in the phrase ‘natural light’ or ‘light of nature.’ It seems to indicate, for DesCartes, an a priori bit of knowledge which is so obvious in its truth that it cannot be doubted. Critics of DesCartes accuse him of a deus ex machina move which begs the question of epistemological certainty when he invokes this natural light. Locke uses a similar phrase to describe the source of Paul’s knowledge:

He was full stored with knowledge of the things he treated of, for he had light from heaven, it was God himself furnished him.

As Locke uses the phrase ‘immediate revelation,’ so he also here speaks of a ‘truth’ which has been ‘revealed’ — truth being one of the usual ingredients of knowledge, as in ‘justified true belief.’

Like Francis’s Bacon’s listing of the sources of experimental error, Locke also indicates that human perception is liable to error, and proposes reliance on revelation as one possible measure against such error:

We are all men, liable to errors, and infected with them; but have this sure way to preserve ourselves, every one, from danger by them, if, laying aside sloth, carelessness, prejudice, party, and a reverence of men, we betake ourselves, in earnest, to the study of the way to salvation, in those holy writings, wherein God has revealed it from heaven, and proposed it to the world, seeking our religion, where we are sure it is in truth to be found, comparing spiritual things with spiritual things.

John Locke’s epistemology, then, may have room for something more than the usual ‘experience vs. reason’ template to describe sources of ideas, of perceptions, and of knowledge. Or, at least, if he does limit the sources to those two, then he may be broadening the definitions of ‘reason’ and ‘experience’ to include more than one might at first suppose.

Schopenhauer: Metaphysician or Empiricist?

Authors who write about the history of philosophy often include Arthur Schopenhauer in a group titled ‘German Idealism’ or ‘Transcendental Idealism’ or something like that. Yet he bears affinities to thinkers like David Hume, who is often placed into a group titled ‘British Empiricism’ or ‘Radical Empiricism’ or similar words.

Schopenhauer’s empirical bent is revealed in his attention to observable data. He explores in detail the discoveries, findings, and methods of the natural sciences. His philosophy of language, likewise, is founded on linguistic data, much of it derived from historical philology and from explorers returning from obscure corners of the planet with new linguistic evidence.

Yet Schopenhauer’s terminology might mislead the reader. He relies on words like ‘Will’ — the capitalization hinting at the centrality of the concept in his thought. The reader can be forgiven for thinking that Schopenhauer is referring to a metaphysical entity instead of empirical evidence.

He has, however, so remade and redefined the word that it now serves as shorthand for a bundle of empirical data, as Lenart Skof writes:

The profound affinity between Schopenhauer and Radical Empiricism is documented by Schopenhauer’s method of observing reality and its phenomena and his reliance of on the achievements of the natural sciences of his time. In the second book of The World as Will and Representation, metaphysical ways of speaking like that of “objectifications of the Will” serve only as metaphors for a number of empirical phenomena, which already in the first book had been freed from the old epistemological modes of subjective knowledge.

Not only does the ‘Will’ seem like a suspiciously metaphysical concept for an alleged empiricist to embrace, but Schopenhauer even begins to discuss Platonic ideas — or ideals — which seem to place him in the middle of a metaphysical tradition.

One way, perhaps, to understand Schopenhauer’s seeming metaphysical discourse as compatible with the hypothesis that he is an empiricist is this: to see the ‘Will’ as being an abbreviation for ‘my experience of the Will.’ The empiricist will deny that there is a metaphysical object called the ‘Will,’ but the empiricist cannot deny that I have some experience of what I call the ‘Will.’

Likewise, I can have the experience of noticing similarities among different objects, and can label a list of those similarities as a Platonic idea. In this way, possibly, Schopenhauer does not follow the metaphysical path of trying to describe what metaphysical objects like the Will or a Platonic idea are, and does not attempt to create an epistemological system explaining how we can know about such objects.

Instead, he turns to concepts of art and morality, in a development which tempts the reader to think him a proto-existentialist. Lenart Skof continues:

The body, as the first representation, revealed to the thinker the world as Will — the immediate world as the effects of matter. However, by shifting into the world of Platonic ideas in the third book, Schopenhauer undertook a task that could only have one possible solution: Dismissing the principle of reason was now only possible through the brilliant artistic act, and through related forms of artistic contemplation of ideas, and, analogously through the world as suffering, and the related conception of his main ‘existentials’ (guilt, conscience, grace, the path of salvation) based on the negation of Will, or asceticism.

