## 1. Introduction



In most of what follows, I will speak simply of *determinism*,
rather than of *causal determinism*. This follows philosophical
practice of sharply distinguishing views and theories of what
causation is from any conclusions about the success or failure of
determinism (cf. Earman, 1986; an exception is Mellor 1994). 



Traditionally determinism has been given various, usually imprecise
definitions. This is only problematic if one is investigating
determinism in a specific, well-defined theoretical context; but it is
important to avoid certain major errors of definition. In order to get
started we can begin with a loose and (nearly) all-encompassing
definition as follows:



> 
> Determinism: Determinism is true of the *world* if and only if,
> given a specified *way things are at a time t*, the way things
> go *thereafter* is *fixed* as a matter of *natural
> law*.
> 



The italicized phrases are elements that require further explanation
and investigation, in order for us to gain a clear understanding of
the concept of determinism.



The notion of determinism may be seen as one way of cashing out a
historically important nearby 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,*i.e., Leibniz's Principle of Sufficient Reason.
Leibniz's PSR, however, is not linked to physical laws;
arguably, one way for it to be satisfied is for God to *will*that things should be just so and not otherwise. This does not
require that physical or causal determinism hold. On the other hand,
on a strict reading Leibniz's PSR may be more demanding than
determinism. Under determinism, particular facts and events are the
way they are due to the laws and the particular facts of how things
stood at an earlier time, for example at the beginning of time. But
there need be no answer to the question "Why were things just
*so* at the beginning of time?", and hence no
*complete* sufficient reason for all facts and
 events.[1]



Since the first clear articulations of the concept of determinism,
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.
Fatalism is therefore clearly separable from determinism, at least to
the extent that one can disentangle mystical forces and gods'
wills and foreknowledge (about *specific* matters) from the
notion of natural/causal law. Not every metaphysical picture makes
this disentanglement possible, of course. But as a general matter, we
can imagine that certain things are fated to happen, without this
being the result of deterministic natural laws alone; and we can
imagine the world being governed by deterministic laws, without
anything at all being *fated* to occur (perhaps because there
are no gods, nor mystical/teleological forces deserving the titles
*fate* or *destiny*, and in particular no intentional
determination of the "initial conditions" of the world).
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:



> 
> We ought to regard the present state of the universe as the effect of
> its antecedent state and as the cause of the state that is to follow.
> An intelligence knowing all the forces acting in nature at a given
> instant, as well as the momentary positions of all things in the
> universe, would be able to comprehend in one single formula the
> motions of the largest bodies as well as the lightest atoms in the
> world, provided that its intellect were sufficiently powerful to
> subject all data to analysis; to it nothing would be uncertain, the
> future as well as the past would be present to its eyes. The
> perfection that the human mind has been able to give to astronomy
> affords but a feeble outline of such an intelligence. (Laplace 1820)
> 



In this century,
 Karl Popper (1982)
 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: 19th
and 20th 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.



The equation of "determinism"with
"predictability" is therefore a *facon de
parler* that at best makes vivid what is at stake in determinism:
our fears about our own status as free agents in the world. In
Laplace's story, a sufficiently bright demon who knew how things
stood in the world 100 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 (2002a), Ismael (2016)
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.


## 2. Conceptual Issues in Determinism



Recall that we loosely defined causal determinism as follows, with
terms in need of clarification italicized:



> 
> Determinism: The *world* is *governed by* (or is
> *under the sway of*) determinism if and only if, given a
> specified *way things are at a time t*, the way things go
> *thereafter* is fixed as a matter of *natural law*.
> 


