In the first three sections of this lecture I have sketched the determinism of classical physics and the indeterminism of present science. The latter was not recognized until the present century. The problem of freedom, however, has been with us since the dawn of philosophy, and it behooves us now to follow up the allusions at the beginning of section 1 and comment on the uneasy union between deterministic science and freedom-conscious moral philosophy which existed throughout the centuries that preceded ours.

A systematic review of all the devices whereby philosophers have tried to harmonize causality and freedom is impossible here. A sketch of three of them must suffice. One, which has the authority of Spinoza and some modern theologians, invokes a distinction between inward and outward experiences. Freedom is a phenomenon of consciousness of which one becomes aware by introspection. Determinism regulates processes from without. A stone in flight, said Spinoza, if it were awakened to consciousness, would deem itself free to move along its predetermined path; it would feel it had chosen its trajectory. The difference between determinism and freedom has been likened to two seemingly contradictory properties of physical objects: The windshield of a car is concave when seen from the inside, convex from the outside. This explanation, in spite of its allegorical appeal, nevertheless leaves freedom in an unsatisfactory state, for when all is said and done it remains a psychological illusion.

Next is a thesis which accounts for freedom by an appeal to ignorance. An omniscient being is not free, since knowing what happens excludes all choice in situations which otherwise permit it. The example sometimes cited is that of a child which is given a choice between a dish of spinach and a piece of pie. His mother, knowing that he dislikes spinach, knows the outcome, concludes therefore that he has no choice, while the child believes he is facing a genuine alternative. It is the limitation of his knowledge about himself which gives him the sense of being free. Again, it is difficult to see how this kind of reasoning explains any more than one's feeling of freedom, not its actual existence.

Last is a view which is found in the writings of Kant and developed in detail to fit modern science by Cassirer. Their philosophy, called transcendental idealism, regards causality as a category of human understanding, a necessary form in which all knowledge of events must be cast. For things in themselves, which lie beyond our comprehension, causality and all other basic modes of thought are irrelevant. This is what is meant by calling causality a transcendental principle of understanding. From this point of view universal causality or determinism, whether of the classical or the quantum mechanical sort, must not be regarded as a metaphysical constraint upon all forms of being. It must be distinguished from what Cassirer calls a "dinglicher Zwang". Freedom, too, is a transcendental principle, but one regulating our actions, and it therefore controls another realm. If both were factual, descriptive attributes of the world they would indeed collide; only their transcendental nature keeps them out of conflict and makes them compatible.

Now it seems to me that classical determinism and freedom do collide — in a factual sense if both are taken as ultimate metaphysical principles, and in the form of logical irreconcilables if they are transcendental modes of explanation which regulate our understanding. Let me illustrate the meaning of this claim by reference to a trivial example (which has no ethical significance, to be sure).

Suppose I am asked to raise my hand, I can do this mechanically without thought and without engaging my will. In that case, habit acquired during my student days will probably cause me to raise my right hand. One may look upon this action as a causal one, whose result is predictable in terms of conditions existing in my brain, of associations acquired, of neural pathways previously established, and so on. But notice: I took care to say that I would probably raise my right hand, thereby implying something less than strict predictability.

But if I am told: raise which ever hand you wish, the sequence of events is different. I am somehow challenged to think and then to make a choice. To believe that, during the moment of reflection preceding the decision to raise my left hand, the configuration of the molecules in my body, the currents in my brain cells, or even the psychological variables composing my mental state have already predetermined that I must raise my left hand is clearly false, for it contradicts the most elementary, the most reliable, self-declarative awareness of choice which accompanies this act. Thus a serious contradiction arises if strict causality is a metaphysical fact.

Nor can the situation be saved by saying, with Kant and Cassirer, that causality is merely a transcendental principle in terms of which we are required to conceive things. For in that case we should require one principle of understanding to comprehend the sequence of events which compose the objective course leading to the raising of my left hand, and a different, incompatible one to explain my feeling of freedom. Human reason does not tolerate two incoherent principles where a single one will do. I shall now show that the loosening of causality required by quantum mechanics enlarges the scope of that principle sufficiently to allow removal of these difficulties and to cover both determination and freedom.

What I hope to accomplish needs careful statement. It might seem to be a proof that quantum mechanics has solved the problem of freedom. This is a vastly different task from showing that quantum mechanics has removed an essential obstacle from the road toward its solution, while the problem remains unsolved in its major details. The following analysis is directed toward this latter, much more modest aim. In approaching it, however, many of the difficulties, whose resolution constitutes the difference between the first and second tasks, will move into view.