The Will, then, is not a metaphysical object, but rather an object of perception. The ‘World as Will’ and the ‘World as Representation’ together compose all experience — and all possible experience.

His own scheme of philosophy, in the development of which he proceeded around or, more precisely, over and above Kant, turns back on itself and can only boomerang. Thus, already in the second book, Schopenhauer is forced to start discussing Platonic ideas as the models of objectifications of the Will, although methodologically, these ideas do not yet belong there at all, as the theme discussed in this book is the world as Will.

Schopenhauer frequently compliments Kant, and it is clear that he has embraced parts of the Kantian system, while rejecting some other parts. In any case, space and time, as the prerequisites for any experience, and as formed by the mind to make experience possible, are central to Schopenhauer and are also the constituent ingredients for causality.

Considered in this way, Schopenhauer is an empiricist or a phenomenologist. He seems to have wrestled with slightly different understandings of Kant’s Ding an sich, at times under the influence of Gottlob Ernst Schulze.

On the one hand, as a student of G.E. Schulze, Schopenhauer was tempted to join Schulze and write that the Ding an sich is an illegitimately postulated construct, and that we have no valid reason to assert that there is such a thing.

On the other hand, Schopenhauer is tempted to retain the Ding an sich in his own system, but to redefine it substantially. Since the Will is behind our sensations and perceptions, as objectified Will, then perhaps the Will is the Ding an sich. If the world is will and representation, then every representation is the will: the will is the cause of, or lies behind, every representation.

If we understand Schopenhauer to assert that even the self is composed of will and representation, then it is only another small step to say, that for Schopenhauer, “I am the Ding an sich.”

Innate Ideas and Musical Taste: Prenatal Auditory Experiences

Walter Murch has a long and successful career in Hollywood. He is a “sound designer” and worked on films like The Godfather, American Graffiti, Apocalypse Now, The Unbearable Lightness of Being, The English Patient, and K-19: The Widowmaker.

Sound design is different from finding or composing music for a film. It is the creation of a sound environment, including ambient noises, and the acoustic properties of settings for dialogues or action.

The study of audiology and acoustics, which informs Murch’s work, originates with psychologists, engineers, musicians, physicists, and philosophers. Biologists and physicians — otologists and neurologists — study both the physical and mental process of sound perception. Murch explains how deeply sound is embedded in the mind, starting four-and-a-half months before birth:

We are conceived. We develop in the womb, and four and a half months after conception, the hearing switch is turned on.

The sounds which are heard prior to birth make a distinct impression on the mind. Immediately upon birth, a baby can recognize its mother’s voice, and when held by the mother, the baby responds to the sound of her heartbeat.

But music is also distinctly heard prior to birth, which gives rise to a series of questions about the formation of musical taste. Is a child born with preferences for certain types of music based on in utero experiences?

Murch notes that, of the five senses, hearing most decisively shapes prenatal experiences:

Sight is not turned on. We live in darkness in the womb. Smell is not operative in the womb. Touch is a kind of a slippery mucal feeling, but hearing is as fully articulated at four and a half months as it will be later. So, the child developing in the womb is a fully auditory creature. And so, each of us in this room was born into consciousness. The developing fetus is a conscious being, developing a sense of the self and the world, such as it is in the womb. All through the process of hearing.

Philosophers have long debated the question of innate ideas: Are there ideas already present in the human mind when a person is born? To analyze this question, the distinction between birth and conception must be examined.

In any case, at birth, one would say that a child must have some ideas — auditory ideas, the memory of auditory experience. Which might lead to a question about what philosophers — like Descartes and Locke — meant when they wrote about “innate” ideas. Did they perhaps mean ideas present at conception?

At birth, the child begins to connect its auditory ideas with sense-data arriving via sight, smell, taste, and touch. In this way, hearing may have a special place of privilege among the five senses. Hearing may be the foundational sense.

Walter Murch continues:

When you’re born, these other senses kick on. Primarily sight and you start to begin to develop this idea that the sound is caused by something. Your mother comes in, and you start to see these strange things called lips beginning to move, and the voice that you have heard in the womb comes out of these lips. And you begin to say, Oh, that’s what made the voice.

Murch’s remarks suggest both a possible argument for innate ideas and a possible reframing of the debate about “innate ideas” as “ideas present at conception” or as “prenatal ideas” — innate ideas cease to be controversial if the natal moment is preceded by months of sense-data and sensory experiences being processed into sensory memories.