### 2.1 The World



Why should we start so globally, speaking of the *world*, with
all its myriad events, as deterministic? One might have thought that a
focus on individual events is more appropriate: an event *E* is
causally determined if and only if there exists a set of prior events
{*A*, *B*, *C* ...} that constitute a
(jointly) sufficient cause of *E*. 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 a variety of reasons this approach is fraught with problems, and
the reasons explain why philosophers of science mostly prefer to drop
the word "causal" from their discussions of determinism.
Generally, as John Earman quipped (1986), to go this route is to
"... seek to explain a vague
concept--determinism--in terms of a truly obscure
one--causation." More specifically, neither
philosophers' nor laymen's conceptions of *events*
have any correlate in any modern physical
 theory.[2]
 The same goes for the notions of *cause* and *sufficient
cause*. A further problem is posed by the fact that, as is now
widely recognized, a set of events {*A*, *B*, *C*
...} can only be genuinely *sufficient* to produce an
effect-event if the set includes an open-ended *ceteris
paribus* clause excluding the presence of potential disruptors
that could intervene to prevent *E*. 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
.75*c* from a few thousand miles away, nor if his phone is
about to ring with news of a tragic nature, ..., and so on.
 Bertrand Russell
 famously argued against the notion of cause along these lines (and
others) in 1912, 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? If it does, then we are left saying
"When *A*, *B*, *C*, ... Ted will then
go to the fridge for a beer, unless *D* or *E* or
*F* or ... or Ted decides not to do so." The
marionette strings of a "sufficient cause" begin to look
rather tenuous.



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. If
Ted is propelled to the fridge by {seeing the game's on;
desiring to repeat the satisfactory experience of other Saturdays;
feeling a bit thirsty; etc}, such things look more like *good
reasons to have decided* to get a beer, not like external physical
events far beyond Ted's control. Compare this with the claim
that {state of the world in 1900; laws of nature} entail Ted's
going to get the beer: the difference is dramatic. 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 1900 only entails that Ted grabs a beer from the fridge by way of
entailing the entire physical state of affairs at the later time.


### 2.2 The way things are at a time *t*



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. Suppose Mary looks up at
the sky on a clear night, and a particularly bright blue star catches
her eye; she thinks "What a lovely star; I think I'll stay
outside a bit longer and enjoy the view." The state of the solar
system one month ago did not fix that that blue light from Sirius
would arrive and strike Mary's retina; it arrived into the solar
system only a day ago, let's say. 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.)



But in making vivid the "threat" of determinism, we often
want to fasten on the idea of the *entire future* of the world
as being determined. No matter what the "speed limit" on
physical influences is, if we want the entire future of the world to
be determined, then we will have to fix the state of things over all
of space, so as not to miss out something that could later come in
"from outside" to spoil things. In the time of Laplace, of
course, there was no known speed limit to the propagation of physical
things such as light-rays. In principle light could travel at any
arbitrarily high speed, and some thinkers did suppose that it was
transmitted "instantaneously." The same went for the force
of gravity. 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.



Ismael (2016) has argued that even this is not enough to secure the
desired logical entailment of the full future: in addition, one must
add an "and nothing else" clause or premise, saying that
in the (putatively) full description of the way things are
at *t*, nothing has been left out that could interfere with the
natural time-evolution of the world-state. In the next section we will
see an example of such a thing that could be "left out" of
the earlier description of the world.



A final assumption may be worth mentioning here, that usually goes
unremarked. It is assumed that the state of the world is completely
*sharp and determinate*. That is, there is no mathematical or
ontological vagueness in the description of the way things are at time
*t*. This assumption goes hand in hand with our usual tendency
to think of the *past* as fully determinate and
"fixed". Without this assumption, in most theoretical
frameworks mathematical predictability of future states would be
impossible.



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.


### 2.3 Thereafter



For a wide class of physical theories (i.e., proposed sets of laws of
nature), if they can be viewed as deterministic at all, they can be
viewed as *bi-directionally* deterministic. 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, as noted just above, we tend to think of the past (and hence,
states of the world in the past) as *sharp and determinate*,
and hence *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.e., determination of all future events, no matter how
remote in time. 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.


### 2.4 Laws of nature



In the loose statement of determinism we are working from, metaphors
such as "govern" and "under the sway of" are
used to indicate the strong force being attributed to the laws of
nature. 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. Indeed, talk of laws
"governing" and so on is so commonplace that it takes an
effort of will to see it as metaphorical. 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 (2007)). 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. (Again, we note that even though
the entailment typically works in the future-past direction also,
we have trouble thinking of this as a legitimate *explanatory*
entailment. In this respect also, we see that laws of nature are being
implicitly treated as the causes of what happens: causation,
intuitively, can only go past-future.)



