A Head In The Cloud: Tutorials, Mini-Tutorials, Micro-Tutorials, and Appreciations From the Blog of Robert Paul Wolff

By Robert Paul Wolff

When Robert Paul Wolff retired in 2008 after a fifty-year career as a university professor, he was somewhat at a loss as to what to do. One of his sons said, "Why don't you start a blog, Dad?" And so, like hundreds of millions of others around the world, he did. The Philosopher's Stone has been running now for more than four years, and Wolff has poured hundreds of thousands of words into the blogosphere. His eight hundred page Autobiography, A Life in the Academy, was originally written day by day for his blog and was posted as it was written. But if the truth be told, Wolff is a teacher more than a blogger, and early on he devised a new format, the "Tutorial," that would permit him to continue what he loves best, explaining difficult ideas in simple and engaging ways to students, colleagues, and readers. In this volume, Wolff has brought together many of these extended explications that he wrote for his blog.

Some of the essays are full-scale Tutorials that appeared in fifteen, twenty, or more daily segments. Among these are "The Thought of Karl Marx," "The Thought of Sigmund Freud," and "The Study of Society." Some of Wolff's expositions were concluded more quickly, and he labeled these Mini-Tutorials or Micro-Tutorials. And from time to time, Wolff simply shared his enthusiasm for a particular book in what he called an Appreciation.

A sampling of the titles of the essays in this volume give some sense of the breadth of Wolff's interests: Afro-American Studies, Erich Auerbach's Mimesis, Ideological Critique, Max Weber's The Protestant Ethic and the Spirit of Capitalism, and Kierkegaard's Philosophical Fragments, among others.

• Language: English
• Publisher: Society for Philosophy & Culture
• Release date: Aug 25, 2013
• ISBN: 9781301093519

Robert Paul Wolff

Robert Paul Wolff is is an American political philosopher and professor emeritus at the University of Massachusetts Amherst. Among his books are About Philosophy (1998), The Ideal of the University (1992), The Autonomy of Reason (1990), Kant's Theory of Mental Activity (1990), and Moneybags Must Be So Lucky (1988).

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Introduction

I launched my blog, The Philosopher’s Stone, on April 29, 2007, as a way of preparing for my imminent retirement. By 2010, I was blogging regularly, and in an extraordinary burst of activity in that year wrote and posted a long Autobiography, A Life in the Academy. When I finished writing the story of my life, there were still many things I wanted to say. As a teacher for more than fifty years, I loved explaining things, taking difficult ideas and clarifying them, bringing together materials drawn from widely separate fields of study. I conceived the idea of writing a series of multi-part explanatory essays that I called Tutorials. I imagined that somewhere in the blogosphere there would be a few hardy souls who would be willing to stay with me for weeks on end as I unfolded a complex intellectual story, and for the past three years, that is what I have been doing.

After writing several Tutorials ranging in length from 12,000 to 24,000 words, I turned to some topics on which I had markedly less to say, labelling my expositions as Mini-Tutorials to distinguish them from the substantial essays with which I had begun my teaching in the cloud. But there was still more I wanted to talk about, so I tried my hand at a number of brief essays about books I have especially enjoyed and from which have learned a great deal. I called these Appreciations, as a way of indicating that I was just recommending books I especially favoured.

In this final volume of my collected essays, I have brought together a selection of Tutorials, Mini-Tutorials, and Appreciations that first appeared on The Philosopher’s Stone.

Part One: Tutorials

The Critique of Pure Reason: Some Introductory Suggestions for Serious Study

Four Sources of the Difficulty of the Critique

Contrary to popular opinion, the Critique is actually written in a clear and accessible style, unlike some works written by Germans considered his philosophical heirs (hem, hem). But for four reasons, it is a very difficult book to master, and it might be useful for me to identify those reasons and say a few words about them.

First of all, the Critique is very much a work of professional philosophy, addressed to the relatively small world of serious students of the subject, and Kant uses the specialist vocabulary that was current in his day. In this respect, his work differs from that of Plato or Rousseau or even Hume, but is like that of Aristotle or Aquinas or Descartes. Contemporary readers would have found much of what Kant says familiar and comprehensible, but two hundred thirty years have passed since the First Edition burst upon the scene, and fashions change. So if we wish to engage with Kant’s thought, we must, in the immortal words of W.S. Gilbert, learn up all the germs of the transcendental terms.