The decision which hand to raise is totally without ethical relevance; it merely illustrates the contrast between instinctive-reflexive, almost mechanical behavior and an action which involves thought and will, thereby engaging to a small extent the quality of freedom. The question of motivation, so essential in ethics, hardly enters at all. Or if it does, if for some conscious reason — perhaps the desire to surprise my partner — I have chosen to lift my left arm when he expected the right one to be raised, that reason is far from the concerns of ethics. The distance from here to choices which can be said to be morally good or bad, which conform or do not conform to ethical principles, which carry responsibility, is very great. Yet somehow it can be travelled by vehicles already at our disposal.

Freedom a prerequisite to ethics

Most theories of ethics, including the one outlined in section 4, achieve their end, the explanation of moral behavior, once the possibility of freedom and motivation is established. These qualities, however, are present at least in embryonic form in the example we chose for discussion; hence we return to it. Its relative simplicity is an important advantage.

Precisely what happened to me as a conscious person during that crucial interval in which I "made up my mind" to raise my left hand? Of the enormous variety of physical and chemical processes which took place in my body I am not aware. I do know, however, that the physical condition before the arm raising and that after the act were connected by a continuous series of objective physical happenings. And the entire series could have been different because of my will, because of a choice of physical possibilities that were open to me.

The mental processes during the crucial interval are likewise difficult to record in detail. Nevertheless the following is perfectly clear. I was aware of having a choice, there was a moment of reflection, perhaps a brief recall of past occasions, then came a glimmer of rudimentary satisfaction in doing the unexpected, next a decision and finally the act. The choice was enacted within consciousness, and it evidently was permitted, but merely permitted, by the physical processes that took place.

One thing, then, is utterly apparent: freedom is not wholly a problem of physical science but one involving biology, physiology and psychology as well. Upon realizing this one immediately confronts the standard question of reducibility: Are the laws of psychophysiology merely elaborate versions of those encountered in the physico-chemical world, or do they differ radically?

Physiology and psychology differ radically because of information in body and mind

The first alternative which assumes the possibility of reducing all behavior to physico-chemical bases need not be tied to the naive supposition that all the laws of these basic sciences are now known, and it will not be construed in this narrow sense here. The second, which maintains a radical difference, takes two essential forms. First, one may interpret the difference as mere transcendence, secondly as outright violation of physico-chemical laws.

I Reducibility
IIa Transcendence
IIb Violation of Laws

To avoid circumlocutions, let us refer to the first alternative, that of reducibility, as I. The second will be labelled II, and we shall designate transcendence by IIa, violation by IIb. As already mentioned, acceptance of I does not commit us to the view that all basic laws of nature are already known.

The precise meaning of IIa involves a theory of levels of complexity among physical phenomena. It is most simply illustrated by recalling the relation between the mechanics of point masses and the statistical mechanics of gases which are here viewed as large assemblages of molecules, in the form of point masses. To describe the mechanical state of each individual molecule one needs to specify its position and its velocity, nothing more. The totality of molecules, the gas, however, exhibits measurable properties like pressure, temperature and entropy which have no meaning with respect to single molecules. In this sense they are radically different from the properties of point masses. Yet if the positions and velocities of all molecules were known, the aggregate observables, i.e. pressure, temperature and entropy, could be calculated. These latter characterize a level of complexity above the mechanics of mass points. Explanation is continuous from below; the concepts of the lower level have meaning on the upper, but not the reverse.

It is seen, therefore, that thesis IIa asserts no incompatibility between concepts and principles on two different levels. The physico-chemical and the physio-psychological can probably be regarded in a similar way as two different levels of complexity, even though the differences are so great that the full connection is not at present in evidence. The view, however, seems reasonable. If it is accepted, and the gap can some day be filled, the higher level concepts can be reached from below and thus be reduced.

The bearing of alternative IIa upon the problem of freedom, which as we have seen is encountered in the upper realm, is now apparent. Freedom cannot appear in the domains of physiology and psychology if indeterminacy is not already lodged in physics. Strict causality among the molecules, applied upward as a principle of nature to explain the behavior of aggregates, cannot entail freedom because of the requirement of continuity from below. It is equally impossible to engender freedom in the realm of psychology when strict determinism rules physics, so long as hypothesis IIa is maintained.