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 (1986), 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. This is the Best Systems Analysis (BSA), with roots
in the work of Hume, Mill and Ramsey, and most recently refined and
defended by David Lewis (1973, 1994) and by Earman (1984, 1986). (cf.
entry on
 laws of nature).
 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, and Lewis
(1981) does this. But it does not follow directly from a Humean
approach to laws of nature, and Loewer (2020, Other Internet
Resources) defends a different Humean compatibilism, to which we will
return in section 6.



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*.
Among those who hold this are influential philosophers such as Nancy
Cartwright, Bas van Fraassen, and John Dupre. 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. See Dupre (2001) for one
such discussion.


### 2.5 Fixed



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. Logical entailment, in a sense broad enough to
encompass mathematical consequence, is the modality behind the
determination in "determinism."


## 3. The Epistemology of Determinism



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.


### 3.1 Laws again



As we saw above, for determinism to be true there have to *be*
some laws of nature. Most philosophers and scientists since the
17th 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 1999) 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 2001), so the first task in the epistemology of determinism
is for fundamentalists to establish the reality of laws of nature (see
Hoefer 2002b).



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
19th and 20th century physicists sometimes set
as their goal: the Final Theory of Everything. But perhaps, as Newton
said of establishing the solar system's absolute motion,
"the thing is not altogether desperate." Many physicists
in the past 60 years or so have been convinced of determinism's
falsity, because they were convinced that (a) whatever the Final
Theory is, it will be some recognizable variant of the family of
quantum mechanical theories; and (b) all quantum mechanical theories
are non-deterministic. 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 19th 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
(1986),ch. XI). 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.


### 3.2 Experience



Determinism could perhaps also receive direct
support--confirmation in the sense of probability-raising, not
proof--from experience and experiment. For theories (i.e.,
potential laws of nature) of the sort we are used to in physics, it is
typically the case that if they are deterministic, then to the extent
that one can perfectly isolate a system and repeatedly impose
identical starting conditions, the subsequent behavior of the systems
should also be identical. 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). The light comes on
exactly 32 *msec* after the switch closes (until the day
the bulb 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.



There have even been studies of paradigmatically "chancy"
phenomena such as coin-flipping, which show that if starting
conditions can be *precisely* controlled and outside
interferences excluded, identical behavior results (see Diaconis,
Holmes & Montgomery 2007). 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.


### 3.3 Determinism and Chaos



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. We will use "randomness" to denote the first
feature, and "sensitive dependence on initial conditions"
(SDIC) for the latter. Definitions of chaos may focus on either or
both of these properties; Batterman (1993) 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 1970 and others). See
 Figure 1.




![Billiard table with convex obstacle](billiard3.jpg)

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?


1. The system is governed by genuinely stochastic, indeterministic
laws (or by no laws at all), i.e., its apparent randomness is in fact
*real* randomness.
2. The system is governed by underlying deterministic laws, but is
chaotic.



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. Patrick
Suppes (1993, 1996) argues, on the basis of theorems proven by
Ornstein (1974 and later) that "There are processes which can
equally well be analyzed as deterministic systems of classical
mechanics or as indeterministic semi-Markov processes, no matter how
many observations are made." And he concludes that
"Deterministic metaphysicians can comfortably hold to their view
knowing they cannot be empirically refuted, but so can indeterministic
ones as well." (Suppes 1993, p. 254) For more recent works
exploring the extent to which deterministic and indeterministic model
systems may be regarded as empirically indistinguishable, see Werndl
(2016) and references therein.



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 30-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 .1 second intervals, the resulting sequence will be far
from random. 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 1997
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.)



The dynamical systems usually studied under the label of
"chaos" are usually either purely abstract, mathematical
systems, or classical Newtonian systems. 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 1990). 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. For example, SDIC is hard to find in the
Schrodinger evolution of a wavefunction for a system with finite
degrees of freedom; but in
 Bohmian quantum mechanics
 it is handled quite easily on the basis of particle trajectories (see
Durr, Goldstein and Zhangi 1992).



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.


### 3.4 Metaphysical arguments



Let us suppose that we shall never have the Final Theory of Everything
before us--at least in our lifetime--and that we also remain
unclear (on physical/experimental grounds) as to whether that Final
Theory will be of a type that can or cannot be deterministic. 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 (1999) 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.


## 4. The Status of Determinism in Physical Theories



John Earman's *Primer on Determinism* (1986) 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. (See also his update on the
subject, "Aspects of Determinism in Modern Physics"
(2007)). Here I will give only a brief discussion of some key issues,
referring the reader to Earman (1986) 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 deepens our
understanding of the richness and complexity of determinism.


