Helmholtz's Kant



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Helmholtz's Kant
Clark Glymour12

One measure of a philosophical book's importance is personal: did it change your mind about anything? In Clark measure, Alberto Coffa's The Semantic Tradition from Kant to Carnap is an important book. "The Semantic Tradition from Kant to Carnap" might more accurately have been titled "Views of Some Vienna Circle Philosophers and Those Who Influenced Them." The topics, including the grounds of mathematical knowledge, inductive inference, the nature of concepts, realism and anti-realism of several kinds, are not confined to "semantics," and many of those who at the time thought best about these subjects and about meaning relations are given short shrift or none at all. Frank Ramsey is barely mentioned, George Boole, Charles Peirce, William James and C.I. Lewis are not discussed. The principals are Kant, Bolzano, Frege, Poincare, Hilbert, Godel, Russell, Wittgenstein, Reichenbach, Popper, Neurath, Carnap, Carnap and Carnap. Coffa's history stops in the 1930s with the collapse of European logical philosophy, and nothing Carnap or Russell or Popper or Reichenbach wrote after that decade is considered, nor are their connections with contemporary philosophy. Important technical enterprises of some of these figures are not developed; we learn about Hilbert on implicit definition and the axiomatic method, but not much about the famous program. The book contains neither classification of possible positions on issues, nor much logical smoothing of transitions from one figure to another. I was taken aback, for example, to read Bolzano's definition of derivative in terms of limit offered as an argument against Kant's opinions on intuition in mathematics. Surely a remote connection, but the very sort of disjointedness that has the ring of historical truth. Even within these limits, the scope of Coffa's book is so large that any reader is invited to ask what it all comes to. Coffa himself doesn't say. The book is filled with assessments of muddle, confusion and error, but Coffa died before writing a conclusion and the book lays out no standard to use in Whiggish history, nor regrets about the tradition, nor prospects. I will focus on regrets.