The second problem is that Kant was a hypochondriac. Although he lived to be eighty (his dates are 1724-1804), Kant was beset by fears about his health. In the late 1770’s, when he was in his fifties and hard at work simultaneously on an extraordinary array of fundamental philosophical problems, he grew fearful that he would not live long enough to get it all on paper. So in 1780-81, he rushed to "bring the Critique to completion," using lengthy chapters and passages that he had in some cases written a decade earlier. The first part of the Critique, for example, usually referred to as The Aesthetic, contains entire segments taken word for word from the Inaugural Dissertation written in 1770 (more of that later), despite the fact that in the intervening time Kant had completely changed his position on almost all of the most basic questions of epistemology and metaphysics. The result is that the text of the First Edition (and also of the Second Edition) is replete with internal contradictions and incompatibilities. One must simply be aware of this fact in reading the text and make allowances for it.

The third problem in reading the Critique is The Architectonic. Kant was a compulsive, enormously imaginative systematiser, constantly thinking up elaborate schemata into which to fit the myriad of philosophical doctrines that he was unfolding. One can understand his need for these pigeonholes and hat racks, because he was attempting, simultaneously, to set out an integrated theory of just about everything: Epistemology, Metaphysics, Rational Theology, Logic, Mathematics, Ethics, Politics, Law, Art. The problem is that he was never satisfied with just one way of organising things – he had four or five, each of which he asserted with absolute confidence was the objective, necessary, indubitable, and only way of arranging his teachings. The Critique itself exhibits at least three different and incompatible principles of organisation. What is more, Kant was so pleased with his Architectonic that he trumpeted its supposed completeness as a proof of its correctness. Here he is in the preface in A:[1]

In this enquiry I have made completeness my chief aim, and I venture to assert that there is not a single metaphysical problem which has not been solved, or for the solution of which the key has not been supplied. Pure reason is, indeed, so perfect a unity that if its principle were insufficient for the solution of even a single one of all the questions to which it itself gives birth we should have no alternative but to reject the principle, since we should then no longer be able to place implicit reliance upon it in dealing with any one of the other questions. (Axiii)

Now, a place for everything and everything in its place is not much of an argument for the fundamental principles of all knowledge, but Kant really seems to have placed great store by this claim, and so we must note it, and then just move on.

Finally, we come to the fourth and most difficult problem in reading the Critique: the sheer depth and difficulty of his most important philosophical arguments, and their incompatibility with the more superficial premises of the Architectonic. Early in his development of what eventually came to be called The Critical Philosophy, Kant worked out in his mind a grand bargain between Science and Ethics that allowed a place for both Newtonian Physics and the absolutely universal, objective, necessary First Principle of morality, the Categorical Imperative. This bargain (if I may continue to speak in this manner) rested on certain theses about the nature of concepts and the limits of human knowledge, and also on a distinction, taken over from the ancient Greeks, between Appearance and Reality. Kant needed this bargain to demonstrate in the First Critique the cognitive validity of Euclidean Geometry (which was mathematics, to Kant) and Newtonian physics (which was science to just about everybody in those days), while also leaving room in the Groundwork of the Metaphysics of Morals and the Critique of Practical Reason for the demonstration of the validity of the principles of morality. Had Kant simply stuck to his original plan, and laid things out in accordance with this grand bargain, he would be remembered as one of the greatest philosophers ever to live. But in the course of writing the central portion of the First Critique, Kant saw and struggled with certain very deep problems with the central theses and concepts of his grand bargain. Like Jacob, who wrestled all night with the Angel of the Lord and would not let him go until he blessed him, Kant wrestled with these problems, and emerged with a new understanding of the nature of consciousness, reason, and knowledge that for all time totally transformed all of Western philosophy.

But Kant was not a young man, he was frantic to get his entire magnificent vision on paper, and it was too late for him to throw out the entire grand bargain and reconsider it from the ground up. So once he resurfaced after his plunge into the depths of the problems (one thinks of Gandalf the Grey emerging from his battle with the Balrog and transformed into Gandalf the White), Kant reverted to the comforting neatness of The Architectonic and went on writing as though the old premises and understandings were still in place, unquestioned.

