C. Ellsworth Hood

What is the thinking out of which scientific innovation arises? This paper is not so much an essay on or about Kant's philosophy, whether critical, interpretive or expository, as it is a thinking with Kant in an effort to elucidate what such thinking is.

There exists a record of conversations Albert Einstein had in 1922 with several French philosophers. This record reveals the he did not presume to be able to answer our question. It, among other sources, also reveals that he had though about it and that Kant was one of his thinking companions. I propose that we begin by thinking with Kant and Einstein. In the conversations referred to, Einstein was asked about the relation between Kant's view and his own. He answered, in part, "In regard to Kant's philosophy, I believe that every philosopher has his own Kant...," a qualification which serves as a word of caution to each of us who works with Kant's philosophy. Of particular relevance to us is what he said a bit later.


Arbitrary concepts are necessary in order to construct science; as to whether these concepts are given a priori or are arbitrary conventions, I can say nothing. Endnote

I would suggest that the either/or is perhaps not exhaustive of the possible modes of thinking out of which scientific concepts, particularly innovative scientific concepts, arise.

Einstein at other times himself said things which will serve well to carry us forward in our thinking. A scientist, he said,


must appear to the systematic epistemologist as a type of unscrupulous opportunist: he appears as a realist in so far as he seeks to describe a world independent of the acts of perception, an idealist in so far as he looks upon the concepts and theories as the free inventions of the human spirit (not logically derivable from what is empirically given); as a positivist in so far as he considers his concepts and theories justified only to the extent to which they furnish a logical representation of relations among sensory experiences. He may even appear as a Platonist or Pythagorean in so far as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research. Endnote

The realist element of Einstein's scientist appears to be contradictory to Kant's insistence that "reason has insight only into that which it creates in accordance with its own plan." Endnote The issue would turn on whether Einstein intends by realism to point to the domain of possible experience part of which is constituted by our rational processes, including our perceptual capabilities, or to a reality totally independent of our knowing processes. If the latter, his scientist does claim knowledge which Kant declares to be impossible.

The idealist element in Einstein's scientist is less problematic. That the basic ideas, concepts and theories cannot be derived from experience is surely common ground with Kant. Whether free invention can be sustained is a further question. The positivist element is quite easy to assimilate into Kant's view of science, at least in its applied dimension. The element that Einstein refers to as Platonist or Pythagorean can readily be seen in Kant's repeated insistence that reason demands an architectonic approach, completeness, the unconditioned ground, system, unity. the scrupulously systematic epistemologist Kant would find Einstein's scientist not so much an unscrupulous opportunist as insufficiently rigorous in his or her thinking.

What is that thinking? From this list of characteristics I would say that it has, in Kantian language, something of theoretical reason, logical explication of experience, mathematics, something of aesthetic judgment, of art, the beautiful and the sublime, and something of metaphysics, of ideas too reich in content to be reducible to either empirical or pure intuition.

Kant and Einstein agree that the theoretical/mathematical/empirical component is necessary to scientific thinking. They also agree that this component is not the innovative thinking we are looking for. In his autobiographical note in Schilpp's Albert Einstein: Philosopher-Scientist, Einstein says, "Invention is not the product of logical thought, even though the final product is tied to a logical structure." Endnote It seems to me this accords with Kant's view of the matter. He says that "in every special doctrine of nature only so much science proper can be found as there is mathematics in it." Endnote Kant is applying to natural science his view that reason has insight only into that which it has created in advance but here the stress lies, as with Einstein, on explication, development, final product. For Kant the rhapsody of experience becomes science just in so far as it is brought into a unity of a system. Endnote Eventually this means it is given mathematical expression because this range of our experience becomes comprehensible to us only to the extent to which we can appropriate it through the categories of the understanding. The schematisms of the categories present, so to speak, space/time pictures of the categories to be brought to a unity in apprehension. Expressed differently, the way we synthesize intuitions (pure and eventually empirical) is by measuring space-time to produce spaces and times. This measuring is mathematics. It is this entire process which leads to Kant's saying in this connection that reason finds only what it creates and that there is only so much science as there is mathematics. But none of this has anything to do with scientific innovation or creativeness. It has to do with systematic expression and explication. What we have here does, however, give a Kantian account of the positivistic and Pythagorean elements in Einstein's scientist. The Pythagorean element is evident in that the logical structure is given mathematical expression. The positivist element appears in the necessary role of empirical intuition in scientific knowing. The mathematical logic shows what could be the case; experience alone shows what is the case.

