The roots of the notion of determinism surely lie in a very common philosophical idea: the idea that everything can, in principle, be explained , or that everything that is, has a sufficient reason for being and being as it is, and not otherwise.
In other words, the roots of determinism lie in what Leibniz named the Principle of Sufficient Reason. But since precise physical theories began to be formulated with apparently deterministic character, the notion has become separable from these roots.
Philosophers of science are frequently interested in the determinism or indeterminism of various theories, without necessarily starting from a view about Leibniz' Principle.
Since the first clear articulations of the concept, there has been a tendency among philosophers to believe in the truth of some sort of determinist doctrine. There has also been a tendency, however, to confuse determinism proper with two related notions: predictability and fate. Fatalism is the thesis that all events or in some versions, at least some events are destined to occur no matter what we do. The source of the guarantee that those events will happen is located in the will of the gods, or their divine foreknowledge, or some intrinsic teleological aspect of the universe, rather than in the unfolding of events under the sway of natural laws or cause-effect relations.
Not every metaphysical picture makes this disentanglement possible, of course. In a looser sense, however, it is true that under the assumption of determinism, one might say that given the way things have gone in the past, all future events that will in fact happen are already destined to occur. Prediction and determinism are also easy to disentangle, barring certain strong theological commitments. As the following famous expression of determinism by Laplace shows, however, the two are also easy to commingle:.
In this century, Karl Popper defined determinism in terms of predictability also, in his book The Open Universe. Laplace probably had God in mind as the powerful intelligence to whose gaze the whole future is open.
If not, he should have: 19 th and 20 th century mathematical studies showed convincingly that neither a finite, nor an infinite but embedded-in-the-world intelligence can have the computing power necessary to predict the actual future, in any world remotely like ours. But even if our aim is only to predict a well-defined subsystem of the world, for a limited period of time, this may be impossible for any reasonable finite agent embedded in the world, as many studies of chaos sensitive dependence on initial conditions show.
Conversely, certain parts of the world could be highly predictable, in some senses, without the world being deterministic. When it comes to predictability of future events by humans or other finite agents in the world, then, predictability and determinism are simply not logically connected at all.
In Laplace's story, a sufficiently bright demon who knew how things stood in the world years before my birth could predict every action, every emotion, every belief in the course of my life. Were she then to watch me live through it, she might smile condescendingly, as one who watches a marionette dance to the tugs of strings that it knows nothing about.
We can't stand the thought that we are in some sense marionettes. Nor does it matter whether any demon or even God can, or cares to, actually predict what we will do: the existence of the strings of physical necessity, linked to far-past states of the world and determining our current every move, is what alarms us.
Whether such alarm is actually warranted is a question well outside the scope of this article see Hoefer a , Ismael and the entries on free will and incompatibilist theories of freedom.
But a clear understanding of what determinism is, and how we might be able to decide its truth or falsity, is surely a useful starting point for any attempt to grapple with this issue.
We return to the issue of freedom in section 6, Determinism and Human Action , below. Recall that we loosely defined causal determinism as follows, with terms in need of clarification italicized:. Why should we start so globally, speaking of the world , with all its myriad events, as deterministic? Then if all—or even just most —events E that are our human actions are causally determined, the problem that matters to us, namely the challenge to free will, is in force.
Nothing so global as states of the whole world need be invoked, nor even a complete determinism that claims all events to be causally determined. For example, the start of a football game on TV on a normal Saturday afternoon may be sufficient ceteris paribus to launch Ted toward the fridge to grab a beer; but not if a million-ton asteroid is approaching his house at.
Bertrand Russell famously argued against the notion of cause along these lines and others in , and the situation has not changed. By trying to define causal determination in terms of a set of prior sufficient conditions, we inevitably fall into the mess of an open-ended list of negative conditions required to achieve the desired sufficiency.
Moreover, thinking about how such determination relates to free action, a further problem arises. If the ceteris paribus clause is open-ended, who is to say that it should not include the negation of a potential disruptor corresponding to my freely deciding not to go get the beer?