This fact poses a fundamental problem for the interpreter of The Critical Philosophy. One can simply take Kant at his word, and trot along beside him, repeating contradictions as though they were compatible. Or, one can confront the profound reality of what is going on in the Critique and make a series of decisions about which parts of Kant’s philosophy to embrace and which to scuttle. No matter what choices one makes, one will be untrue to Kant in some way or other, and critics will have no trouble quoting chapter and verse to demonstrate that one has misread Kant. This is the problem I confronted fifty years ago when, as a young man, I strove to wrestle with the Critique and make it yield up its secrets to me. Other commentators have made different choices, driven by their different philosophical concerns and convictions. It is a testament to the greatness of Kant’s great work that it can sustain a number of incompatible strong readings, as the literary critics would put it.

The Philosophical Situation as Kant Saw It

It is essential, in approaching any great philosophical work, to begin with a reasonably clear picture of the philosophical state of play as it was understood by the author at the time he or she was writing. All philosophy is written in a context of argument and debate into which the author seeks to insert himself or herself. Questions may appear urgent or unavoidable to the author that strike us, many centuries later, as marginal or even incomprehensible. What makes a work of philosophy great is that it seizes on this debate and wrests from it an entirely new and revolutionary insight.

I begin with this banal observation because Kant’s conception of what was happening in late eighteenth century European philosophy is now widely thought to have been, in a number of respects, inaccurate or just wrong. But it was Kant’s understanding of the theoretical situation, and his grand plan for a Critical Philosophy, at least initially, was entirely informed and guided by that understanding.

Briefly, the story is that for almost two centuries, a great debate had been taking place between Rationalists and Empiricists about a wide range of great questions, including the existence of God, the nature of space, time, and causation, whether reason or sensibility is the source of human knowledge, and the scope, limits, even the very possibility of such knowledge. The debate was launched by Descartes’ Meditations on First Philosophy. The principal voices on the rationalist side of the debate were those of Descartes himself and Leibniz, together with such lesser figures as Christian Wolff, whose version of the rationalist position had a very great influence on Kant during his formative years. On the empiricist side the major figures were the great trio of British philosophers, Locke, Berkeley, and Hume (or as my old professor Henry Aiken used to like to refer to them, Locke, Stock, and Barrel). The rationalists claimed that the distinguishing mark of genuine knowledge is certainty, that the faculty of reason is the source of knowledge, that sense perception is a faulty source of knowledge, yielding inadequate or even contradictory beliefs, and that by the proper use of reason we can in fact know the existence and nature of God and the fundamental laws of the physical universe, as well as the truths of mathematics. The empiricists claimed that all knowledge derives from sense perception, reason merely being a tool for comparing and rearranging the ideas we derive from the senses, that sense perception cannot give us knowledge of God, indeed, that it may even be unable to give us certain and indubitable knowledge of the causal relations of objects in space and time. Because of the accident of their nationalities, the debate was thought of as taking place between Continental Rationalists and British Empiricists. When I was a lad, Philosophy Departments in the United States routinely offered courses on Continental Rationalism and British Empiricism, as though the disputes between the two groups of thinkers were political and territorial rather than philosophical.

A great deal of fine scholarly work in the past half century has called this picture thoroughly into question, but Kant accepted it pretty much lock, stock, and barrel (I could not resist). He referred to it as a contest between Dogmatism and Scepticism. His philosophical education at the provincial University of Konigsberg was grounded in Leibnizean rationalism, in the version advanced by Christian Wolff and taught to Kant by a Wolffian disciple, Martin Knutzen. Kant’s earliest published writings are forays into the debate very much from a Leibnizean point of view.

As a young philosopher, Kant conceived a rather neat and facile way of representing the state of the debate between the Dogmatists and the Sceptics. He conceived the dispute as having settled by the middle of the eighteenth century into what he called an Antinomy – that is to say, a debate in which each side is adept at refuting the claims of its opponents, but is unable to defend itself against its opponents’ refutations. The customary way to analyse an antinomy of this sort is to identify some unacknowledged premise on which both sides are basing their arguments, and, after bringing it to light, show it to be false, thus undermining the positions of both camps. Although by the time he published the Critique Kant had moved far beyond the terms of this debate, he never gave up his neat formulaic way of understanding the positions of his predecessors, and as readers already familiar with the text of the Critique are aware, there is a rich, complex one hundred page section of the work entitled The Antinomy of Pure Reason, in the course of which he puts to rest many of the old disputes.