Another aspect of Einstein's scientist is made evident by a different feature of Kant's stress on system. He makes the, when reflected upon, rather startling pronouncement that "no one attempts to establish a science unless he has an idea upon which to base it." Endnote this idea determines " a priori not only the scope of the manifold content but also the positions which the parts occupy relative to one another." Endnote Whence such ideas, ideas whose role is to bring the range of data to the coherent relation we find in system? The language is strong. The idea determines not only the range of data but the relationships of the contents as well. It clearly is a controlling idea. Whence such ideas? Einstein's either/or, a priori or arbitrary convention, returns to haunt us as does the idealist--and probably Platonist--element of his scientist.

Kant is quite aware dass wir im Dunkeln herumtappen a good deal of the time and that often it is in the context of this groping about that we come up with an idea which establishes a science, an idea capable of integrating the complex of data into a unified whole. But this only indicates the accidental circumstances in which such ideas are formulated: it does not tell us what the thinking is which produces them or whether we have haeres the thinking which produces innovation in science. We are, however, hot on the trail, a trail which leads into difficult terrain. We shall have to look into the metaphysical foundations of science.

There really are two questions involved here and we need to separate them. One is the question: Whence the ideas which give logic to the sciences? The other is: Whence the ideas which produce innovation in science? The answer to the second question provides the answer to the first when to the new idea, the new determination of scope and delineation of relation of content, is added the appropriation of experimental fact through the mathematical exposition which we have already considered. Once the idea is present, then we can go to work spelling out its logic, delineating the parts, exploring the relations--which we do by translating the idea into mathematical expressions and checking our mathematical constructions over against experience. Here, in Kant's language, we "approach nature to be taught by it, not, however, with the attitude of a pupil but of a judge who compels witnesses to answer the questions he has formulated." Endnote Our question is what is this thinking in which these questions are formulated. Again, a priori, arbitrary convention or what?

Let us take our cue as to how to proceed from Kant's refusal to admit Newton among the ranks of those of genius. While Newton may be a great head, Kant says, he refuses him the status of genius because


we can readily learn all that Newton has set forth in his immortal work on The Principles of Natural Philosophy, however great a head was required to discover it.... The reason is that Newton could make all his steps, from the first elements of geometry to his own great and profound discoveries, intuitively plain and definite as regards consequences..... But a Homer or a Wieland cannot show how his ideas, so rich in fancy and yet so full of thought, come together in his head...." Endnote

I am not so sure but what Kant sold Newton short here, but his distinction between a great head and a genius is clearly relevant to our discussion. Newton is denied the status of genius because all that he says can be brought finally into the purview of the understanding. There is nothing in it, Kant's view, which in any necessary way evades the categories. The whole scheme can be brought to pure intuitive construction and checked against empirical intuition as well. It is a grand triumph, a grand synthesis, a marvelous idea which structures an entire science, determining its limits and delineating the relations of the contents and is amenable to mathematical expression throughout. Lots of work, but without genius, for genius is the ability to bring forth ideas too rich in thought to be reduced to concepts and to be able to express these ideas in works of art. But since the aesthetic idea is not reducible to concept, there are no rules and precepts which can be given. An artist can only "excite like ideas in his pupils if nature has endowed them with a like proportion of mental powers." Endnote It seems to me that once Newton's idea was formulated, the science it structured was amenable to reduction to concept and any great head, and many a lesser one as well, could work out the logic. The grasping and shaping of the original idea seems to be another matter. Even if everything in the idea is reducible to the understanding, is the idea itself so reducible and particularly is the original thinking of it so reducible? Was the idea exhausted in its thought content by the conceptual structure which resulted or was this all of that idea which translated into the conceptual, eventually mathematically expressible, system? To the extent that Newton's grand idea does not contain more thought than can be reduced to concept, to the extend that it does not excite more thought than can be so assimilated and expressed by others, Newton is merely a great head. My question is whether the original thinking did not transcend this limit. If it did, aesthetics enters at the very heart of science.