For our present purpose, therefore, IIa can be identified with I: neither permits freedom unless strict determinism is abandoned in physics.

Only alternative IIb provides the possibility of freedom in the face of unrelieved classical causality as it is understood in pre-quantum physics. That view cannot be rejected out of hand; indeed it is very prevalent. Since it is forced to assume the occurrence of violations of the normal order of nature, it is tantamount to a belief in miracles. As for myself, I refuse to regard freedom as a miracle so long as other avenues of explanation are open. This is the case if alternative I or IIa is adopted, provided physical indeterminacy is taken seriously.

Here Margenau parts company with his lifelong colleague and mentor,
Ernst Cassirer

I judge IIa to be the safest hypothesis, and propose to describe its consequences. This is a somewhat unpopular course; it forces us to part company with many distinguished moral philosophers who see the autonomy of ethics threatened when a relation of any sort is assumed to exist between that august discipline and science. For centuries, humanists have been impressed by the slogan already discredited in section 4 of this lecture, that science deals with facts, ethics with values, and these two categories are so disparate that they must forever stand apart. If unanalyzed this is a foolish and a dangerous dogma. Some feel that a view which finds a root of freedom in physical science denigrates and demeans the high estate of ethics whose legitimate concerns should not seek refuge in the indeterminacies of natural events. Ethics, says Cassirer, should not be forced to build its nests in the gaps of physical causation, but he fails to tell where else it should build them, if at all.

The view proposed here can hardly be criticised as debasing ethics, or as depriving it of autonomy. For in the first place, if, in espousing indeterminacy, physics abdicates control over part of its former domain, entrusting it to other hands, it does not threaten ethics. The new mood of physics is not one of intransigeance but of renunciation.

Indeterminacy not a solution to problem of freedom, but the first step

Secondly, embracing the belief that freedom is made possible by indeterminacies in nature will not solve the problem of freedom. As will appear later, it permits only one first step towards its solution, but an important step to a place from which freedom can be seen as a scientific challenge, where it appears no longer as a fallacy or an illusion. Beyond it lies an open countryside in which ethics must travel without the guidance of science if it wishes to explore the meaning of good and bad, the origin of moral values — in short if it wishes to convert the offer of science, which might be named chance, into responsible choice.

Another consideration must be borne in mind. Throughout this lecture one single physical law is continually called upon to do extremely heavy duty, namely Heisenberg's indeterminacy principle. It is unreasonable to suppose that this item of knowledge is absolute in its present understanding, forever immune to reformulation and refinement. Future discoveries will doubtless place it in a new light, but it is difficult to see how its essence, which is drawn upon in the present context, can ever be relinquished. No one, of course, can rule out this possibility. But it seems far more likely, and here is where I would place my bet, that further principles even more widely restrictive of Laplacian causality will enter science, in which case the position here taken will be re-enforced.

Quantum indeterminacy, being the only item of its kind now firmly known, must thus be placed in the center of the present discussion. Also, the time has come to be specific. An important argument has been directed against the use to which that principle is here to be put, namely the argument which asserts that indeterminacy is limited to the atomic realm and loses its validity in the macrocosm.

Its importance in atomic and subatomic phenomena is crucial, for without it the behavior of elementary particles makes no sense. But a complex organ like the human brain, the cortex, even a brain cell or a neuron consist of vast numbers of elementary particles, and it is well known that the statistics of large numbers usually add up to certainties. While the motion of a single molecule in a gas must be specified with wide margins of probabilities, the entire gas behaves in predictable fashion. Insurance companies can only assign a probability to the occurrence of death in a given period for a specific individual, but they are almost certain of the number of deaths in a large group of people. So, too, it can be argued that the organic structures which carry the physical function of free decision are predictable in their total action even in view of elementary uncertainty; in other words, that the indeterminacy of atomic events is ironed out in the macrocosm. The assertion is respectable, for since we do not understand the function of physiological complexes in terms of atomic processes it can not be disproved. Another, slightly different consideration, leads to the same result. If the principle of indeterminacy is written for position (x) and velocities (v) it reads

Δx •Δv ≥ h/ 2m

m being the mass of the object whose motion is being studied. Now for an electron the quantity on the right of this inequality is about 1 (in c.g.s. units). Hence if we assume its position to be wholly uncertain within the volume of the atom, where it usually resides, and assign to Δx the value 10-8 cm (size of an atom), Δv must be about 108 cm/sec; the indeterminacy in velocity amounts to more than 100 times the speed of an I.C.B.M. Many unforeseeable things can happen within that range of ignorance.