They are also too short. For the typical set of prior events that can intuitively, plausibly be thought to be a sufficient cause of a human action may be so close in time and space to the agent, as to not look like a threat to freedom so much as like enabling conditions. So we have a number of good reasons for sticking to the formulations of determinism that arise most naturally out of physics. And this means that we are not looking at how a specific event of ordinary talk is determined by previous events; we are looking at how everything that happens is determined by what has gone before.
The state of the world in only entails that Ted grabs a beer from the fridge by way of entailing the entire physical state of affairs at the later time. The typical explication of determinism fastens on the state of the whole world at a particular time or instant , for a variety of reasons.
We will briefly explain some of them. Why take the state of the whole world, rather than some perhaps very large region, as our starting point? One might, intuitively, think that it would be enough to give the complete state of things on Earth , say, or perhaps in the whole solar system, at t , to fix what happens thereafter for a time at least.
But notice that all sorts of influences from outside the solar system come in at the speed of light, and they may have important effects. So evidently, for Mary's actions and hence, all physical events generally to be fixed by the state of things a month ago, that state will have to be fixed over a much larger spatial region than just the solar system.
If no physical influences can go faster than light, then the state of things must be given over a spherical volume of space 1 light-month in radius. In the time of Laplace, of course, there was no known speed limit to the propagation of physical things such as light-rays. In such a world, evidently, one has to fix the state of things over the whole of the world at a time t , in order for events to be strictly determined, by the laws of nature, for any amount of time thereafter.
In all this, we have been presupposing the common-sense Newtonian framework of space and time, in which the world-at-a-time is an objective and meaningful notion.
Below when we discuss determinism in relativistic theories we will revisit this assumption. For a wide class of physical theories i. That is, a specification of the state of the world at a time t , along with the laws, determines not only how things go after t , but also how things go before t.
Philosophers, while not exactly unaware of this symmetry, tend to ignore it when thinking of the bearing of determinism on the free will issue. The reason for this is that we tend to think of the past and hence, states of the world in the past as done, over, fixed and beyond our control. Forward-looking determinism then entails that these past states—beyond our control, perhaps occurring long before humans even existed—determine everything we do in our lives.
It then seems a mere curious fact that it is equally true that the state of the world now determines everything that happened in the past. We have an ingrained habit of taking the direction of both causation and explanation as being past—-present, even when discussing physical theories free of any such asymmetry.
We will return to this point shortly. Another point to notice here is that the notion of things being determined thereafter is usually taken in an unlimited sense—i. But conceptually speaking, the world could be only imperfectly deterministic: things could be determined only, say, for a thousand years or so from any given starting state of the world. For example, suppose that near-perfect determinism were regularly but infrequently interrupted by spontaneous particle creation events, which occur only once every thousand years in a thousand-light-year-radius volume of space.
This unrealistic example shows how determinism could be strictly false, and yet the world be deterministic enough for our concerns about free action to be unchanged. Part of understanding determinism—and especially, whether and why it is metaphysically important—is getting clear about the status of the presumed laws of nature.
In the physical sciences, the assumption that there are fundamental, exceptionless laws of nature, and that they have some strong sort of modal force, usually goes unquestioned. We can characterize the usual assumptions about laws in this way: the laws of nature are assumed to be pushy explainers. They make things happen in certain ways , and by having this power, their existence lets us explain why things happen in certain ways.
For a defense of this perspective on laws, see Maudlin Laws, we might say, are implicitly thought of as the cause of everything that happens. If the laws governing our world are deterministic, then in principle everything that happens can be explained as following from states of the world at earlier times. Interestingly, philosophers tend to acknowledge the apparent threat determinism poses to free will, even when they explicitly reject the view that laws are pushy explainers. Earman , for example, advocates a theory of laws of nature that takes them to be simply the best system of regularities that systematizes all the events in universal history.
Yet he ends his comprehensive Primer on Determinism with a discussion of the free will problem, taking it as a still-important and unresolved issue. Prima facie this is quite puzzling, for the BSA is founded on the idea that the laws of nature are ontologically derivative, not primary; it is the events of universal history, as brute facts, that make the laws be what they are, and not vice-versa. Taking this idea seriously, the actions of every human agent in history are simply a part of the universe-wide pattern of events that determines what the laws are for this world.