### 4.1 Classical mechanics



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:



![object accelerates to reach infinity](disappearer.jpg)

Figure 2: An object accelerates so as to
reach spatial infinity in a finite time




By the time *t = t\**, the object has literally disappeared from
the world--its world-line never reaches the *t = t\**
surface. (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 (1992) showed that such
acceleration can be accomplished by gravitational forces from only 5
finite objects, without collisions. No mechanism is shown in these
diagrams.) This "escape to infinity," while disturbing,
does not yet look like a violation of determinism. But now recall that
classical mechanics is time-symmetric: any model has a time-inverse,
which is also a consistent model of the theory. The time-inverse of
our escaping body is playfully called a "space
invader."



![space invader comes from infinity](space-invader.jpg)

Figure 3: A 'space invader'
comes in from spatial infinity




Clearly, a world with a space invader does fail to be deterministic.
Before *t = t\**, there was nothing in the state of things to
enable the prediction of the appearance of the invader at *t* =
*t\*
 +*.[3]
 One might think that the infinity of space is to blame for this
strange behavior, but this is not obviously correct. In finite,
"rolled-up" or cylindrical versions of Newtonian
space-time space-invader trajectories can be constructed, though
whether a "reasonable" mechanism to power them exists is
not
 clear.[4]



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 120 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 120 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 (1998) and
the entry on
 supertasks
 for a review). Frequently, the puzzle presented is to decide, on the
basis of the well-defined behavior before time *t* =
*a*, what state the system will be in at *t* =
*a* itself. 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. Coupled with some of the other breakdowns of
determinism in CM, one begins to get a sense that most, if not all,
breakdowns of determinism rely on some combination of the following
set of (physically) dubious mathematical notions: {infinite space;
unbounded velocity; continuity; point-particles; singular fields}. The
trouble is, it is difficult to imagine *any* recognizable
physics (much less CM) that eschews everything in the set.



![Norton's dome](dome_with_eqn.gif)

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 (2003). 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. The ball may also start into motion sliding down the
dome--at any moment in time, and in any radial direction. This
example displays "uncaused motion" without, Norton argues,
any violation of Newton's laws, including the First Law. And it
does not, unlike some supertask examples, require an infinity of
particles. Still, many philosophers are uncomfortable with the moral
Norton draws from his dome example, and point out reasons for
questioning the dome's status as a Newtonian system (see e.g.
Malament (2007)).


### 4.2 Special Relativistic physics



Two features of special relativistic physics make it perhaps the most
hospitable environment for determinism of any major theoretical
context: the fact that no process or signal can travel faster than the
speed of light, and the static, unchanging spacetime structure. The
former feature, including a prohibition against tachyons (hypothetical
particles travelling faster than
 light)[5]),
 rules out space invaders and other unbounded-velocity systems. The
latter feature makes the space-time itself nice and stable and
non-singular--unlike the dynamic space-time of General
Relativity, as we shall see below. For source-free electromagnetic
fields in special-relativistic space-time, a nice form of Laplacean
determinism is provable. Unfortunately, interesting physics needs more
than source-free electromagnetic fields. Earman (1986) ch. IV surveys
in depth the pitfalls for determinism that arise once things are
allowed to get more interesting (e.g. by the addition of particles
interacting gravitationally).



### 4.3 General Relativity (GTR)



Defining an appropriate form of determinism for the context of general
relativistic physics is extremely difficult, due to both foundational
interpretive issues and the plethora of weirdly-shaped space-time
models allowed by the theory's field equations. The simplest way
of treating the issue of determinism in GTR would be to state flatly:
determinism fails, frequently, and in some of the most interesting
models. Here we will briefly describe some of the most important
challenges that arise for determinism, directing the reader yet again
to Earman (1986, 2007), and also Earman (1995) for more depth.