For a brain cell, m is at least one trillion times as great as it is for an electron, hence the uncertainty is a billion times smaller. Even if we assume again that Δx = 10^-8 cm, we find Δv = 1 millimeter per sec. But for something as large as a cell it is unreasonable to allow Δx so small a value, which is far beyond the limit of detection. If we increase it 1,000-fold, the indeterminacy in velocity goes down to 10^-3 mm/sec, a value so small as to be quite uninteresting.

But this argument is really no more cogent than the former. For one might well ask: who is interested in the motion of a brain cell, or a neuron as a whole? It is very likely that crucial processes within such miniature organisms are triggered by single electrons and photons which are very strongly affected by quantum mechanical indeterminacy. Although little is known about the details of these reactions there is a good deal of conclusive evidence to support the claim that quantum indeterminacy can project important effects into the world at large, that organisms, in particular, can have their behavior and their fate strongly influenced by interaction with elementary physical entities. Again observe: even if we succeed in showing this we are still far from having established freedom. I am not suggesting that the release of erratic behavior governed only by the laws of chance is tantamount to freedom. I am saying that it is a physical precondition for human freedom. As to the influence of atomic chance upon the macroworld, here are a few examples.

Meteorology is not an exact science, and I am particularly reluctant to draw upon it because my knowledge of it is most inadequate. Everyone knows, however, that large atmospheric disturbances spring from minute pressure and velocity changes taking place within small regions in the upper air. A few molecules with abnormally large velocities can trigger a movement which may develop into a cyclone. I had always thought that the nucleus of a large disturbance would have to contain a sizeable number of molecules. However, a distinguished meteorologist recently told me that a fluctuation in velocity no larger than is compatible with Heisenberg's principle can be the cause of a low. And on looking at the mathematics, I convinced myself of this possibility. Only the probability of its happening is extremely small.

Scientists working in the psychophysics of vision have shown that a receptor in the human retina is sensitive to the incidence of very few photons of light, in certain regions of the spectrum perhaps to a single one. This means that a conscious response can be elicited by physical entities whose behavior is controlled by the uncertainty principle, a response which is in the customary sense without original cause. To be sure, it was triggered by the impinging photons, hence there was an immediate cause. But the coming of the photons was unpredictable; therefore the ensuing sensation, the stimulus-response episode was causeless. Yet that sensation might have informed a subject in a dark night that "something was there", perhaps something threatening, and he could have taken measures to avert the danger.

A more impressive illustration of the intrusion of atomic chance into the living world is afforded by the mutation of genes, which is known to result sometimes from the impact of a single X-ray quantum. Such mutations. can be advantageous to the individual undergoing them, but more often they are debilitating, sometimes lethal. A documented example is found in the literature.' It is impressive because it affected the fate of nations. It is well known that hemophilia, the bleeding disease, was an affliction of the ruling families of Russia and of Spain ever since the middle of the 19th century, troublesome in politics and a threat to royal succession. The origin of this disease may well be hidden in the indeterministic realm of atomic processes. Haldane has suggested after considerable search that the hemophilic condition began with a gene mutation in the nucleus of a cell in one of the testicles of Edward, Duke of Kent, Queen Victoria's father, in the year 1818.

From there on the incidence of the disease is open to study. There were three hemophiliacs among Victoria's nine children, seven among her grandchildren, six in the fourth generation. The latter included Alexis, the crown prince of Russia, whose mother, neurotically anxious about his condition, sought help from the monk Rasputin. How he thus gained a fateful foothold in the affairs of the Czarist family is a matter of history. Hemophilia among the sons of Alphonso XIII, the King of Spain, who was a grandson of Queen Victoria, apparently affected the stability of the throne.

Clearly, it is difficult to maintain that atomic indeterminacy has nothing to do with the inhabitants of the macrocosm.

Having made this point, I now turn to a few logical arguments which have been levelled against the possibility of freedom, quite apart from physical indeterminacy. Professor J. J. C. Smart has attempted to dispose of freedom as an inconsistent concept by employing a simple and seemingly cogent logical argument. He constructs two theses which he assumes to be exhaustive of all possibilities and also mutually exclusive. One is Laplacian determinism as we have discussed it earlier, the other is the view that "there are some events that even a superhuman calculator could not predict, however precise his knowledge of however wide a region of the universe at some previous time." Freedom, he holds, violates both of them and is therefore ruled out. Certainly the requirement of impeccable logic is to be imposed on every phase of scientific and philosophic reasoning; nevertheless logic, in spite of its merited vogue, is not the sole arbiter of truth. There are instances where the diffuseness of the meaning of terms makes its formal application impossible and its conclusions spurious in spite of all the reverence it commands. In the present instance, its use to settle the argument concerning freedom is as ineffectual as the application of arithmetic to ideas.