Kant’s entire life was spent in the port city of Konigsberg (now Kaliningrad), on the shores of the Baltic Sea, in what was then Prussia. After an early stint as a tutor to the sons of a Prussian Junker (one would like to have been a fly on that wall!), he secured a position as a privatdozent, or authorised lecturer, at the University of Konigsberg. His early writings gained him sufficient recognition to lead to at least one offer of a Professorship (of poetry!!) at another university, but Kant chose to remain in his home town, and in 1770, he was appointed Professor of Logic and Metaphysics. The formal ceremonies of installation called for the candidate to present a public lecture in Latin, an Inaugural Dissertation, and Kant used the opportunity to lay before his audience a quite new doctrine designed to resolve the dispute between Rationalism and Empiricism. The Inaugural Dissertation of 1770, as it is always referred to, was the very first version of what would become, in the Critique, The Critical Philosophy.

The Inaugural Dissertation of 1770

Although a wide range of philosophical issues make an appearance in the Inaugural Dissertation, one principal focus of Kant’s attention is a half century old controversy about the nature of space. Leibniz and Isaac Newton, both of whom could lay claim to having invented the Calculus (there were giants in the earth in those days, as the Good Book says), took opposed positions on the question whether space is independent of the objects in it. Leibniz maintained that the only real things are unitary, immaterial substances, which he called monads. Space, he argued, is simply the totality of the external relations among the infinity of monads (among which, by the way, are human minds). Speaking mathematically, one can conceive of monads in Leibniz’s metaphysical system as dimensionless points, having only location. Each monad was thought by Leibniz to embody a certain quantum of force (living force, or, as Kant expressed it, "lebendige kraft"). Thus, the entire universe is a plenum of point sources of force or density or impenetrability. It follows from Leibniz’s account that there cannot be empty space, space entirely devoid of substances. Descartes, you will recall, argued that the defining characteristic of material substance is extension, which also implies the impossibility of a void (which is to say, extension devoid of material substance. Descartes invented what we call Cartesian Geometry in support of his view).

Newton took the opposed position, that space is prior to and independent of what fills it. He did not offer a philosophical account of the nature of space, as Leibniz had done, simply describing it somewhat obscurely as God’s sensorium. Newton’s position was dictated by what he considered requisite for his physical theories, and in one passage in the Principia, he famously said that he eschewed hypotheses, which is to say fruitless metaphysical speculations.

The debate between what came to be described as The Metaphysical Philosophy and the Physical Philosophy found public expression in a series of five brilliant epistolary exchanges in 1715 and 1716 between Leibniz himself and Samuel Clarke, a follower of Newton. The letters were published in both French and English and served as the best known contemporary statement of Leibniz’s views (the more important Monadology had not been published at the time).

The dispute can fairly be described as a stand-off. Leibniz’s elegant and carefully worked out metaphysics of monads was vastly superior to Newton’s offhand description of space as God’s sensorium (time, by the way, was pretty much a poor relation in the debate, although both authors treated it as formulaically on a par with space). But on one crucial point, Clarke clearly had the better of Leibniz. Leibniz had argued, against the Newtonian position of the absolute existence of space, that if God chose to create the universe three feet to the left of where it was currently positioned, or if He were to cause the entire universe of physical substances to accelerate, this fact would be totally unobservable by us, and hence be as nothing. But Clarke, relying on Newton’s laws of motion and their mathematical implications, replied quite correctly that an acceleration or deceleration would in fact produce observable effects within our world, and thus be real.