#### 4.3.1 Determinism and manifold points



In GTR, we specify a model of the universe by giving a triple of three
mathematical objects, <*M,
**g**,**T***>. *M* represents
a continuous "manifold": that means a sort of unstructured
space (-time), made up of individual points and having smoothness or
continuity, dimensionality (usually, 4-dimensional), and global
topology, but no further structure. What is the further structure a
space-time needs? Typically, at least, we expect the time-direction to
be distinguished from space-directions; and we expect there to be
well-defined distances between distinct points; and also a determinate
*geometry* (making certain continuous paths in *M* be
straight lines, etc.). All of this extra structure is coded into
**g**, the metric field. So *M* and
**g** together represent space-time. **T**
represents the matter and energy content distributed around in
space-time (if any, of course).



For mathematical reasons not relevant here, it turns out to be
possible to take a given model spacetime and perform a mathematical
operation called a "hole diffeomorphism" *h\** on
it; the diffeomorphism's effect is to shift around the matter
content **T** and the metric **g** relative
to the continuous manifold
 *M*.[6]
 If the diffeomorphism is chosen appropriately, it can move around
**T** and **g** after a certain time *t =
0*, but leave everything alone before that time. Thus, the new
model represents the matter content (now *h\**
**T**) and the metric (*h\****g**) as
differently located relative to the points of *M* making up
space-time. Yet, the new model is also a perfectly valid model of the
theory. This looks on the face of it like a form of indeterminism:
GTR's equations do not specify how things will be distributed in
space-time in the future, even when the past before a given time
*t* is held fixed. See
 Figure 5:



![Holediffeomorphismshifts contents of spacetime](hole-diffeo-new.jpg)

Figure 5: "Hole"
diffeomorphism shifts contents of spacetime




Usually the shift is confined to a finite region called *the
hole* (for historical reasons). Then it is easy to see that the
state of the world at time *t = 0* (and all the history that
came before) does not suffice to fix whether the future will be that
of our first model, or its shifted counterpart in which events inside
the hole are different.



This is a form of indeterminism first highlighted by Earman and Norton
(1987) as an interpretive philosophical difficulty for realism about
GTR's description of the world, especially the point manifold
*M*. They showed that realism about the manifold as a part of
the furniture of the universe (which they called "manifold
substantivalism") commits us to an automatic indeterminism in
GTR (as described above), and they argued that this is unacceptable.
Note that this indeterminism, unlike most others we are discussing in
this section, is empirically undetectable: our two models
<*M*, **g**, **T**> and the
shifted model <*M*, *h\****g**,
*h\****T**> are empirically
indistinguishable.



A huge range of responses to the Hole Argument have been published
since 1989; after an initial burst of articles in the late 1980s and
early-mid 1990s, there was a relatively quiet period, followed by a
revival of interest from 2011 onward (see
 the hole argument
 for in-depth consideration of a number of responses to the argument).
One popular family of responses (e.g., Hoefer 1996, Pooley 2006)
departs from the observation that the differences represented by the
models <*M*, **g**, **T**> and
<*M*, *h\****g**,
*h\****T**> are purely *haecceitistic*
and therefore may be rejected if one adopts an anti-haecceitistic
metaphysics. Following Belot & Earman (2001), anti-haecceitist
substantivalism is sometimes called "sophisticated
substantivalism".


#### 4.3.2 Singularities



The separation of space-time structures into manifold and metric (or
connection) facilitates mathematical clarity in many ways, but also
opens up Pandora's box when it comes to determinism. The
indeterminism of the Earman and Norton hole argument is only the tip
of the iceberg; singularities make up much of the rest of the berg. In
general terms, a singularity can be thought of as a "place where
things go bad" in one way or another in the space-time model.
For example, near the center of a Schwarzschild black hole, curvature
increases without bound, and at the center itself it is undefined,
which means that Einstein's equations cannot be said to hold,
which means (arguably) that this point does not exist as a part of the
space-time at all! Some specific examples are clear, but giving a
general definition of a singularity, like defining determinism itself
in GTR, is a vexed issue (see the entry on 
 singularities and black holes
 and Earman (1995) for extensive treatments; Callender and Hoefer
(2001) gives a brief overview). We will not attempt here to catalog
the various definitions and types of singularity.



Different types of singularity bring different types of threat to
determinism. In the case of ordinary black holes, mentioned above, all
is well outside the so- called "event horizon", which is
the spherical surface defining the black hole: once a body or light
signal passes through the event horizon to the interior region of the
black hole, it can never escape again. Generally, no violation of
determinism looms outside the event horizon; but what about inside?
Some black hole models have so-called "Cauchy horizons"
inside the event horizon, i.e., surfaces beyond which determinism
breaks down.