His remarks also offer the possibility that musical taste is shaped by prenatal experiences.

Faraday’s Visual Approach to Science: An Allergy to Mathematics

Michael Faraday is credited with a number of discoveries and inventions, and has decisively informed the understanding of electromagnetism from the early 1800s until the present, and into the foreseeable future. Faraday’s discoveries and inventions are noteworthy in and of themselves, but beyond that, also because of his conception of scientific methodology.

As historian Geoffrey Cantor writes,

That Faraday expounded an empiricist view of science all commentators agree. Yet there are many incompatible strands within empiricism.

Faraday modified his views over the years, going from an initial allergy to mathematics to a tolerance of it. “Faraday’s rather complex, and apparently inconsistent, view on scientific method,” may be due to this metamorphosis.

Questions about the proper method for pursuing science were very important to him and he felt obliged on numerous occasions to expound his views on this subject so as to defend himself and his scientific work against alternative, but false, conceptions of science.

Cantor notes that there may be some distance between Faraday’s “methodological pronouncements” and “the actual methods he employed in the laboratory.” But the distance, if any, is slight, for “the two were closely related.” If someone had asked him “why he held those views,” he most probably would have answered that he was forced to hold them by the weight of empirical evidence, and if his methods and views changed slightly over the years, it would be because of the discovery of new evidence.

Faraday expressed a distaste for imagination, arguing that fantasy has no role in science, and coming close to echoing Newton’s famous hypotheses non fingo. Yet, for a thinker who largely rejected any role for imagination in scientific method, Faraday’s method centered around images: the etymological connection between ‘image’ and ‘imagination’ is not without cause. Cantor argues that Faraday doesn’t exile imagination completely and that Faraday retains a tightly-governed “proper role of the imagination.”

The famous near-absence of equations in many of Faraday’s writings, and his numerous drawings and diagrams attest to the visual nature of his thought. By contrast, other scientists of Faraday’s era, as well as before and after his era, had embraced the marriage between mathematics and natural sciences — especially between mathematics and physics.

Newton (1642 - 1727) clearly is an example of this marriage, yet Newton attached some importance to visualization. Indeed, John Hutchinson (1674 - 1737) criticized Newton’s inclusions of diagrams in scientific texts. Hutchinson wrote that Newton’s diagrams were “a cobweb of circles and lines to catch flies in.”

To be sure, it can be argued that a visual approach and a mathematical approach to electromagnetism are not that different, because the fields which Faraday described in words and pictures can also be captured in equations. But to that argument it can be replied that diagrams and drawings might offer a more intuitive understanding than equations, and that the intuitive understanding might be in some ways deeper and might offer more insights into the workings of electromagnetism.

Jim Al-Khalili describes Faraday’s skills:

What Faraday lacked in formal scientific training, particularly in mathematics, he made up for by his exceptional talent as an experimentalist. And although he was initially distrustful of mathematics, regarding it as obstructing rather than helping our understanding of the workings of Nature, he would, later in life, change his view in the light of the work of James Clerk Maxwell. In fact, Maxwell himself regarded Faraday as being an excellent theoretician and claimed this was the reason he was able to put Faraday's theories into the language of analytical mathematics.

Faraday’s search for principles, and his formulations of what those principles are or might be, were shaped in part by his Sandemanian and Glasite beliefs, as Geoffrey Cantor notes:

In his writings Faraday made repeated attempts to express the divinely fashioned natural economy in terms of metascientific principles, most importantly his principle of the conservation of forces. In his work of the 1820s and early 1830s the economy of nature was more implicit than explicit. By the late 1830s, however, it was beginning to emerge in a variety of different metascientific statements and to take on a more fixed form. Only with his far more explicit formulation of the principle of force conservation in the mid-1850s do we see it proposed as an incorrigible principle and one which must take precedence over all scientific theorizing.

The conservation of forces would seem to be, at first glance, a quantitative and therefore mathematical concept. Yet it seems that Faraday might have arrived at it visually.

Questions for Ludwig Boltzmann: Entropy and Methodology

Boltzmann’s significant and sometimes counterintuitive advancements in spacetime physics and philosophy have been well documented by Lawrence Sklar in Space, Time, and Spacetime and Philosophy and Spacetime Physics, and by other writers as well. In Vorlesungen über Gastheorie, Boltzmann himself sets his ideas forth.