Smart's algorithm was challenged neatly by Harris, who rightly insists that the two alternatives above are not mutually exclusive. If freedom were identical with Smart's second alternative we would call it erratic behavior or caprice. What makes Harris' point important is, first of all, the looseness which afflicts the term event (state, or observation, or measurement would be more acceptable), and second the fact that physical indeterminacy is precisely the kind of intermediate alternative which is neither coincident with Smart's proposition one nor with proposition two.

One of the most serious confusions about freedom arises in connection with the uniqueness of history. The course of events in the universe is a single flow; there is no ambiguity about the happenings at any given time, aside from our knowledge of them, and if a superhuman intellect knew everything that happened up to a certain time T, he would perceive, in looking backward, not only clear determinism but a rigid, filled space-time structure of events. He could in fact, if he were a mathematician, write a formula — with a proper qualitative text defining the nature of all events — which would represent all history up to T. Where, then, can freedom enter in the presence of that timeless formula which, although it was unknown at times before T, nevertheless "existed" in a mathematical sense?

The answer involves recognition of the fact that retrodiction is not the same as prediction. Indeterminacy permits the former but not the latter. Only Laplacian determinism makes inferences along the time axis symmetric in both directions. On classical mechanics, full knowledge of the state of a physical system at time T allows in principle the calculation of its state at any time before or after T. Indeterminacy introduces a peculiar asymmetry into states with respect to their temporal implications: the past is certain and the future is not. This causal irreversibility of time is, and must always be, asserted along with the affirmation of freedom.

Nor is this without consequences with respect to the nature of time. The recent controversy concerning emergence or becoming, and the sense in which time is a fourth dimension of space is strongly affected by it. Relativity theory, which is thus far an outgrowth of classical mechanics and does not incorporate indeterminacy, speaks in Laplace's voice and precludes creativity and emergence of features not already foreshadowed in the presence. In the controversy to which reference has just been made, Capec is right in arguing for emergence, not for any philosophic reason but for the simple scientific fact that ordinary 4-dimensional relativity, the basis for the claim of frozen passage, is not applicable to the atomic domain.

Having reviewed the most common objections met by those who affirm human freedom, and having attempted to expose their weaknesses, let me now summarize and state my case.

Classical determinism made freedom intrinsically impossible, unless its application to psycho-physical phenomena is arbitrarily interdicted.

Historic arguments designed to reconcile freedom with classical causality were able merely to establish a subjective illusion, a personal feeling of freedom.

Modern physics, through Heisenberg's principle of indeterminacy, has loosened Laplacian determinism sufficiently to allow uncaused atomic events, permitting in certain specifiable situations the incidence of genuine chance.

The consequence of such microcosmic indeterminacies, while usually insignificant in the molar world, do ingress into the macrocosm at least in several known instances. It is very likely that they play a role in delicate neuro-physical and chemical processes.

Physics thus makes understandable the occurrence of chance, of true alternatives upon which the course of events must seize. Physics alone, in its present state, can account for unpredictable, erratic human behavior.

Human freedom involves more than chance: it joins chance with deliberate choice. But it needs the chance. In so far, and so long, as science can say nothing about this latter active, decisive, creative element it has not fully solved the problem of freedom.

But it has lifted it out of the wastebasket of illusions and paradoxes and re-established it as a challenging problem to be further resolved.

And now an afterthought. Suppose physical science, perhaps with the aid of sister disciplines like psychology, philosophy and theology, had solved the problem of choice supervening upon chance to explain freedom, would this fuller understanding not restore determinism? If we can explain how the agency effecting choice selects from the alternatives presented by physics a particular one, will the inclusion of that agency into the scheme of things not leave us where we started, i.e. with an amplified Laplacian formula?

The answer cannot be forseen. It may be affirmative, but I strongly doubt it. For if that agency were one which looked into the future rather than into the past, were drawn by purposes rather than impelled by drives, partook of the liveliness of the incalculable human spirit — freedom in a unique sense would survive.