It is then hard to see how the most elegant summary of this pattern, the BSA laws, can be thought of as determiners of human actions. The determination or constraint relations, it would seem, can go one way or the other, not both. On second thought however it is not so surprising that broadly Humean philosophers such as Ayer, Earman, Lewis and others still see a potential problem for freedom posed by determinism.
For even if human actions are part of what makes the laws be what they are, this does not mean that we automatically have freedom of the kind we think we have, particularly freedom to have done otherwise given certain past states of affairs. It is one thing to say that everything occurring in and around my body, and everything everywhere else, conforms to Maxwell's equations and thus the Maxwell equations are genuine exceptionless regularities, and that because they in addition are simple and strong, they turn out to be laws.
It is quite another thing to add: thus, I might have chosen to do otherwise at certain points in my life, and if I had, then Maxwell's equations would not have been laws. One might try to defend this claim—unpalatable as it seems intuitively, to ascribe ourselves law-breaking power—but it does not follow directly from a Humean approach to laws of nature.
Instead, on such views that deny laws most of their pushiness and explanatory force, questions about determinism and human freedom simply need to be approached afresh. A second important genre of theories of laws of nature holds that the laws are in some sense necessary.
For any such approach, laws are just the sort of pushy explainers that are assumed in the traditional language of physical scientists and free will theorists. But a third and growing class of philosophers holds that universal, exceptionless, true laws of nature simply do not exist.
For these philosophers, there is a simple consequence: determinism is a false doctrine. As with the Humean view, this does not mean that concerns about human free action are automatically resolved; instead, they must be addressed afresh in the light of whatever account of physical nature without laws is put forward. We can now put our—still vague—pieces together. Determinism requires a world that a has a well-defined state or description, at any given time, and b laws of nature that are true at all places and times.
If we have all these, then if a and b together logically entail the state of the world at all other times or, at least, all times later than that given in a , the world is deterministic.
How could we ever decide whether our world is deterministic or not? Given that some philosophers and some physicists have held firm views—with many prominent examples on each side—one would think that it should be at least a clearly decidable question. Unfortunately, even this much is not clear, and the epistemology of determinism turns out to be a thorny and multi-faceted issue. As we saw above, for determinism to be true there have to be some laws of nature.
Most philosophers and scientists since the 17 th century have indeed thought that there are. But in the face of more recent skepticism, how can it be proven that there are?
And if this hurdle can be overcome, don't we have to know, with certainty, precisely what the laws of our world are , in order to tackle the question of determinism's truth or falsity? The first hurdle can perhaps be overcome by a combination of metaphysical argument and appeal to knowledge we already have of the physical world. Philosophers are currently pursuing this issue actively, in large part due to the efforts of the anti-laws minority.
The debate has been most recently framed by Cartwright in The Dappled World Cartwright in terms psychologically advantageous to her anti-laws cause. Those who believe in the existence of traditional, universal laws of nature are fundamentalists ; those who disbelieve are pluralists. This terminology seems to be becoming standard see Belot , so the first task in the epistemology of determinism is for fundamentalists to establish the reality of laws of nature see Hoefer b.
Even if the first hurdle can be overcome, the second, namely establishing precisely what the actual laws are, may seem daunting indeed. In a sense, what we are asking for is precisely what 19 th and 20 th century physicists sometimes set as their goal: the Final Theory of Everything. Both a and b are highly debatable, but the point is that one can see how arguments in favor of these positions might be mounted.
The same was true in the 19 th century, when theorists might have argued that a whatever the Final Theory is, it will involve only continuous fluids and solids governed by partial differential equations; and b all such theories are deterministic. Here, b is almost certainly false; see Earman ,ch.
Even if we now are not, we may in future be in a position to mount a credible argument for or against determinism on the grounds of features we think we know the Final Theory must have. Determinism could perhaps also receive direct support—confirmation in the sense of probability-raising, not proof—from experience and experiment.
For theories i. And in broad terms, this is the case in many domains we are familiar with. Your computer starts up every time you turn it on, and if you have not changed any files, have no anti-virus software, re-set the date to the same time before shutting down, and so on … always in exactly the same way, with the same speed and resulting state until the hard drive fails.