When we turn to Kant's discussion of the sublime, which too enters when one considers the thinking out of which scientific innovation arises, the aesthetic element enters in a least two points. One point is perhaps surprising. The primary unit by which we measure, and therefore the basic mathematical unit, is itself found to be an intuition which appears to be arbitrary. In a sense it is so. But in another sense that very character as arbitrary indicates where to look for innovative scientific thinking. It may come as a surprise that the logical structure which gives science its tremendous precision should have intrinsic to itself an arbitrariness, that the way theoretical concepts and their relationships and empirical concepts and their relationships are made clear, definite and exact should contain arbitrary intuition on our part but so it does, Kant argues. It is an arbitrariness which, however, in no way threatens the logic of quantity itself. "The estimation of magnitude by means of concepts of number (or their signs in algebra) is mathematical, but that performed by mere {bloss} intuition (by the measurement of the eye) is aesthetical." Endnote Kant's question is which sort of measuring is involved in the measuring which produces the fundamental unit of measure applied in our mathematical reasoning. How great something is is a function of how many units it encompasses. "But since the magnitude of the measure must then be assumed known and this again is only to be estimated mathematically by means of numbers...we can never have a first or fundamental measure and can therefore never have a definite concept of a given magnitude." Endnote Kant, a few pages later, develops the theme in the opposite direction. We can take a man as measuring unit for a tree, the tree for a mountain, the mountain for the earth's diameter and that for the planetary system and so on indefinitely. Endnote There is, neither in pure nor in empirical intuition, neither in our logic of measure itself nor in any empirically given reality, either a smallest or a largest unit. That there is neither empirically should cause no surprise. Kant has worked out the reasons for this state of affairs in the antinomies of pure reason. That there is none in the pure logic of measure is his point here. We appropriate measure originally by a measurement which is "in the end aesthetical." Endnote We adopt, by the eye, so to speak, a unit and from there we set out to measure the universe. What we take as a unit of measure seems arbitrary. Scientific thinking eventuates in a rigorously precisely measure universe, this is true, but that rigorous measuring itself is, in part, aesthetic. Our definite and precisely measured universe rests upon no "definite concept of a given magnitude." Endnote that this is so in no way undermines the exactness, precision,logical unity or validity of mathematics or science. What it does is make clear that the measuring of measure is an act of judgment. This is, in part, why Kant calls it aesthetic: no precept or rule can be given. We adopt as unit of measure what suits the measuring we are setting out to accomplish rather like the way the artist adopts a "logic" to present his or her idea in empirical form. Once adopted, a rigorous relationship is entailed.

That the measuring of measure is a direct intuition ( I here gloss the whole difficult relation between intuition and judgment in this connection) shows the power of reason to measure which in turn is a hint as to where to look for the thinking which produces innovation in science. We are moving in on Einstein's either/or, either a priori or arbitrary convention, and can begin to discern that perhaps what looks arbitrary is a certain kind of a priori judgment.

Further analysis of the sublime will assist us here. Kant says that a basic difference between a theoretical idea or concept which eventuates in science and an aesthetic idea which eventuates in beautiful art is that the aesthetic idea contains more thought than can be reduced to or expressed in concepts. That thought-rich content can, however, be grasped in aesthetic intuition and then rendered in art. The sublime presents content too rich in thought to be captured in intuition. What have we here? Kant introduces terminology to assist in discussion of this topic. Aesthetical ideas, he says, are inexponible representations of the imagination. They are too rich in thought to be captured in concept, hence are beyond the reach of what can be expounded for to expound is to render in concept. The power to produce such ideas is genius. There are also rational ideas which are indemonstrable representations of reason. They are too rich in thought to be captured in intuition. Endnote Kant develops his view by differentiating the mathematically great and impressive from what transcends all imagination. We can increase our comprehension of size by increasing our unit and thereby bringing whatever we are explicating to intuitive clarity but eventually we reach a limit along this path. We can continue to make the measured intelligible to ourselves by adding unit to unit even when we cannot grasp the totality as unity in apprehension. Yet even this does not satisfy the idea of reason and cannot do so because the idea demands precisely this completeness of unity. Once again there is here an echo of the first and second antinomies of pure reason. The rational idea Kant employs in his discussion is that of the infinite. We can neither capture this in intuition nor reduce it to concept, but we can think it. This alerts us to the real power of our minds. "The bare capability of thinking the infinite without contradiction requires in the human mind a faculty itself supersensible," Endnote is how Kant expresses it.