Kantian Psychology
Coffa's history begins with Kant, who is presented chiefly as a foil for the semantic tradition, a stalking horse for the role of "intuition" in mathematical knowledge. What seems interesting to me is the way Kant's issues bounded the scope of the philosophy Coffa considers.
I understand that some historians read the accounts of space, time, causation and knowledge in the Critique of Pure Reason as purely logical, or purely "conceptual" efforts, while others, Patricia Kitcher for example, read the book as a psychological theory, a theory of how the mind works and, in view of that constitution, of what the mind can and cannot know. The psychological reading seems the more charitable to Kant, since a psychological theory presented with bad arguments may still be a useful, engaging, even true picture of mind, but a purely logical or "conceptual" investigation frequently marked by bad arguments is nothing of value at all.
But if Kant's theory was psychology, it does not seem to me to have been psychology as we usually think of it. Other than Helmholtz and Hilbert, Kant is the only figure in Coffa's survey who was also a practicing empirical scientist. The sciences he practiced were planetary physics, geology and chemistry, not psychology. The arguments of the transcendental aesthetic and elsewhere in the first Critique may (or, I reluctantly suppose, may not) have had Newton's "deduction from the phenomena" as their model, as Kant' prize essay proposes, but unlike Newton's Principia, Kant's Critique was only half an empirical project. If Kant took as his premises generalizations from common experience, the procedure he used to produce a theory of mind from such slim data could not consistently create the basis for a scientific, empirical inquiry into the functioning of mind. Kant's data were not associations, or correlations between physical measures and human judgments, or reaction times, or errors, or the co-occurrences of incapacities, none of the stuff that became the mainstay of psychology by the end of the 19th century. Kant's data were that certain non-logical claims are known to be irrefutable by any possible experience. If so, these are data of psychology, of a kind, data that say humans have a special sort of knowledge. The result, the theory inferred from the data, is about the constitution and construction of any possible experience. The method, so far as I can understand it, is to be deduction from the phenomena of synthetic aprioricity. That is what I take a "transcendental" argument to be.
There are only so many synthetic a priori propositions, and when they are collected and their implications unraveled, Kantian psychology is done. There are no subtle experiments to conduct in Kantian psychology, no clever designs, nothing for sooty empirics to do. Psychology it may be, but it is psychology as a logical project. No surprise then that Kant's theory of mind inspired or challenged chiefly physicists and mathematicians in the 19th century, not psychologists. Brentano paid Kant some respect, but gave Mill far more; Fechner thought Aristotle the more important thinker for psychology. The focus of late nineteenth century physiological psychologists was not Kant but Darwin. By comparison, Josiah Willard Gibbs introduced his Elementary Principles of Statistical Mechanics with the remark that its intent was to show that the science of heat could be given an a priori basis, and George Boole styled the axioms of his idiosyncratic probabilistic account of causal inference "conditions of any possible experience."
Kantian psychology becomes a project at all only if the deductions are thought deficient, or incomplete, or if the premises are reconsidered. Reconsideration of the premises was, as Coffa notes, an occupation of late nineteenth century mathematical Kantians impressed with non Euclidean geometry, and later of mathematical Kantians impressed with the theory of relativity. I have never understood why everyone did not find Kant's proofs deficient. In any case, a demonstration of the error of one of Kant's non-empirical premises, the completeness of Aristotelian logic, was a consequence, if not a motive, of the great positive logical project of the 19th century, Frege's. In Coffa' account, which in this I have no reason to doubt, Russell, Reichenbach, Carnap and most of the rest labored in the gap between Kant's conclusions and the demonstrated error of Kant's empirical and logical premises.
The labor was indoors work. Cognition and language present two sides. Inside, thoughts have content, one thought is the same as another, two thoughts are different, one entails another, some are true and some false, some warranted and some not. Outside, people are biological systems that send signals to one another, that use complicated internal mechanisms--including perhaps representations with a logical structure--to adapt and coordinate their behavior in response to environment and signals. In Kant's vision, as in Frege's and Russell's and Carnap's, the inside work was a limited project; the difficult part lay in getting it right, not in getting it done. The outdoors project, by contrast, was vast and uncharted, and for philosophers in the semantic tradition, ignored. Psychology progressed exactly by finding doors to pass between the two.
Kant and Inductive Inference
Coffa says the semantic tradition is footnotes to Kant. Better, I think, if the footnoting has been more thorough. Certain features of Kant's system might have led to original thought about scientific inference and the limits of knowledge, but so far as I can tell from Coffa's history and the little I read, they did not. Kant left unexplained how the coordination of experiences among individuals comes about and leads to a common set of judgements about the sequence, location and features of events and objects. One answer is no answer: not everything can be explained. Another, Kemp Smith's response that the shared forms of intuition and the shared "rules" of the understanding and the schematism guarantee coordination, seems mysterious or incompetent. After all, common functions applied to different inputs, different matters of experience, need not produce outputs that bear any simple, systematic relation. Unless the functions are trivial, coordination of outputs requires some coordination of inputs, and that was one of Helmholtz's complaints. A third response, that things in themselves are common causes of the matters of experience in several individuals, invites a modern perspective on perception but violates the Kantian philosophical categories. Causal relations do not apply to the noumenal world; perhaps one should say so much the worse for those philosophical caegories. Nor was it clear how Kant's account of the sources of phenomenal causation was to guarantee the reliability of ordinary scientific inference. Exactly what causal knowledge was guaranteed, and how? Of Coffa's characters, only Helmholtz and Schlick seem to have thought at all on these lines.3