The reader will be aware that Boltzmann argues that the universe is mostly in a state of equilibrium, with only rare instances of imbalance:

Man kann sich die Welt als ein mechanisches System von einer enorm großen Anzahl von Bestandteilen und von enorm langer Dauer denken, so dass die Dimensionen unseres Fixsternhimmels winzig gegen die Ausdehnung des Universums und Zeiten, die wir Äonen nennen, winzig gegen dessen Dauer sind. Es müssen dann im Universum, das sonst überall im Wärmegleichgewichte, also todt ist, hier und da solche verhältnismässig kleine Bezirke von der Ausdehnung unseres Sternenraumes (nennen wir sie Einzelwelten) vorkommen, die während der verhältnismässig kurzen Zeit von Äonen erheblich vom Wärmegleichgewichte abweichen, und zwar ebenso häufig solche, in denen die Zustandswahrscheinlichkeit gerade zu- als abnimmt.

Even more significant is his claim that in these rare pockets of disequilibrium, change is as likely to increase entropy as decrease it. This amounts to saying that time is as likely to move forward as backward, because, for Boltzmann, the motion toward entropy is time. For him, motion toward entropy does not happen within time, but rather that motion is time. The source of our observable universe is an anomaly, development away from equilibrium: our observable universe is a pocket within a larger universe.

Describing Boltzmann’s views, Craig Callender writes:

Boltzmann, however, explained this low-entropy condition by treating the observable universe as a natural statistical fluctuation away from equilibrium in a vastly larger universe.

Surveying Boltzmann’s conclusions, then, many questions might arise. Among them are these three:

First, Boltzmann’s hypotheses about the universe are based on, or prompted by, his investigation in gas theory. To which extent is it a valid methodological move, to apply the principles of gas theory to the entire universe? Aside from the observation that the universe includes solids and liquids, and is not composed of gas alone, it seems in other ways, too, that it is a great leap to assume that the principles which govern and explain the behavior of a gas inside a glass container sitting on Boltzmann’s laboratory table are sufficient to explain and govern the entire universe. Can Boltzmann validly generalize to the entire cosmos from a sealed beaker filled with nitrogen, oxygen, carbon dioxide?

Second, to which extent is Boltzmann’s assumption justified, that the universe is largely, almost entirely, in a state of equilibrium? And that any disequilibrium is a small, relatively microscopic, anomalous pocket within this larger universe? The glass container, filled with a gas, on Boltzmann’s laboratory table may well be largely, even entirely, in a state of equilibrium, but to assume the same of the entire universe seems again like an unwarranted generalization. Unlike the glass container in the laboratory, the universe contains near-perfect vacuums between galaxies, contrasted with the most dense possible compressions of matter elsewhere in the same universe. It contains the coldest possible and the hottest possible points. It seems that these would be pieces of evidence that perhaps disequilibrium is more pervasive in the universe than Boltzmann seems to indicate.

Third, do Boltzmann’s results contain a hidden assumption or requirement that there be some type of “meta-time” within which time operates? In order for Boltzmann to indicate that there would simultaneously be pockets within the larger universe, and that time in these different pockets could be going in different directions, there needs to be a larger meta-time in order for these to be happening “simultaneously.”

In addition to the above three questions, there are doubtless many more questions which can, and should, be posed both in order to understand and in order to evaluate Boltzmann’s work.

Faraday’s Method: Electromagnetism as Visual Intuitive Phenomena

In America — and perhaps in other parts of the world as well — secondary and postsecondary educational institutions have worked to create in the minds of students an almost instinctive or reflexive connection between mathematics and the natural sciences. Those who work in schools will automatically say “science” when prompted with the words “math and … ”

Yet the marriage between math and science may be merely a flirtation or friendship. The bond and similarity between the two is not as strong as is commonly supposed.

The thinkers who began the enterprises of modern mathematics and modern science saw them as two very different activities. The home of a priori rational certainty was found in mathematics, while approximation and tentativeness lived in the sciences.

The quadratic formula is the same in textbooks printed today or two hundred years ago — and will be the same centuries into the future. By contrast, the atomic weight of various isotopes of lead or gold, when calculated out to large numbers of significant figures, might be revised or refined over the years as successive editions of textbooks are printed for chemistry and physics classes.

There is a danger in overemphasizing the importance of mathematics in the natural sciences — and here one can also mean the observational sciences and empirical sciences. The non-mathematical aspects of scientific activity risk being ignored: the intuitive aspects.