These cases of repeated, reliable behavior obviously require some serious ceteris paribus clauses, are never perfectly identical, and always subject to catastrophic failure at some point. But we tend to think that for the small deviations, probably there are explanations for them in terms of different starting conditions or failed isolation, and for the catastrophic failures, definitely there are explanations in terms of different conditions. Most of these bits of evidence for determinism no longer seem to cut much ice, however, because of faith in quantum mechanics and its indeterminism.
Indeterminist physicists and philosophers are ready to acknowledge that macroscopic repeatability is usually obtainable, where phenomena are so large-scale that quantum stochasticity gets washed out. But they would maintain that this repeatability is not to be found in experiments at the microscopic level, and also that at least some failures of repeatability in your hard drive, or coin-flipping experiments are genuinely due to quantum indeterminism, not just failures to isolate properly or establish identical initial conditions.
If quantum theories were unquestionably indeterministic, and deterministic theories guaranteed repeatability of a strong form, there could conceivably be further experimental input on the question of determinism's truth or falsity. Unfortunately, the existence of Bohmian quantum theories casts strong doubt on the former point, while chaos theory casts strong doubt on the latter. More will be said about each of these complications below.
If the world were governed by strictly deterministic laws, might it still look as though indeterminism reigns? This is one of the difficult questions that chaos theory raises for the epistemology of determinism. A deterministic chaotic system has, roughly speaking, two salient features: i the evolution of the system over a long time period effectively mimics a random or stochastic process—it lacks predictability or computability in some appropriate sense; ii two systems with nearly identical initial states will have radically divergent future developments, within a finite and typically, short timespan.
Definitions of chaos may focus on either or both of these properties; Batterman argues that only ii provides an appropriate basis for defining chaotic systems. A simple and very important example of a chaotic system in both randomness and SDIC terms is the Newtonian dynamics of a pool table with a convex obstacle or obstacles Sinai and others.
See Figure 1. Figure 1: Billiard table with convex obstacle. The usual idealizing assumptions are made: no friction, perfectly elastic collisions, no outside influences. The ball's trajectory is determined by its initial position and direction of motion. If we imagine a slightly different initial direction, the trajectory will at first be only slightly different.
And collisions with the straight walls will not tend to increase very rapidly the difference between trajectories. But collisions with the convex object will have the effect of amplifying the differences.
After several collisions with the convex body or bodies, trajectories that started out very close to one another will have become wildly different—SDIC. In the example of the billiard table, we know that we are starting out with a Newtonian deterministic system—that is how the idealized example is defined. But chaotic dynamical systems come in a great variety of types: discrete and continuous, 2-dimensional, 3-dimensional and higher, particle-based and fluid-flow-based, and so on.
Mathematically, we may suppose all of these systems share SDIC. But generally they will also display properties such as unpredictability, non-computability, Kolmogorov-random behavior, and so on—at least when looked at in the right way, or at the right level of detail.
This leads to the following epistemic difficulty: if, in nature, we find a type of system that displays some or all of these latter properties, how can we decide which of the following two hypotheses is true? In other words, once one appreciates the varieties of chaotic dynamical systems that exist, mathematically speaking, it starts to look difficult—maybe impossible—for us to ever decide whether apparently random behavior in nature arises from genuine stochasticity, or rather from deterministic chaos.
There is certainly an interesting problem area here for the epistemology of determinism, but it must be handled with care. It may well be true that there are some deterministic dynamical systems that, when viewed properly , display behavior indistinguishable from that of a genuinely stochastic process.
For example, using the billiard table above, if one divides its surface into quadrants and looks at which quadrant the ball is in at second intervals, the resulting sequence is no doubt highly random. But this does not mean that the same system, when viewed in a different way perhaps at a higher degree of precision does not cease to look random and instead betray its deterministic nature. If we partition our billiard table into squares 2 centimeters a side and look at which quadrant the ball is in at.
And finally, of course, if we simply look at the billiard table with our eyes, and see it as a billiard table , there is no obvious way at all to maintain that it may be a truly random process rather than a deterministic dynamical system. See Winnie for a nice technical and philosophical discussion of these issues.
Winnie explicates Ornstein's and others' results in some detail, and disputes Suppes' philosophical conclusions. It is natural to wonder whether chaotic behavior carries over into the realm of systems governed by quantum mechanics as well.
