A paper I wrote for my philosophy of classical physics course at University of Kentucky (fall 2000). I wrote it in about four of five hours, so it's not that great. But anyway...

## Introduction

Because it requires so little conceptual baggage, because it is so easy to understand, and because it so deeply touches upon our desire to know what it is to be human, the question of free will is one of the oldest of philosophy. From the beginning of human civilisation, people have wondered about fate, destiny, and the role these play in their lives. Around the sixteenth century, Western culture began to develop sophisticated systems of physics which hoped to some day explain everything. The data and knowledge all seemed to point to a single result---that the universe behaves in a very mechanistic manner. However, if that is truly the case, where does free will fit in? Is the human soul somehow able to influence the world in a nondeterministic way? Is our free will merely illusory? Philosophers have tried, and are still trying, to answer important questions such as these.

For the purposes of our discussion, we must define some important terms. Physics is the system we use for describing and prediction the behaviour of matter and energy. The appellation classical physics'' is given to physics predating quantum mechanics. Quantum mechanics and related physics fall under the designation of modern physics''. Determinism is the belief that all physical events are precisely determined by external forces before they occur (The Ism Book). Free will is the ability of an object---usually a mind---to determine its own course of action. Alternately, it is the belief that such ability exists, and can be attributed to the human mind. Finally, compatibilism is the claim that free will and determinism are not, in fact, mutually exclusive. This view is also known as reconciliationism'' (Dennett).

## Views on classical physics

Some of the earliest philosophical theories of free will in our intellectual tradition were those of the Epicureans and the Stoics. The Epicurean atomists, who were in general surprisingly in agreement with today's science, generally claimed that the atoms of which the universe was constructed behaved mechanistically. However, they claimed that these atoms could occasionally make random swerves, and that allowed for free will (Dennett). Stoics were, on the other hand, fatalistic and deterministic, and claimed that our free will resided in our ability to adjust our expectations down to meet what was determined by fate. That these two opposite views have not be reconciled to this day demonstrates how tricky a question free will is.

Later, in the seventeenth century, the search for a mechanical description of the world grew stronger. René Descartes claimed not only that inanimate objects behaved deterministically, but also that animals were nothing more than automata. Descartes' dualism posited the existence of only two substances: matter and spirit. According to him, the two substances could never interact---except in the human soul or mind. Spirit could, through the soul, influence the matter of the brain, and thereby the nerves, muscles, and finally the world outside the body. According to Descartes, our vivid sensation of free will is enough evidence to show that it must be true (Descartes). Since matter behaves deterministically, and determinism (according to most philosophers, especially Descartes and his contemporaries and predecessors) is contradictory with free will, the free will of the human soul must come from the spirit and not the matter.

Another early rationalist who argued on the question of free will was Baruch Spinoza. Spinoza went further than Descartes with his determinism. Unlike the dualists, he did not posit humans (or animals, or anything) as an exception to physical determinism. In his Ethics, he proves from some basic axioms that the universe is deterministic and that free will does not exist. He derives from his seven axioms Proposition XXVI: A thing which has been determined to any action was necessarily so determined by God, and that which has not been determined by God cannot determined itself to action''; this seems to indicate determinism, or at the very least a lack of free will. He proceeds to make this denial of free will more explicit with Proposition XXXII, The will cannot be called a free cause, but only necessary''. He, in fact, goes beyond determinism in the Ethics. He claims, in his Proposition XXXIII: Things could have been produced by God in no other manner and in no other order than that in which they have been produced'' (Spinoza). That is, not only can things proceed only in a certain way in this universe, but they could not proceed differently in any universe. Thus, this world is the only possible one.

Opposed to both Spinoza and Descartes was Leibniz. According to this philosopher, though most bodies behave deterministically, there also exist more concentrated bodies, called minds or souls. These have at least the appearance of free will: There is no creature . . . who could predict with certainty what another mind would choose . . . as it can be predicted in another case, at least by an angel, how some body will act if the course of nature not be interrupted'' (Leibniz). That is, the free will of human souls prevents a purely deterministic account of the universe. No created being could predict the behaviour of a human mind. However, he does not claim to infringe on God's omniscience: This does not, however, prevent the future actions of the mind . . . from being fixed by God''. Thus Leibniz may actually believe free will to be illusory: it is necessarily impossible that we be able to predict the behaviour of another mind, but the future actions of that mind are known by God and hence fixed.

Leibniz also believes that there is no causal correlation between thoughts and physical actions, but rather that God ensures harmony'' between mental and physical states (Wilson). This is in direct opposition to Descartes' dualism, which states that the mind directly influences the brain. Thus Leibniz allows free will to coëxist with determinism, though it is determinism of a most peculiar sort.

Immanuel Kant, in his Prolegomena to Any Future Metaphysics, presents as one of the classical antinomies of physics the questions of free will. His third antinomy consists, in his own words, of the thesis that, on the one hand, There are in the World Causes through Freedom'', and that, on the other hand, There is no Liberty, only Nature''. According to Kant, the opposed assertions . . . may both be true''. He resolves the contradiction by claiming that it applies concepts applicable only to facts to perceptions. According to section 53 of his \emph{Prolegomena}, If natural necessity is referred merely to appearances, and freedom merely to things in themselves, no contradiction arises . . . . Nature therefore and freedom can without contradiction be attributed to the very same thing, but in different relations---on one side as phenomenon, on the other as a thing in itself''.