Another way for a model spacetime to be singular is to have points or
regions go missing, in some cases by simple excision. Perhaps the most
dramatic form of this involves taking a nice model with a space-like
surface *t* = *E* (i.e., a well-defined part of the
space-time that can be considered "the state state of the world
at time *E*"), and cutting out and throwing away this
surface and all points temporally later. The resulting spacetime
satisfies Einstein's equations; but, unfortunately for any
inhabitants, the universe comes to a sudden and unpredictable end at
time *E*. This is too trivial a move to be considered a real
threat to determinism in GTR; we can impose a reasonable requirement
that space-time not "run out" in this way without some
physical reason (the spacetime should be "maximally
extended"). For discussion of precise versions of such a
requirement, and whether they succeed in eliminating unwanted
singularities, see Earman (1995, chapter 2).



The most problematic kinds of singularities, in terms of determinism,
are *naked singularities* (singularities not hidden behind an
event horizon). When a singularity forms from gravitational collapse,
the usual model of such a process involves the formation of an event
horizon (i.e. a black hole). A universe with an ordinary black hole
has a singularity, but as noted above, (outside the event horizon at
least) nothing unpredictable happens as a result. A naked singularity,
by contrast, has no such protective barrier. In much the way that
anything can disappear by falling into an excised-region singularity,
or appear out of a white hole (white holes themselves are, in fact,
technically naked singularities), there is the worry that anything at
all could pop out of a naked singularity, without warning (hence,
violating determinism *en passant*). While most white hole
models have Cauchy surfaces and are thus *arguably*
deterministic, other naked singularity models lack this property.
Physicists disturbed by the unpredictable potentialities of such
singularities have worked to try to prove various *cosmic
censorship hypotheses* that show--under (hopefully) plausible
physical assumptions--that such things do not arise by stellar
collapse in GTR (and hence are not liable to come into existence in
our world). To date no very general and convincing forms of the
hypothesis have been proven (see the entry on 
 singularities and black holes,
 section 4) so the prospects for determinism in GTR as a mathematical
theory do not look terribly good.


### 4.4 Quantum mechanics



As indicated above, QM is widely thought to be a strongly
non-deterministic theory. Popular belief (even among most physicists)
holds that phenomena such as radioactive decay, photon emission and
absorption, and many others are such that only a
*probabilistic* description of them can be given. The theory
does not say what happens in a given case, but only says what the
probabilities of various results are. So, for example, according to QM
the fullest description possible of a radium atom (or a chunk of
radium, for that matter), does not suffice to determine when a given
atom will decay, nor how many atoms in the chunk will have decayed at
any given time. The theory gives only the probabilities for a decay
(or a number of decays) to happen within a given span of time.
Einstein and others thought that this was a defect of the theory that
should eventually be removed, perhaps by a supplemental *hidden
variable*
 theory[7]
 that restores determinism; but subsequent work showed that no such
hidden variables account could exist. At the microscopic level the
world is ultimately mysterious and chancy.



So goes the story; but like much popular wisdom, it is partly mistaken
and/or misleading. Ironically, quantum mechanics is one of the best
prospects for a genuinely deterministic theory in modern times.
Everything hinges on what interpretational and philosophical decisions
one adopts. The fundamental law at the heart of non-relativistic QM is
the Schrodinger equation. The evolution of a wavefunction
describing a physical system under this equation is normally taken to
be perfectly
 deterministic.[8]
 If one adopts an interpretation of QM according to which that's
it--i.e., nothing ever interrupts Schrodinger evolution, and
the wavefunctions governed by the equation tell the complete physical
story--then quantum mechanics is a perfectly deterministic
theory. There are several interpretations that physicists and
philosophers have given of QM which go this way. (See the entries on
 quantum mechanics
 for general discussion and
 Everettian quantum mechanics
 and
 many-worlds interpretation of quantum mechanicsfor
 discussion of the most prominent such interpretation).