There is an objection, of course, to say that seemingly non-mathematical properties like color and shape can in fact be reduced to mathematics: color is a wavelength which can be represented by a number; shape can be captured in an algebraic equation.

To this objection, one might respond by positing that a color is more than the number of its wavelength and a shape is more than its corresponding algebraic equation. As the human mind seeks correlations and systemic connections, a color or a shape functions differently, and is treated by the mind differently, than a number or an equation. It is in this seeking that scientific discoveries are made and insights gained.

Two scientists who were champions of mathematics — James Clerk Maxwell and Ludwig Boltzmann — nonetheless praised the intuitive and conceptual work of Michael Faraday. Faraday’s discoveries and descriptions of electromagnetic phenomena were shockingly free of mathematics, as historian Alan Hirschfeld writes:

Maxwell, the consummate mathematician, nonetheless understood the power of mathematics to mislead when not anchored in experiment or observation. In Faraday’s Researches, he encountered science in its purest form, “untainted” by mathematical manipulation. Here, he decided, would be the entry point for his own investigations into electricity and magnetism. In a later reflection, Maxwell sounds almost relieved that Faraday had stuck to his particular brand of investigation, thereby blazing a trail that Maxwell himself could follow.

Boltzmann explains one of Faraday’s many intuitive, i.e. non-mathematical, breakthroughs:

While the older system had held the centers of force to be the only realities, and the forces themselves to be mathematical conceptions, Faraday saw distinctly the continuous working of the forces from point to point in the intermediate space. The potential, which had hitherto been only a formula for lightening the work of calculation, was for him the bond really existing in space, the cause of the action of force.

Boltzmann uses the word ‘saw’ in the text above, emphasizing Faraday’s visual technique. Faraday’s work with magnetic fields was largely the work of observing patterns, e.g., the movement of iron filings. “By the light of his own clear conceptions,” Boltzmann writes, Faraday made “such great discoveries.” Boltzmann also explains Faraday’s effect on Maxwell:

Maxwell also, when he undertook the mathematical treatment of Faraday’s ideas, was from the very outset impelled by their influence into a new path.

Maxwell himself praises Faraday’s non-mathematical approach:

It was perhaps for the advantage of science that Faraday, though thoroughly conscious of the fundamental forms of space, time, and force, was not a professed mathematician. He was not tempted to enter into the many interesting researches in pure mathematics which his discoveries would have suggested if they had been exhibited in a mathematical form, and he did not feel called upon either to force his results into a shape acceptable to the mathematical taste of the time, or to express them in a form which mathematicians might attack. He was thus left at leisure to do his proper work, to coordinate his ideas with his facts, and to express them in natural, untechnical language.

Faraday was talented at drawing diagrams and sketches of magnetic fields and various configurations which were part of his experiments. The etymology of the word ‘intuition’ arises from verbs meaning to ‘see’ or to ‘look’ and Immanuel Kant chose the word ‘intuition’ — or rather, the German equivalent, Anschauung — which might prompt the reader to investigate any similarities between Kant’s thought and Faraday’s thought.

In any case, Faraday filled notebooks with drawings and illustrations, and it was in them and through them that he founded the modern science of electromagnetism and made his many significant discoveries: it was in and through the images and illustrations, not by means of equations and formulas.

Aside from Faraday’s visual method, there was a second feature of his thought which may have shaped his investigations and conclusions. His entire adult life was spent working in an organization known as the “Sandemanian” or “Glasite” church, as Alan Hirschfeld writes:

The Sandemanian church continued to hold a central place in Faraday’s life. He attended services and ritual feats, enjoyed the sense of community and, with rare exception, clung to its precepts.

The worldview of this faith shaped his exploration of electromagnetism. In the same way that a sort of spiritual humility caused Augustine to recognize the limits of human reason and caused Francis Bacon to formulate the sources of experimental error, so also Faraday was motivated to caution in his hypothesizing and to thoroughness in observation and experimentation.

Faraday understood the laws and principles of electromagnetism as being the products of God’s thought. He wrote: “for the book of nature, which we have to read is written by the finger of God.” Faraday understood lawlike phenomena, and nature’s laws, to be deliberately and rationally planned: “God has been pleased to work in his material creation by laws.”

There is a connection between Faraday’s intuitive approach to electromagnetism and his understanding of God. Verbs of sight were both metaphor and literally truth for Faraday in his investigations of electromagnetism: he was “looking” into God’s work and “saw” the rationality of it.