One final, very small, but elegant point. Leibniz argued that if Newton were right, then God could have chosen to create a mirror image of the universe. But since properties like to the left of and to the right of, or above and below, are simply relations of pre-existing monads, there could not be, as he put it, a sufficient reason for God to create the universe in one way rather than another, for an image and its mirror are identical in all the relations of their parts. In a paper written shortly before the Inaugural Dissertation, Kant refuted Leibniz, arguing that there are in nature many pairs of objects which are incongruous (cannot be made to overlap), even though they are identical in all of the relations of their parts. His most famous example is a left hand and a completely similar right hand, which cannot be made congruent (at least not in three dimensional space – in four dimensional space, one could flip a right hand glove through the fourth dimension and make it congruent with its left hand counterpart, just as in three dimensional space one can flip a triangle oriented one way to make it congruent with a mathematically similar triangle – all the sides and angles equal – oriented the other way).

In the Dissertation, Kant puts forward an ingenious theory that not only resolves the dispute between the Leibnizeans and the Newtonians, but also, at the same time, splits the difference between the rationalist claim that reason is the sole source of reliable knowledge and the empiricist counterclaim that sense perception is the foundation of human knowledge. Viewed in retrospect from the perspective of Kant’s fully developed epistemological theories in the First Critique, we can see the position of the Dissertation as a half-way house on Kant’s epic journey from the Wolffian metaphysics of his youth to the revolutionary teaching of the Critical Philosophy. Not for nothing is the doctrine of the Dissertation referred to by Kant scholars as Semi-Critical. It is useful for us to approach the full-blown teaching of the Critique by way of the doctrines of the Dissertation because this will enable us to pinpoint just exactly what the problem was that forced Kant to move beyond the comfortable middle position achieved in the Dissertation.

And now, a word about terminology. There was in Kant’s day a familiar and non-controversial pair of distinctions between the ways in which the mind can stand in relation to an object. These are distinctions with a long and distinguished pedigree, traceable back at least to the disputations of the scholastic philosophers of the twelfth and thirteenth centuries. The mind can stand in immediate relation to an object, or in a mediate or indirect relation to an object. And this relation can be passive or active.

When I perceive an object with my senses – when I see it, hear it, smell it, taste it, or feel it – my mind (these folks all agreed) is in direct or immediate relation to a single individual thing. I see this horse, I feel this tree with my hand, I hear that piano. Furthermore, the mind’s relation to the object is passive, not active. It does not create the object. It waits upon the object to affect the senses, in whatever manner that occurs. When God brings an object into existence by creating it, His relation to it also is immediate and direct, but in His case the relation is active, not passive. The object does not affect Him. He creates it.

The immediate relation of the mind to an object was called intuition. In the case of human beings, this intuition is sensuous and passive. Thus, sense perception is passive or sensuous intuition. In the case of God (and no one else), His intuition is intellectual, or active, or creative. If one wishes, one can put this last point in the subjunctive without altering the meanings of the terms: If there were a god, his intuition would be intellectual.

When the mind apprehends an object by means of concepts, its relation to the object is indirect, mediate. It is mediated by a general or universal notion, under which it subsumes the individual that the mind is apprehending. So, I invoke the general concept horse, which of course applies to many objects, and subsume my perception of an object before me under that general concept, as when I form the judgment, This is a horse. Conception is always active, not passive, but it is not always creative. When I form a general concept of a house, and then act so as to build the house – when, in short, I make my concept actual, or actualise it – then my conception is both active and creative. But when I bring concepts to bear on my perceptions and form judgments of the type or kind or species of thing I am perceiving, my conception, while still active, is not creative.[2]

And so we come to the Dissertation, whose full title is On the Form and Principles of the Sensible and Intelligible World. As the title suggests, Kant sets up his discourse as an Antinomy, a dispute between the Dogmatists and the Sceptics, the Rationalists and the Empiricists, the Leibnizeans and the Newtonians. He is going to try to show that this seemingly irresoluble dispute can be dissolved in such a way that the positive claims of each side are secured, and the attacks of each side on the other evaporate.

Just to anticipate where all this is going, so that you do not get lost in the details of the arguments, Kant is going to go through a four stage process in evolving from the Dissertation doctrine to the full-blown Critical position that emerges in the Critique. First, he presents in the Dissertation what he hopes is a balanced compromise between Leibniz and Newton. Then, almost immediately after delivering his inaugural lecture, he recognises that his defence of the Leibnizean or Metaphysical side is deeply flawed, and he gives it up, embracing instead a radically new position very heavily weighted toward the Empiricist camp. Third, before he can even put this new position in writing, he re-encounters the deeply sceptical arguments of David Hume, arguments that cast doubt even on the Empiricist position to which he has retreated. This encounter, which as he says in a famous line awakened me from my dogmatic slumbers, drives him to undertake almost a decade of profound, revolutionary philosophical reasoning that results, in 1781, in the formulation and presentation of the entirely new Critical doctrine of the Critique of Pure Reason.