What kind of thinking is this? Is it a priori? Is it arbitrary convention? Or what? Is there something here analogous to what we encountered in our discussion of the fundamental unit of measure? Is there a thinking here which is a priori as independent of experience and yet is not merely arbitrary but appears so because it is not demonstrable? Is the apparent arbitrariness rooted in its being an a priori, original thinking which grasps and shapes something of the, in Kant's terms, supersensible, intelligible substrate and which as such forms a first foundation of the sort of ideas of specific interest to us, ideas which eventuate in innovation in science? I believe it. We quite obviously have taken a step into what Kant calls the metaphysical foundations of science. The foundation of science and of innovation in science is in judgments analogous to those in art; judgments, original thoughts, so rich in though that they are not only not reducible to concept but are not reducible to intuition either. Yet they are not arbitrary. They are thinkings which are appropriate to convey something of what is--and it is at this late stage that the realist element in Einstein's scientist reappears in a new light. It is a new light because while these ideas are appropriate to convey something of what is, they do not give us knowledge of reality itself. Nevertheless our scientific knowledge is founded upon such ideas. Their ability to help us organize our experiences of reality makes possible our scientific knowing because they determine the domain and regulate the relationships of the relevant contents of that knowing. They provide the logos, the logic, which guides the entire constructive process of scientific knowing. Scientific innovation arises when a new idea provides a new logic.

At a number of points Kant brings into his discussion ideas the thinking of which, he argues, necessitates in the human mind a faculty which is supersensible. These ideas reveal the supersensible character of our thinking in that in them we reach into the supersensible and bring over into our range of experience what we there grasp. What is brought over appears in the manner in which it has been grasped by our ideas. Kant indicates in various ways and various discussions that aesthetic and moral ideas reveal the supersensible in us and place us in rapport with the supersnesible. Does the thinking which eventuates in scientific innovation do likewise? Each sort of idea--Kant is discussing aesthetic and rational ideas as distinct from concepts of the understanding--has to have principles of employment in our reason, some way in which these ideas too rich in thought to be reduced to concept can be appropriated by us. Endnote

In art the idea is taken up in aesthetic fashion according to that mode of employment of reason. It is given presentation in aesthetic intuition and, assuming sufficient skill, results in a work of art. The thinking of the idea Kant assigns to genius, the ability of the supersensible in us to fashion ideas which transcend all possible experience. Does not that thinking also have within it something of the metaphysical? Is there not in the original idea a thinking of what is, a grasping of reality which is presented symbolically: I have here introduced the term symbol in a way not used by Kant. His discussion of the symbolic does, it seems to me, make such a use legitimate. Symbolic expression is how we appropriate ideas "Thinkable by reason but to which no sensible intuition can be adequate." Endnote The symbolic expression is an intuition supplied by a procedure analogous to schematism, "that is, merely analogous to the rule of this procedure, not to the intuition itself." Endnote What is this procedure analogous to schematism? Is it not reason formulating a coherent order for itself into which it integrates the content of the thinking, whether that content be aesthetic, moral, metaphysical or even empirical? The thinking of the idea becomes aesthetical when the procedure analogous to schematism is a producing of coherent order which combines thought too rich to be reduced to concept in an intuition which as coherent order symbolizes the idea of what is in a work of art. the aesthetic genius os one who can so synthesize. The successful artist is one who can then produce the work.

In morality the idea is taken up in practical employment of reason and is given presentation in human life and conduct. Since Kant explicitly develops the metaphysical foundations of morality and argues that beauty is a symbol of the moral because it awakens awareness of the intelligible and specifically of freedom, it seems unnecessary to say more ont his subject here. Objective moral behavior is coherent symbolization of the supersensible idea of freedom.