Helmholtz and Schlick aside, until Reichenbach the figures in Coffa's history were generally disinterested in understanding causal inference. Russell wanted to be rid of causation altogether, and arguably so did Carnap and also Reichenbach and Hilbert's student, Hempel. Frege, who thought so carefully about so much else, proposed to analyze "A causes B" as material implication. The period from 1880 to the 1930s saw a revolution in the conduct of biological and human sciences brought about by the novel use of statistical methods in England and America. None of this seems to have made any impression on Vienna Circle philosophers.
Another feature that might, if pursued, have led to fruitful philosophy of science has to do with logical features of reliable inquiry. Kant's discussions in the first Critique often invite appealing word pictures, pictures that seem more persasive than his arguments. No matter his tedious and unoriginal logical writings, Kant had wonderful logical acumen, perhaps better than any of his predecessors except Leibniz. Michael Friedman argues that Kant's account of geometry was consequent from his realization that Aristotelian logic could not account for Euclid's proofs. For more than two thousand years before, no one else seems to have noticed. Kant's rebuttal of the ontological argument is a logical insight still with us. But consider his antinomies of reason, specifically the antinomy of infinite divisibility. Kant's solution in the Prolegomena is that space as a completed thing does not exist, only the finite segments of experience of space and spatial division. As Michael Friedman puts it ("Matter and Material Substance in Kant's Philosophy of Nature: The Problem of Infinite Divisibility" preprint, p. 13)
The general idea of the solution to the Antinomies is then simply that "the empirical progress" of representations constituting experience is a potentially infinite, but never actually completed series. The objects of experience are therefore never given as a completed totality, and it thus makes no sense to assert that this totality is either finite or infinite--with respect to its composition or with respect to its division.
There is an immediate puzzle4: the variables of most universally quantified sentences range over a "potentially infinity" of objects, but I see no evidence that Kant and Kantians regarded the universal claims of science as generally without truth values. Moreover, one need only read Sextus to note that no finite empirical progress of representations can reliably decide the truth or falsity of arbitrary universal propositions. If there is something special about infinite divisibility and its connection to the empirical progress of representations, what is special needs to be explained. There is in fact a nice logical feature of their connection which, as in other cases, Kant may have understood without describing. Purely universal hypotheses can be decided in the limit--there is a procedure for guessing their truth value from finite initial segments of an infinite sequence of singular instances that is only wrong at most a finite number of times. But the hypothesis of infinite divisibility is not decidable in the limit--it goes, as Kant says, beyond all possible experience. 5
It may not have been easy to read Kant as implicitly posing questions about causation and coordination, or learning in the limit, but those questions emerged outside of the "semantic tradition." Philosophical thought about the relation between causation and coordination, and about the logic of reliable inquiry, was pursued by Peirce, who introduced randomization in experimental design and made explicit the view of inquiry as an unending sequence of conjectures that aim to converge on truth. Some 19th century mathematicians--Boole, Cayley and Dedekind--gave careful thought to aspects of causal inference.6 Nothing like that appears in the tradition Coffa considers until Reichenbach's later work, roughly half a century later. The mathematics of complexity, first Borel's and much later Kleene's, had straightforward analogies in the structure of inductive inference, but only mathematicians such as Lebesgue seem to have noticed and they did not much care. If these hierarchies came to the attention of semantic philosophers, Carnap and Reichenbach and Russell, they did not make the connection; no philosopher made it until Putnam, well after mid-century.
Cognitive Physiology
The pivotal figure in Coffa's history is Helmholtz, although Coffa does not remark on the pivot. Helmholtz figures in Coffa's history as the source of the idea that to imagine a theory's truth is to imagine what one would experience if it were true, and of the idea, too briefly described, that "structural" features of things in themselves may be inferred from the coordination of experiences. The more important fact, not unconnected with Helmholtz's take on interpretation and inference, is that Helmholtz founded an un-Kantian, unsemantical-tradition project that is now center stage, the project of cognitive physiology.
Helmholtz read Kant as an interesting, and mostly wrong, psychologist. He paid no attention to Kant's arguments which, like the arguments of his own father, a man attached to metaphysical philosophy, he likely thought pure junk. But it is an empirical matter to separate the respective roles in perception of the human constitution and its external environment. That sort of a posteriori separation of the a priori and the a posteriori made sense to Helmholtz and formed one of his many projects.7 The larger project that encompased Helmholtz, Du Bois Reymond, Brucke and their students, was cognitive physiology. Trained together in physiology by Johannes Muller, all three shared the opinion that physiology must be the empirical discovery of natural laws of functioning entirely consonant with physics and chemistry and without vital forces. But since so many physiological phenomena have a connection with perception and thought, that perspective must lead eventually to a physiology of cognition. By the closing years of the 19th century, it had. Ramon Cajal's discovery of synaptic nerve connections suggested the same idea to everyone who learned of it: the brain is a signaling network. Brucke's two Sigmund students, Exner and Freud, integrated Cajal's discovery with the neural anatomy of their day to offer more or less systematic speculations on the internal mechanisms of memory, perception, recognition, reasoning, illusion, hallucination and dreaming. Freud's was a full blown connectionist psychology.