The problem, as Kant sees it, lies in forming an adequate representation of a world, which is to say a totality of interacting substances (at this point Kant has in mind Leibnizean monads – he is still very much writing in the philosophical tradition in which he was educated). The term representation, or vorstellung, is Kant’s most general term for a cognitively significant content of consciousness. It thus plays somewhat the same role in his writings that idea plays in Locke’s Essay or that perception plays in Hume’s Treatise.[3] There is, he thinks (or so he says), no problem in forming an intellectual representation of a totality or world of substances, which is all that is needed to get Leibnizean metaphysics going. But it seems to be impossible to form an adequate sensible representation of such a world, of the sort required by Newtonian Physics.

The source of this difficulty is that space (and time, but Kant is concerned here with space) is infinitely divisible into ever smaller regions, each containing some degree of force or substance. To form an adequate representation would require going through the process of division step by step, and as there would be an infinite number of such steps – each one a further division of some region of space – the process would take an infinitude of time and be impossible to complete. Thus, the Leibnizeans always have an unanswerable objection against the Newtonians, namely that the latter are unable to formulate a useable conception of their object of study. The Newtonians in their turn respond that the Leibnizeans cannot provide the content that their intellectual representations require if they are to yield genuine knowledge.[4]

To resolve this problem, Kant revives and deploys for his own purposes the ancient distinction between appearance and reality. Leibnizean metaphysics, he says, gives us an adequate intellectual representation of the world as it is in itself, of reality. Newtonian physics, in contrast, provides us with knowledge of that world of monads as they appear to us in sensibility (i.e., through sense perception), hence of appearances. The spatio-temporal organisation of material things is not a characteristic of them as they are, objectively and independently of us. Rather, the mind itself imposes on things a certain spatio-temporal form or organisation when it is affected by them and forms sense perceptions of them. This spatio-temporal form of sensibility – or form of sensible intuition – lies ready in the mind, prior to all experience. It is not abstracted from experience, as Hume and others thought, but instead exists in the mind a priori.

It is time to pause again for some terminological clarifications. As surely all of you know, the terms a priori and a posteriori appear again and again in Kant’s mature writings, along with two other terms, analytic and synthetic. Indeed, the bastard phrase "synthetic a priori" might be considered his ham operator call sign. But as is so often the case, even those who should know better misuse these terms in confusing ways.

A priori and a posteriori are adverbs, and they modify verbs – usually, the verb to know, but also, as in the last sentence two paragraphs ago, the verb to exist. As Kant uses them, they mean roughly prior to, or independently of, experience and posterior to, or dependent on, experience. A proper Kantian use of the terms would be, for example, "We know the truth of the Causal Maxim a priori, but we only know the truth of particular judgments about the characteristics of the material world a posteriori."

Analytic and synthetic are adjectives. They modify nouns, principally the nouns judgment and proposition. A proposition is said to be analytic if (to put it as simply as possible) the concept of the predicate does not add anything to the concept of the subject. It is said to be synthetic if it does add something not contained in the subject concept. Thus Triangles have three angles is analytic because having three angles is contained in the concept of being a triangle. Horses are used as beasts of burden is synthetic. And so forth. Analytic propositions are also called tautologies, or sometimes miserable tautologies (logicians can be very judgmental).

Everyone (in Kant’s day – never mind about now) thought it was obvious that the truth of an analytic proposition can be known a priori, since all one need do is unpack what is contained in the subject concept of the proposition, without reference to any experience. So one would say that analytic propositions are knowable a priori. Sometimes, for compactness, the knowable was elided, and one simply says that analytic propositions are a priori, but in that statement, a priori is not being used as an adjective. It is still an adverb, modifying the missing verb to know. Until Kant came along, it was widely taken as obvious that synthetic propositions are only knowable a posteriori, that is by appeal to observation or experience. So one might say, compactly, that synthetic propositions are (knowable) a posteriori. But it is never correct to say that there are synthetic a posteriori propositions, as though that were some classification of types of propositions. Kant himself never writes that way, although that fact is obscured by the translations. He always writes "synthetische urteile a priori, not synthetische a priori urteile."