More commonly in the 20th century--and this is part of the basis
for the popular wisdom--physicists resolved the
 quantum measurement problem
 by postulating that some process of "collapse of the
wavefunction" occurs during measurements or observations that
interrupts Schrodinger evolution. The collapse process is usually
postulated to be indeterministic, with probabilities for various
outcomes, *via* Born's rule, calculable on the basis of a
system's wavefunction. The once-standard Copenhagen
interpretation of QM posits such a collapse. It has the virtue of
solving certain problems such as the infamous Schrodinger's
cat paradox, but few philosophers or physicists can take it very
seriously unless they are instrumentalists about the theory. The
reason is simple: the collapse process is not physically well-defined,
is characterised in terms of an anthropomorphic notion
(*measurement*) and feels too *ad hoc* to be a
fundamental part of nature's
 laws.[9] In recent decades, it is more common to preset the
"collapse of the wavefunction" as a merely
*effective* or *apparent* phenomenon, usually by
appealing to some sort of "decoherence" that renders the
continuing existence of superpositions empirically undetectable. On
this approach, the deterministic and unitary evolution of quantum
states is not interrupted (see the entry on the
 many-worlds interpretation of quantum mechanics).



In 1952 David Bohm created an alternative theoretical framework for
non-relativistic QM that realizes Einstein's dream of a hidden
variable theory, restoring determinism and definiteness to
micro-reality. In
 Bohmian quantum mechanics,
 unlike other interpretations, it is postulated that all particles
have, at all times, a definite position and velocity. In addition to
the Schrodinger equation, Bohm posited a *guidance
equation* that determines, on the basis of the system's
wavefunction and particles' initial positions and velocities,
what their future positions and velocities should be. As much as any
classical theory of point particles moving under force fields, then,
Bohm's theory is deterministic. Amazingly, he was also able to
show that, as long as the statistical distribution of initial
positions and velocities of particles are chosen so as to meet a
"quantum equilibrium" condition, his theory is empirically
equivalent to standard Copenhagen QM. However, and unfortunately, as
Wallace (2020) has forcefully argued, Bohmian mechanics and its later
extensions do not yet offer an alternative to the standard quantum
field theories of the Standard Model of particle physics. One approach
to extending Bohmian mechanics to general quantum field theories, that
of John Bell, changes the theory to being stochastic rather than
deterministic.



This small survey of determinism's status in some prominent
physical theories, as indicated above, does not really tell us
anything about whether determinism is true of our world. Instead, it
raises a couple of further disturbing possibilities for the time when
we do have the Final Theory before us (if such time ever comes):
first, we may have difficulty establishing whether the Final Theory is
deterministic or not--depending on whether the theory comes
loaded with unsolved interpretational or mathematical puzzles. Second,
we may have reason to worry that the Final Theory, if indeterministic,
has an empirically equivalent yet deterministic rival (as illustrated
by Bohmian quantum mechanics.)



## 5. Chance and Determinism



Some philosophers maintain that if determinism holds in our world,
then there are no *objective chances* in our world. And often
the word 'chance' here is taken to be synonymous with
'probability', so these philosophers maintain that there
are no non-trivial objective probabilities for events in our world.
(The caveat "non-trivial" is added here because on some
accounts, under determinism, all future events that actually happen
have probability, conditional on past history, equal to 1, and future
events that do not happen have probability equal to zero. Non-trivial
probabilities are probabilities strictly between zero and one.)
Conversely, it is often held, if there are laws of nature that are
irreducibly probabilistic, determinism must be false. (Some
philosophers would go on to add that such irreducibly probabilistic
laws are the basis of whatever genuine objective chances obtain in our
world.)



The discussion of quantum mechanics in section 4 shows that it may be
difficult to know whether a physical theory postulates genuinely
irreducible probabilistic laws or not. If a Bohmian version of QM is
correct, then the probabilities dictated by the Born rule are not
irreducible. If that is the case, should we say that the probabilities
dictated by quantum mechanics are not objective? Or should we say that
we need to distinguish 'chance' and
'probability' after all--and hold that not all
objective probabilities should be thought of as objective
*chances*? The first option may seem hard to swallow, given the
many-decimal-place accuracy with which such probability-based
quantities as half-lives and cross-sections can be reliably predicted
and verified experimentally with QM.



