Moreover, there is a burgeoning literature of physical orquasi-physical systems, usually set in the context of classicalphysics, that carry out supertasks (see Earman and Norton (1998) andthe entry on for a review). Frequently, the puzzle presented is to decide, on thebasis 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 resultcan then be seen as a failure of determinism.
A second class of determinism-breaking models can be constructed onthe basis of collision phenomena. The first problem is that ofmultiple-particle collisions for which Newtonian particle mechanicssimply does not have a prescription for what happens. (Consider threeidentical point-particles approaching each other at 120 degree anglesand colliding simultaneously. That they bounce back along theirapproach trajectories is possible; but it is equally possible for themto bounce in other directions (again with 120 degree angles betweentheir paths), so long as momentum conservation is respected.)
The popularization of chaos theory in the relatively recent pastperhaps made it seem self-evident that nature is full of genuinelychaotic systems. In fact, it is far from self-evident that suchsystems exist, other than in an approximate sense. Nevertheless, themathematical exploration of chaos in dynamical systems helps us tounderstand some of the pitfalls that may attend our efforts to knowwhether our world is genuinely deterministic or not.
The dynamical systems usually studied under the label of“chaos” are usually either purely abstract, mathematicalsystems, or classical Newtonian systems. It is natural to wonderwhether chaotic behavior carries over into the realm of systemsgoverned by quantum mechanics as well. Interestingly, it is muchharder to find natural correlates of classical chaotic behavior intrue quantum systems (see Gutzwiller 1990). Some, at least, of theinterpretive difficulties of quantum mechanics would have to beresolved before a meaningful assessment of chaos in quantum mechanicscould be achieved. For example, SDIC is hard to find in theSchrödinger evolution of a wavefunction for a system with finitedegrees of freedom; but in it is handled quite easily on the basis of particle trajectories (seeDürr, Goldstein and Zhangì 1992).
Fatalism is, according to Carter’s metaphysics textbook, is the notion that future events are necessary in the same way that past events are necessary because the past is ‘closed’ and unalterable. Fatalism holds that the future is ‘closed’ without presupposing causal determinism. Fatalism holds that any statement about the future is either true or false.
There have even been studies of paradigmatically “chancy”phenomena such as coin-flipping, which show that if startingconditions can be precisely controlled and outsideinterferences excluded, identical behavior results (see Diaconis,Holmes & Montgomery 2004). Most of these bits of evidence fordeterminism no longer seem to cut much ice, however, because of faithin quantum mechanics and its indeterminism. Indeterminist physicistsand philosophers are ready to acknowledge that macroscopicrepeatability is usually obtainable, where phenomena are solarge-scale that quantum stochasticity gets washed out. But they wouldmaintain that this repeatability is not to be found in experiments atthe microscopic level, and also that at least some failuresof repeatability (in your hard drive, or coin-flipping experiments)are genuinely due to quantum indeterminism, not just failures toisolate properly or establish identical initial conditions.
Determinism could perhaps also receive directsupport—confirmation in the sense of probability-raising, notproof—from experience and experiment. For theories (i.e.,potential laws of nature) of the sort we are used to in physics, it istypically the case that if they are deterministic, then to the extentthat one can perfectly isolate a system and repeatedly imposeidentical starting conditions, the subsequent behavior of the systemsshould also be identical. And in broad terms, this is the case in manydomains we are familiar with. Your computer starts up every time youturn it on, and (if you have not changed any files, have no anti-virussoftware, re-set the date to the same time before shutting down, andso on …) always in exactly the same way, with the same speedand resulting state (until the hard drive fails). The light comes onexactly 32 µsec after the switch closes (until the daythe bulb fails). These cases of repeated, reliable behavior obviouslyrequire some serious ceteris paribus clauses, are neverperfectly identical, and always subject to catastrophic failure atsome point. But we tend to think that for the small deviations,probably there are explanations for them in terms ofdifferent starting conditions or failed isolation, and for thecatastrophic failures, definitely there are explanations interms of different conditions.
Even if the first hurdle can be overcome, the second, namelyestablishing precisely what the actual laws are, may seem dauntingindeed. In a sense, what we are asking for is precisely what19th and 20th century physicists sometimes setas their goal: the Final Theory of Everything. But perhaps, as Newtonsaid of establishing the solar system's absolute motion, “thething is not altogether desperate.” Many physicists in the past60 years or so have been convinced of determinism's falsity, becausethey were convinced that (a) whatever the Final Theory is, it will besome recognizable variant of the family of quantum mechanicaltheories; and (b) all quantum mechanical theories arenon-deterministic. Both (a) and (b) are highly debatable, but thepoint is that one can see how arguments in favor of these positionsmight be mounted. The same was true in the 19th century,when theorists might have argued that (a) whatever the Final Theoryis, it will involve only continuous fluids and solids governed bypartial differential equations; and (b) all such theories aredeterministic. (Here, (b) is almost certainly false; see Earman(1986),ch. XI). Even if we now are not, we may in future be in aposition to mount a credible argument for or against determinism onthe grounds of features we think we know the Final Theory musthave.
In OBJECTIVISM: THE PHILOSOPHY OF AYN RAND, Peikoff never explicitly defines determinism or free will, but instead weaves a tortuous web of implied distinctions.
If my opinions are the result of the chemical processes going on in my brain, they are determined by the laws of chemistry, not those of logic." Popper identifies materialism with determinism, but both he and Haldane seem to accept this argument as a self-evident truth, which I would paraphrase "Iknow I have knowledge, therefore I know I am not determined." Descartes wouldbe proud.
As we saw above, for determinism to be true there have to besome laws of nature. Most philosophers and scientists since the17th century have indeed thought that there are. But in theface 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, withcertainty, precisely what the laws of our world are, in orderto tackle the question of determinism's truth or falsity?