Interestingly, it is much harder to find natural correlates of classical chaotic behavior in true quantum systems see Gutzwiller Some, at least, of the interpretive difficulties of quantum mechanics would have to be resolved before a meaningful assessment of chaos in quantum mechanics could be achieved.
The popularization of chaos theory in the relatively recent past perhaps made it seem self-evident that nature is full of genuinely chaotic systems. In fact, it is far from self-evident that such systems exist, other than in an approximate sense. Nevertheless, the mathematical exploration of chaos in dynamical systems helps us to understand some of the pitfalls that may attend our efforts to know whether our world is genuinely deterministic or not. Is there nothing left that could sway our belief toward or against determinism?
There is, of course: metaphysical argument. Metaphysical arguments on this issue are not currently very popular. But philosophical fashions change at least twice a century, and grand systemic metaphysics of the Leibnizian sort might one day come back into favor.
Conversely, the anti-systemic, anti-fundamentalist metaphysics propounded by Cartwright might also come to predominate. As likely as not, for the foreseeable future metaphysical argument may be just as good a basis on which to discuss determinism's prospects as any arguments from mathematics or physics.
John Earman's Primer on Determinism remains the richest storehouse of information on the truth or falsity of determinism in various physical theories, from classical mechanics to quantum mechanics and general relativity. Here I will give only a brief discussion of some key issues, referring the reader to Earman and other resources for more detail. Figuring out whether well-established theories are deterministic or not or to what extent, if they fall only a bit short does not do much to help us know whether our world is really governed by deterministic laws; all our current best theories, including General Relativity and the Standard Model of particle physics, are too flawed and ill-understood to be mistaken for anything close to a Final Theory.
Nevertheless, as Earman stressed, the exploration is very valuable because of the way it enriches our understanding of the richness and complexity of determinism.
Despite the common belief that classical mechanics the theory that inspired Laplace in his articulation of determinism is perfectly deterministic, in fact the theory is rife with possibilities for determinism to break down. One class of problems arises due to the absence of an upper bound on the velocities of moving objects.
Below we see the trajectory of an object that is accelerated unboundedly, its velocity becoming in effect infinite in a finite time. See Figure 2 :. Figure 2: An object accelerates so as to reach spatial infinity in a finite time. Never mind how the object gets accelerated in this way; there are mechanisms that are perfectly consistent with classical mechanics that can do the job. In fact, Xia showed that such acceleration can be accomplished by gravitational forces from only 5 finite objects, without collisions.
No mechanism is shown in these diagrams. But now recall that classical mechanics is time-symmetric: any model has a time-inverse, which is also a consistent model of the theory. Clearly, a world with a space invader does fail to be deterministic.
A second class of determinism-breaking models can be constructed on the basis of collision phenomena. The first problem is that of multiple-particle collisions for which Newtonian particle mechanics simply does not have a prescription for what happens.
Consider three identical point-particles approaching each other at degree angles and colliding simultaneously. That they bounce back along their approach trajectories is possible; but it is equally possible for them to bounce in other directions again with degree angles between their paths , so long as momentum conservation is respected.
Moreover, there is a burgeoning literature of physical or quasi-physical systems, usually set in the context of classical physics, that carry out supertasks see Earman and Norton and the entry on supertasks for a review.
A failure of CM to dictate a well-defined result can then be seen as a failure of determinism. In supertasks, one frequently encounters infinite numbers of particles, infinite or unbounded mass densities, and other dubious infinitary phenomena. The trouble is, it is difficult to imagine any recognizable physics much less CM that eschews everything in the set. Figure 4: A ball may spontaneously start sliding down this dome, with no violation of Newton's laws. Reproduced courtesy of John D.
Norton and Philosopher's Imprint. Finally, an elegant example of apparent violation of determinism in classical physics has been created by John Norton As illustrated in Figure 4 , imagine a ball sitting at the apex of a frictionless dome whose equation is specified as a function of radial distance from the apex point.
This rest-state is our initial condition for the system; what should its future behavior be? Clearly one solution is for the ball to remain at rest at the apex indefinitely. But curiously, this is not the only solution under standard Newtonian laws. Every year older collections are updated with the latest values and new areas will be added as science progresses. The material in this new edition compiles cleaning applications into one easy reference that has been fully updated to incorporate new applications and techniques.
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