At this point, I must talk for a bit about Euclidean Geometry. When I was a boy, we actually studied Euclid’s Elements in High School geometry class. Euclid was the gold standard for math in Kant’s day, and everyone was fully conversant with the definitions, axioms, postulates, and theorems in Euclid’s Elements.

The dream of Leibniz, and of a great many famous philosophers and logicians since, was to derive all of mathematics from logic, thereby demonstrating that the propositions of mathematics, like those of logic, can be known with absolute certainty a priori. Kant was convinced that this was in fact false – that mathematical propositions make assertions that go beyond what is contained in the definitions of the terms with which they are expressed. Thus, he believed, mathematical propositions are synthetic, not analytic. But he was also sure that we know the truth of mathematical propositions a priori, not a posteriori (as Hume actually thought, by the way, although that has nothing to do with this discussion). This posed a real puzzle for Kant. How could there be propositions that, although synthetic, could be known with certainty, a priori? (The famous Kantian conundrum inaccurately described as the problem of synthetic a priori propositions.)

Why did Kant think that Euclidean Geometry is not analytically deducible from the definitions, axioms, and postulates? Well, take an actual look at the theorems in Euclid’s Elements, or at any modern version of the same material. Each Theorem asserts some proposition, about lines or angles or triangles or circles, and somewhere in the proof, usually near the beginning, there is a construction. Euclid will tell us, for example, to describe a circle about a point (one of the axioms says we can do that). Then we are to select a point outside the circle, and connect it by a straight line to the point that serves as the centre of the circle. (Another axiom says we can always connect two points by a straight line.) Now, we are told, where the line thus produced intersects with the circle, label that point A.

How do we know that the line intersects the circle? Just look at it! The centre of the circle is a point inside the circle, and the point selected is, by construction, outside the circle. Of course a line connecting the two points must cross the circle somewhere. And there you have it. Nothing in the definitions, axioms, and theorems laid down at the beginning of the Elements implies that such a line must intersect the circle, but it is immediately and indubitably obvious that it must. Mind you, this is not a well-established empirical generalisation, grounded in endless thousands of attempts to connect points outside circles with centres of those circles. It is immediately apparent to the mind by construction, whether one actually draws such a circle and line or merely considers it in one’s mind.

Kant realised that some very powerful explanation was required for this familiar and often overlooked fact about Geometry. His solution was that space itself is not an independently existing container of things – an unding or non-thing, as he rather dismissively characterised Newton’s account – but rather is the form of our sensuous perception of things, a form lying ready in the mind that is imposed by the mind on its perceptual experience. When we do Geometry, we are simply spelling out the innate mind-dependent spatial structure of that form of intuition.

A few hasty clarifications for modern readers. First, Kant says little or nothing about algebra, or even about arithmetic. You might think that the mind-dependent perceptual form – time – bears the same relationship to algebra that space does to geometry, but Kant does not go that way. Second, anyone living today will immediately ask, How do we know that everyone has the same innate forms of intuition? Could they evolve over time? Could they be culturally dependent? These questions seem never to have occurred to Kant, or to his contemporaries, although a century later they would have occurred to everybody.

So the metaphysics of monads is certain, and knowable a priori, and true of things as they are in themselves – including substances, God, and all that good stuff. Newtonian physics is not true of things as they are in themselves. It and the geometry on which it is based are true only of things as they appear to the human mind in the space and time that the mind imposes upon its experiences. Could there be other rational beings with different forms of intuition? Yes, though Kant is not really interested in that possibility (space travel was a long time in the future).

Now, we may imagine some thoughtful reader of the Dissertation asking: I can see how we can know the truths of mathematics a priori inasmuch as they merely spell out the mind-dependent spatial form imposed by the mind on its perceptual experience, but how can I know the truths of metaphysics a priori, considering that they are asserted unconditionally and universally of things as they are in themselves?