## Modern physics

The beginning of the twentieth century saw the development of a new system of physics which flew in the face of established Western scientific thought. The theorists of quantum mechanics (QM), in response to questions about black-body radiation and the photoelectric effect, began to develop a system of physics in which energy could be described solely in integral units. Though at first innocuous, quantum mechanics soon posed serious questions about the nature of being.

One important result in quantum mechanics is the Heisenberg uncertainty principle (HUP). According to HUP, there exist pairs of quantum numbers such that, the more precisely one measures the one, the less precisely one knows the value of the other. The most common examples given are position and velocity, though other such quantum pairs exist (Omnes). This absolute limitation on our knowledge seems to spell doom for the ability to use physics to accurately predict the future.

Another important aspect of QM is the role of the observer. According to some interpretations of QM, the observer plays a significant role in the behaviour of physical entities. Without some kind of observer measuring certain quantities, it appears that those quantities are never in fact precisely determined. This raises the question of what, precisely, is an observer'', and whether the behaviour---or the very existence---of the universe depends intrinsically on the human mind. Here is a major blow against determinism---or at least for compatibilism. If the events of the universe depend on the actions of minds, it appears we have a way for free will to influence the universe without somewhere violating the laws of physics. However, such a result is rather unsavoury to physicists. Some have claimed that, in this context, an object may collapse a waveform as an observer'' if the possible results of that collapse are sufficiently distinct (Penrose). Unfortunately, this question lies outside the realms of physics, since it is impossible to obtain useful information from an experiment that we never observe.

## Free will and determinism

Though they are generally considered to be mutually exclusive, it is possible to provide a framework in which determinism and free will coëxist. There is, however, a major paradox that must be answered first: suppose the universe is deterministic, and we can perform some calculation to predict any future state of an object given the universe's current state. Then, if we have free will, we should be able to subvert these predictions---if physics predicts I will raise my right hand at time T, I may choose not to, and vice versa. There is no reason why the mere process of prediction should restrict my ability to raise or not raise my hand, so I in fact do not possess free will with respect to raising my hand. Since we could perform the same calculations for any action I might perform, I do not possess free will at all.

There are a number of ways of dealing with this problem. The first is Leibniz's solution: to say that, though it be fixed in God's eyes, the course of action of a human mind is unpredictable to anything other than God. This is a rather weak response, though, as it appears to be an ad hoc attempt to reconcile free will with divine omnipotence, and does not completely address the topic of physical determinism. It is a complete solution to the problem only if we can show that divine omnipotence implies determinism---which has not been demonstrated sufficiently for our purposes.

There is another way we can use a similar response. Anything which would be doing the prediction---be it a human mind, a computer, or something else---must be able to influence the rest of the world. After all, if it were not, there would be no paradox: I would not know of the prediction, so I would not be able to deliberately choose to violate it. Since the predicting object would be influencing the world, it must take its own actions into account---otherwise, it introduces a margin of error which may be large enough to allow a decision. In order to measure how it influences the rest of the world, though, the object must somehow precisely represent itself; then, though, it must precisely represent the representation, and so on ad infinitum. This, though, requires the object to be infinitely complex and infinitely fast (if it is to predict its influence on the world before it exerts that influence). Thus such an object is logically impossible, as is predicting the future course of the universe.

There is still a problem with this resolution of the paradox, though. We have shown that determinism does not, at least in this method, eliminate the possibility of free will, but we have not shown how free will might exist in such a universe---how does free mind influence matter? What in our physics allows this to happen? We may resort to Lucretius's swerves'' or to uncertain quantum behaviour, but we still cannot find a mechanism that would allow such influence. Here, one may result to observer-dependence of quantum events---by observing certain things and not others, we in fact cause things to happen. Thus we may influence the world in ways consistent with a mostly deterministic physics.

## Conclusion

The world appears to behave, on a large scale, mostly deterministically. This is not perfect determinism, however---and, on the quantum scale, it would seem that the world is not very deterministic at all. In any event, it is by Heisenberg's uncertainty principle, and by other arguments, impossible to have a completely predictive physics. Thus, regardless of the question of determinism, it is not overtly paradoxical to believe in materialism and in free will at the same time. While there is currently no satisfactory explanation of free will, we do know that the concept is not inherently anti-scientific, as has been claimed in the past. Especially with the advent of quantum mechanics, it would do us well to reëvaluate our positions on physics and determinism. Finally, philosophers too infrequently consider the compatibilist possibility---that, somehow, determinism and free will can coëxist. This, I believe, will eventually prevail---as a coöperative effort, rather than a compromise.

## Works Cited

Dennett, Daniel C. Elbow Room: the Varieties of Free Will worth Wanting. Cambridge, MA: the MIT Press, 1984.

Descartes, René. Meditations on First Philosophy. In From Descartes to Kant: readings in the Philosophy of the Renaissance and Enlightenment. Eds. T.V. Smith and Marjorie Green. Chicago: the University of Chicago Press, 1940.

Kant, Immanuel. Prolegomena to Any Future Metaphysics. In Smith and Green, eds.

Leibniz, Gottfried Wilhelm. Necessary and Contingent Truths''. In Smith and Green, eds.

Omnes, Roland. The Interpretation of Quantum Mechanics. Princeton, NJ: the Princeton University Press, 1994.

Penrose, Roger. The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford: Oxford University Press, 1989.

Saint-André, Peter. The Ism Book. 6 Dec. 2000 http://www.openthought.org/ismbook.

Spinoza, Baruch. Ethics. In Smith and Green, eds.

Wilson, Margaret Dauler. Ideas and Mechanism: essays on early modern philosophy. Princeton, NJ: Princeton University Press, 1999.