Helmholtz's project, an empirical science of cognition tied to human biology, development, anatomy and physiology, survived behaviorism and, along with molecular genetics, is today one of the two principal forms under which human capacities are studied. By the end of the 19th century it was influential almost everywhere. William James' Principles of Psychology, and his psychological essays, are works at least partly in that mold. Even Karl Pearson described the brain as a telephone system. But the news, or the interest, did not spread to the philosophers in the semantical tradition. There is nothing of that sort of psychology in Russell, and when in the 1920s Carnap made some slim use of psychology, it was Gestalt psychology, connected but only distantly with the tradition Helmholtz founded. One must suppose the semantical philosophers had heard something, read something, but saw in the project of cognitive physiology nothing of significance for their philosophical projects. It is hard to say just why the semantical philosophers had no interest, and Coffa doesn't help, other than to suggest (to me) that they had been warned off by Frege's attack on "psychologism." Perhaps the philosophers thought that while cognitive physiologists had thoughts with meanings and entailments, they didn't study them, any more than physicists did. But of course that is just what psychologists such as Helmholtz and Fechner had long been doing, studying the correlations between features of external circumstances and the occurrences to people in those circumstances of thoughts with various kinds of contents. Or it may be that the philosophers, Carnap in particular, saw their enterprise as concerned with a special normative quality, "justification," that had almost nothing to do with empirical matters. The theory of meaning relations in Carnap and Reichenbach and others was an internal and normative subject to which empirical inquiry did not apply.
The Aufbau and Its Legacy
Carnap's Aufbau has a small role in Coffa's history, but it seems to me in a way the philosophical pinnacle of the semantic tradition, somehow amplifying both the good and the bad of it.8 What was the point of such a work? Carnap says it was to show how various ordinary and scientific claims are "justified." The justification consists of a series of definitions that aim to establish an informal equivalence between such claims, on the one hand, and, on the other, formal claims of class relations among finite sets whose ur-elements are syntactic expressions interpreted as claims of recollection of similarity between "elementary experiences." Characteristically, Carnap says nothing about the reliability of memory. There are philosophical absurdities to the work; for example, claims about the future, predictions, real generalizations, are impossible in the system, and according to Coffa, deliberately so.
Coffa says nothing about the aspect of the Aufbau I think most extraordinary. Until he tired of the elaboration, Carnap accompanied his definitions with "fictive procedures" for computing values of what was defined from values of what defined it. Carnap's construction is an algorithm, a program. With a more empirical stance, the Aufbau, or something like it, would have been a piece of mathematical psychology. With a different theoretical stance, the Aufbau, or something like it, would have been a design for automated reasoning, a kind of android architecture. Carnap himself pursued neither of these variations of his work, hewing to "reconstruction" and "justification." His students were more imaginative. Walter Pitt, Carnap's doctoral student, collaborated with a neurophysiologist to produce the first formal model of reasoning in a neural net, work that later helped give employment to thousands. Herbert Simon, a student of Carnap's sufficiently impressed later to dedicate a book to his teacher, subsequently helped create both artificial intelligence and the kind of theories of human information processing that compute on representations not unlike those in the Aufbau.
Summing Up
Various strands in contemporary philosophy can usefully be viewed as the remains of Coffa's semantic tradition. Some stand on their own intellectual legs. Theories of truth, logical consequence and entailment are the most obvious and from a logical point of view the most interesting. A certain kind of logical metaphysics, best represented in the writings of David Lewis, has historical connections with the semantic tradition. Otherwise, philosophical logic has virtually become a branch of computer science, an enterprise for which the Aufbau is a kind of unrecognized and unintended paradigm.
Several of the strands of contemporary philosophy concerned with mind and language are a legacy of the semantic tradition. The legacy has been a kind of impotence, especially when filtered through the ordinary language tradition that abandoned the committment to formal rigor characteristic of Coffa's semantic tradition. Nowhere is that clearer than in the philosophy that has issued from Oxford in the last three decades, especially from students influenced by Michael Dummett. The Oxford tradition shares a taste for "transcendental" arguments, for formulating questions in the form "What is it to be an x?," for insisting answers be given by Boolean functions, an aversion to mathematical formulations logical or otherwise, and a reliance on Cartesian arguments from imagination to possibility. The tradition maintains relations to the sciences of cognition that are inevitably desparate. The dictats of the semantic tradition--the verification principle, for example--could be serious and important when there was no serious empirical study of language; their latter-day counterparts cannot.
The kind of mathematical psychology the Aufbau might have been has no hold in philosophy at all. Goodman's continuation in The Structure of Appearance was equally remote from empirical constraints. Philosophers received with almost complete disinterest the single attempt by a latter day member of Coffa's semantic tradition to formulate a clear hypothesis about the a priori structure of mind necessary for humans to develop adult conceptions of space, time, objects, persons and their causal relations.9
As I read Coffa's book, I was impressed with what the semantic tradition did not think about and did not do, with the odd channels that those we now think of as the best philosophers of the time cut through the riot of philosophical issues all around them. The tradition shows a taste, marks of what is now sometimes called a philosophical mind, that in time has moved much of philosophy to the eddies of intellectual culture. The philosophy in Coffa's "semantic tradition" was mostly de-natured, de-scienced, anti-empirical in its own methods. Either problems were so formulated that empirical inquiry could not possibly address them, or no relevant inquiries were proposed or considered. Separated from American pragmatism, the "semantic tradition" gave almost no thought to norms or justifications as prudential consequences of relations of means to ends, and in particular almost never thought of inductive inference in those terms. In consequence, while theories of deductive reasoning and mathematical knowledge were rich and bore connections with mathematical developments, theories of scientific inference were trivial and utterly uninformed by developments either in logic or in statistics. As I read Coffa's history, I came slowly to the conclusion, new and uncomfortable to me, that it was the very "semantic tradition" that left most philosophers virtually useless when, thirty years ago, explorations of thought, meaning, and cognition took a naturalistic--a psychologistic--turn.
Perhaps these are not the conclusions my friend Alberto would have wished to cause. But he did, at least in my case; I thought none of this before I read his book. I wish he were here today, and everyday, to argue with me the small and the large of it all.