Almost immediately after delivering the Dissertation (and getting tenure – a rare commodity in those days), Kant realised that he had no answer at all to this pressing question. How indeed is it possible to have knowledge a priori of the independently real? Kant concluded that it was in fact impossible, and that he would therefore have to give up for all time the ancient search for metaphysical knowledge. So much for Rational Theology, which had for two thousand years and more been the Queen of the Philosophical Disciplines, and for Leibnizean metaphysics besides.

This was, as by now should be clear, a huge decision on Kant’s part, a dramatic tilt in the direction of the position of the Empiricists, the Sceptics. Kant announced this break with the philosophical tradition in which he had been raised in a letter to his friend Marcus Herz, who had occupied the ceremonial position of Respondent to Kant’s Inaugural lecture. Kant promised Herz that very shortly he would publish a book entitled A Critique of Reason, in which he would present his new position to the world. But then, Kant was struck by a thunderbolt that transformed his life, his thought, and our entire philosophical tradition.

It came about like this. An irritating little man named James Beattie published in England an attack on people he considered rank heretics and sceptics – among whom he included David Hume. The book, called An Essay on the Nature and Immutability of the Truth, was a series of refutations of such famous sceptics as Descartes, Locke, and Hume, and it appeared in 1770. It consisted of arguments roughly like this: "x says that y. But common sense tells us that not-y. So x is wrong." Naturally, it was a smash success, and went through annual editions in 1770, 71, 72, 73, 74, and 75. But, God bless Beattie, he included in his book lengthy extracts from the sceptics he thought he was eviscerating. Hume, who cared very deeply for his own literary reputation, and who was by now actually quite famous as the author of a six volume History of England, was stung by Beattie’s contemptuous dismissal of his anonymous, juvenile work, A Treatise of Human Nature. In a new edition of his essays brought out in ‘72, Hume disavowed the Treatise as a work of youth and took umbrage at Beattie’s extensive quotations from it. Beattie replied rather grandly by removing from the ‘73 edition and all subsequent ones the passages from the Treatise that he had included in the original edition, including passages in which Hume stated his devastating critique of causal judgments.

Kant could not really read English, but a translation of Beattie’s work appeared in German in 1772, and thanks to the goodness of the gods (whose existence Kant had given up any hope of proving), the translator used Beattie’s 1st edition, with the passages from Hume intact. Kant read the translation, and being of course light years smarter than Beattie or anyone else then alive save Hume, immediately recognised that Hume’s arguments constituted a mortal threat to the new position he had just then taken up as a necessary retreat from metaphysics. Hume’s arguments called into question even the knowability a priori (or indeed any other way) of Newtonian physics, which Kant thought he had made safe by restricting it to the realm of things as they appear to us in space and time. Clearly, a much, much deeper and more elaborate defence of science was required. Kant set aside his plans for the immediate release of a Critique of Reason and embarked upon the labours that resulted, nine years later, in the Critique of Pure Reason and the rest of the Critical Philosophy.

What is really important is the challenge presented to Kant by Hume’s sceptical critique of the sorts of causal judgments that appear in Newtonian Physics. Hume’s argument is quite simple – deceptively so – and easy to state. It can be summarised like this: The object or event we identify as a cause is distinct and distinguishable from the object or event we identify as its effect. Since the cause and the effect are thus distinguishable, it is possible to imagine one occurring without the other, our imagination having the power to separate distinguishable ideas from one another and call them to mind separately. But if we can imagine the one without the other, then we can have no ground for saying that one necessitates the other, which is what is meant by saying that one is the cause of the other. (By contrast, it is beyond the powers of our imagination, or of any imagination, to call to mind the idea of a bachelor who is married, or of a triangle with four interior angles.) Hence, causal judgments, involving as they do an assertion of necessity of connection between cause and effect, are never warranted by reason.

This argument appears in section iii of part three of the first book of the Treatise, Why a cause is always necessary.

We can never demonstrate the necessity of a cause to every new existence, or new modification of existence, without shewing at the same time the impossibility there is, that any thing can ever begin to exist without some productive principle; and where the latter proposition cannot be prov’d, we must despair of ever being able to prove the former. Now that the latter proposition is utterly incapable of a demonstrative proof we may satisfy ourselves by considering, that as all distinct ideas are separable from each other, and as the ideas of cause and effect are evidently distinct, ‘twill be easy for us to conceive