Whether objective chance and determinism are really incompatible or
not may depend on what view of the nature of laws is adopted. On a
*"pushy explainers"* view of laws such as that
defended by Maudlin (2007), probabilistic laws are interpreted as
irreducible dynamical transition-chances between allowed physical
states, and the incompatibility of such laws with determinism is
immediate. But what should a defender of a Humean view of laws, such
as the BSA theory (section 2.4 above), say about probabilistic laws?
The first thing that needs to be done is explain how probabilistic
laws can fit into the BSA account at all, and this requires
modification or expansion of the view, since as first presented the
only candidates for laws of nature are true universal generalizations.
If 'probability' were a univocal, clearly understood
notion then this might be simple: We allow universal generalizations
whose logical form is something like: "Whenever conditions
*Y* obtain, Pr(*A*) = *x*". But it is not
at all clear how the meaning of 'Pr' should be understood
in such a generalization; and it is even less clear what features the
Humean pattern of actual events must have, for such a generalization
to be held true. (See the entry on
 interpretations of probability
 and Lewis (1994).)



Humeans about laws believe that what laws there are is a matter of
what patterns are there to be discerned in the overall mosaic of
events that happen in the history of the world. It seems plausible
enough that the patterns to be discerned may include not only strict
associations (whenever *X*, *Y*), but also stable
statistical associations. If the laws of nature can include either
sort of association, a natural question to ask seems to be: why
can't there be non-probabilistic laws strong enough to ensure
determinism, and on top of them, probabilistic laws as well? If a
Humean wanted to capture the laws not only of fundamental theories,
but also non-fundamental branches of physics such as (classical)
statistical mechanics, such a peaceful coexistence of deterministic
laws plus further probabilistic laws would seem to be desirable.
Loewer (2004), Frigg & Hoefer (2015) and Hoefer (2019) offer forms
of this peaceful coexistence that can be achieved within a Humean
account of laws.



## 6. Determinism and Human Action



In the introduction, we noted the threat that determinism seems to
pose to human free agency. It is hard to see how, if the state of the
world 1000 years ago fixes everything I do during my life, I can
meaningfully say that I am a free agent, the author of my own actions,
which I could have freely chosen to perform differently. After all, I
have neither the power to change the laws of nature, nor to change the
past! So in what sense can I attribute freedom of choice to
myself?



Philosophers have not lacked ingenuity in devising answers to this
question. There is a long tradition of
 compatibilists
 arguing that freedom is fully compatible with physical determinism; a
prominent recent defender is John Fischer (1994, 2012). Hume went so
far as to argue that determinism is a *necessary condition* for
freedom--or at least, he argued that some causality principle
along the lines of "same cause, same effect" is required.
There have been equally numerous and vigorous responses by those who
are not convinced. Can a clear understanding of what determinism is,
and how it tends to succeed or fail in real physical theories, shed
any light on the controversy?



Physics, particularly 20th century physics, does have one
lesson to impart to the free will debate; a lesson about the
relationship between *time* and determinism. Recall that we
noticed that the fundamental theories we are familiar with, if they
are deterministic at all, are time-symmetrically deterministic. That
is, earlier states of the world can be seen as fixing all later
states; but equally, later states can be seen as fixing all earlier
states. We tend to focus only on the former relationship, but we are
not led to do so by the theories themselves.



Nor does 20th (21st) century physics countenance
the idea that there is anything ontologically special about the past,
as opposed to the present and the future. In fact, it fails to use
these categories in any respect, leading some philosophers to argue
that they are merely perspectival and, in a physical sense,
 illusory.[10]
 So there is no support in physics for the idea that the past is
"fixed" in some way that the present and future are not,
or that it has some ontological power to constrain our actions that
the present and future do not have. It is not hard to uncover the
reasons why we naturally do tend to think of the past as special, and
assume that both physical causation and physical explanation work only
in the past present/future direction (see the entry on
 thermodynamic asymmetry in time).
 But these pragmatic matters have nothing to do with fundamental
determinism. If we shake loose from the tendency to see the past as
special, when it comes to the relationships of determination, it may
prove possible to think of a deterministic world as one in which each
part bears a determining--or partial-determining--relation
to other parts, but in which no particular part (region of space-time,
event or set of events, ...) has a special, privileged determining
role that undercuts the others. Hoefer (2002a), Ismael (2016), and
Loewer (2020, Other Internet Resources) use such considerations to
argue in distinct but closely related ways for the compatiblity of
determinism with human free agency.