1 This paper was presented at an American Philosophical Association Symposium on Alberto Coffa’s The Semantic Tradition from Kant to Carnap.

2I cannot play any musical instrument, which doesn't entirely explain why I sometimes wake in fright from a dream in which I stand, useless violin in hand, on the stage of Carnegie Hall. I had the same experience after agreeing to comment on Alberto Coffa's book, which surveys a great swath through a century and a half of philosophy. Quite as much as I don't play, I don't scholar. After I wake from my dream, I eventually calm myself in the recognition that in the real world no one really expects any music from me; I hope the same applies to scholarship. Attributions to historical figures occur without footnotes because I have no recollection of the source from which I acquired the opinion. I hope that at least most of them are true.

3Very similar remarks apply to a Kantian treatment of unobservable scientific objects, events and processes.

4Actually several. If space is the form of external sensibility, why is its divisibility, whether infinite or finite, not a priori? Is the topology of space, for example its Euclidean space form, a priori or a posteriori, or without truth value? Similar questions apply to the form of internal sensibility. Is it a priori that time is not isomorphic to mod ten gizzillion arithmetic?

5The example, and the point, are due to Kevin Kelly, The Logic of Reliable Inquiry, Oxford, 1995, p. 54.

6For a review of some of these contributions, see T. Hailperin, Boole's Logic and Probability, North Holland, 1986, Chapter 6.

7See Hermann von Helmholtz, Epistemological Writings, Reidel, 1977.

8There are reasonable alternative selections, for example The Logical Syntax of Language.

9I refer to Russell's Human Knowledge: Its Scope and Limits.





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