What about the thinking which results in innovation in science? That it contains something of the metaphysical in Kant's view seems not to need justification. His Metaphysical Foundations of Natural Science provides ample evidence by itself. But what is the thinking which produces the ideas at the basis of science? And, does that thinking contain an aesthetic dimension as the aesthetic contains something of the metaphysical? It seems to me that here too we begin with our supersensible faculty, to use Kant's term, and reach into the supersensible by our idea of reason. Then we move toward appropriation of the content of that idea but this time the principle of employment is headed toward the theoretical. Before we reach that employment, however, we pass through both metaphysical and na aesthetic dimension. As with the move to aesthetic expression, there is a symbolic intuition, produced by that "procedure analogous to schematism." which contains something of the metaphysical and something of the aesthetic. It is metaphysical in that it is a presentation of what is, produced by the procedure of formulating a coherent order and integrating the content in terms of that order. The aesthetic element is in the freedom with which this coherent order and integrating the content in terms of that order. The aesthetic element is in the freedom with which this coherent order is formulated. We have, in a way, imagined a world to be, though thought it into being is probably a better way to say it. Now come into operation the principles of employment of theoretical reason. This imagined world is here not produce as art but is schematized, mathematized and eventually guides experiment. It is here that we learn of nature not as pupils but a judges who compel witnesses to answer questions we have formulated. We know how to formulate these questions because they arise out of our idea as formulated, symbolically, by the coherent order we produce by that procedure analogous to schematism.

We can now see that Newton probably ought to be included among the ranks of those of genius. His grand synthesis from the first elements of geometry to the workings of applied mechanics can be made intuitively plain and definite, as Kant says. His thinking that the world is of this order seems to me to be both metaphysics and aesthetics, as I have delineated their roles above, and that the original idea out of which these attributes arise is itself a manifestation of the supersensible faculty thinking that which is too rich to be reduced to intuition or concept, that it is genius, if you will. It became reduced to intuition and concept when adapted to the principles of the employment of theoretical reason.

What, then, is this thinking out of which scientific innovation arises? Are the concepts which delimit a science, establish its range and regulate its order a priori or arbitrary convention, to refer again to the options cited by Einstein in 1922? Or have they some other possible origin, as Einstein's scientist as unscrupulous opportunist would suggest? What has been argued here is that the originative ideas which produce the logic of science function as regulative ideas, to use Kant's terminology. Their origin is in genius, the supersensible faculty of human reason to think more than can be captured in either intuition or concept.Their employment entails both metaphysics and aesthetics for, whether issuing in art or science--or morality, for that matter--the employment entails the formulation of a coherent order of possible reality by a process of judgment analogous to schematism. It thinks a world ordered by the logos, logic, of the idea of reason. It is metaphysical in that this coherence is a regulative idea produced by reason itself and applied a priori to experience; it is aesthetic because it is freely organized coherence which gives to the idea a mode of presentation produced by a procedure of judgment analogous to the procedure of schematism. From here on the principles specific to the functions of reason, aesthetic, moral and theoretical, that over. the idea, mediated through the presentation judgment, continues to operate as regulative in the further development of works of art, moral behavior and what of most interest to us, theoretical and finally empirical science. In Kant's words, "it determines a priori not only the scope of the manifold content but also the positions which the parts occupy relative to one another." Endnote It should be evident now why another of Kant's declarations, i.e., that "reason has insight only into that which it creates in accordance with its own plan" Endnote should cause no alarm to the scientist. Innovation arises out of reason's formulating a plan, thinking an idea too rich in thought to be captured in intuition, concept and certainly too rich in thought to be captured in the established canons of scientific dogma which began themselves as products of such thinking.

It is a different world depending on which originative idea guides our science. One world is Newton's whose atom-producing God "in the beginning formed matter into solid, massy, hard, impenetrable, movable even, so hard as never to wear, or break in pieces." Endnote Another is in Kant's metaphysic of nature in which "all that is real in the objects of our external senses...must be regarded as moving forces. The so-called solid, or absolute impenetrability [of the Newtonian atom] is banished from natural science as an empty concept." Endnote In the same discussion Kant says that matter is nothing but moving forces. There is a way of looking at it to which this seems to be an earlier edition of the argument between some of the quantum mechanics types who are heirs of the Newtonian atomic idea and some of the unified field types who are heirs of Kant's fluid play of forces. Do we have here the origins of Einstein's refusal to accept quantum mechanics as an ultimately complete theory? I am tempted to answer that everyone has his own Einstein and that as of now the genius who will resolve the tension between the fundamental idea of quantum theory and the fundamental idea of unified field theory has yet to appear, as to whether the old one plays games of dice in the realm of physics, I can say nothing.


Originally published in THE PROCEEDINGS OF THE 6TH INTERNATIONAL KANT CONGRESS. Copyright University Press of America. Posted with permission of the publisher. Published Essays