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David Layzer's Theory of Free Will
The Arrow of Time
As early as 1971, in an unpublished manuscript on The Arrow of Time, Layzer wrote about the connection between indeterminacy and ethics.
We regard the future as being radically different from the past. We know the past through tangible records, including those contained in our own nervous systems, but we can only make more or less incomplete predictions about the future. Moreover, we believe that we cannot change the past but that we can influence the future, and we base our ethical and judicial systems on this premise. For such notions as praise and blame, reward and punishment, would be meaningless if the future were not only unknown but also in some degree indeterminate. Cosmogenesis
Layzer may have first written on human freedom in his 1990 book Cosmogenesis.
In his concluding chapter, Layzer discusses the problem of human freedom and especially creativity. Although he offers no resolution of the free will problem, he places great emphasis on an unpredictable creativity as the basis of both biological evolution and human activity in a universe with an open future.
To be fully human is to be able to make deliberate choices. Other animals sometimes have, or seem to have, conflicting desires, but we alone are able to reflect on the possible consequences of different actions and to choose among them in the light of broader goals and values. Because we have this capacity we can be held responsible for our actions; we can deserve praise and blame, reward and punishment. Values, ethical systems, and legal codes all presuppose freedom of the will. So too, as P. F. Strawson has pointed out, do "reactive attitudes" like guilt, resentment, and gratitude. If I am soaked by a summer shower I may be annoyed by my lack of foresight in not bringing an umbrella, but I don't resent the shower. I could have brought the umbrella; the shower just happened. Freedom has both positive and negative aspects. The negative aspects — varieties of freedom from — are the most obvious. Under this heading come freedom from external and internal constraints. The internal constraints include ungovernable passions, addictions, and uncritical ideological commitments. The positive aspects of freedom are more subtle. Let's consider some examples. 1. A decision is free to the extent that it results from deliberation. Absence of coercion isn't enough. Someone who bases an important decision on the toss of a coin seems to be acting less freely than someone who tries to assess its consequences and to evaluate them in light of larger goals, values, and ethical precepts. 2. Goals, values, and ethical precepts may themselves be accepted uncritically or under duress, or we may feel free to modify them by reflection and deliberation. Many people don't desire this kind of freedom and many societies condemn and seek to suppress it. Freedom and stability are not easy to reconcile, and people who set a high value on stability tend to set a correspondingly low value on freedom. But whether or not we approve of it, the capacity to reassess and reconstruct our own value systems represents an important aspect of freedom. 3. Henri Bergson believed that freedom in its purest form manifests itself in creative acts, such as acts of artistic creation. Jonathan Glover has argued in a similar vein that human freedom is inextricably bound up with the "project of self-creation." The outcomes of creative acts are unpredictable, but not in the same way that random outcomes are unpredictable. A lover of Mozart will immediately recognize the authorship of a Mozart divertimento that he happens not to have heard before. The piece will "sound like Mozart." At the same time, it will seem new and fresh; it will be full of surprises. If it wasn't, it wouldn't be Mozart. In the same way, the outcomes of self-creation are new and unforeseeable, yet coherent with what has gone before. Although philosophical accounts of human freedom differ, they differ surprisingly little. On the whole, they complement rather than conflict with one another.Recently, Layzer has written two more papers on Free Will, "Naturalizing Libertarian Free Will," and "Free Will as a Scientific Problem." Naturalizing Libertarian Free Will
In an unpublished 2010 paper on free will entitled Naturalizing Libertarian Free Will (Word doc), Layzer describes how his strong cosmological principle adds a new and fundamental form of objective indeterminacy to the world. Indeterminacy is necessary, he says, to eliminate the presumption of determinism (which is incompatible with libertarian free will) and make room for indeterminism. Note that Layzer's indeterminacy enters physics not through the measurement postulate of quantum mechanics that applies in the microscopic domain, but via a cosmological condition he calls his strong cosmological principle that comes from the astronomical domain of an assumed infinite universe.
The proposition that physical laws and antecedent conditions determine the outcomes of all physical processes (other than quantum measurements) is widely regarded as the cornerstone of a naturalistic worldview. Defenders of libertarian free will who accept this proposition must therefore choose between two options:Layzer's strong cosmological principle introduces a new kind of objective indeterminacy. It implies that macroscopic phenomena involve objective, non-epistemic, chance.(1) They can argue (against prevailing opinion among neurobiologists) that some brain processes involved in choice and decision-making are, in effect, quantum measurements – that is, that they involve interactions between a microscopic system initially in a definite quantum state and a macroscopic system that registers some definite value of a particular physical quantity. (2) They can argue that our current physical laws – specifically, the laws of quantum mechanics – need to be revised. For example, the physicist Eugene Wigner has argued that Schrödinger’s equation must be modified to account for certain conscious processes (perceiving the outcome of a quantum measurement). This paper explores a third possibility: that the presumption of determinism is false. (p.2) It entails a picture of the physical universe in which chance prevails in the macroscopic domain (and hence in the world of experience). Because chance plays a key role in the production of genetic variation and in natural selection itself, evolutionary biologists have long advocated such a picture. Chance also plays a key role in other biological processes, including the immune response and visual perception. I argue that reflective choice and deliberation, like these processes and evolution itself, is a creative process mediated by indeterminate macroscopic processes, and that through our choices we help to shape the future. (p.2)Layzer is not concerned "with idealized (and often trivial) choices between two given alternatives but with what I’ve called reflective choice, in which the alternatives may not be given beforehand, or not completely given, and in which one works out and evaluates the possible consequences of each imagined alternative. Much of the work involved in such processes undoubtedly does not rise to the level of consciousness. But consciousness accompanies the parts of the process that seem to us most crucial.Layzer's "alternatives that may not be given beforehand" are generated during the first stage of our two-stage model of free will. They need a continuous source of macroscopic indeterminacy, where Layzer's source is found in the initial conditions of the universe.
The probabilistic source of a new objective indeterminacy and chance
In Layzer's strong cosmological principle (SCP), the source of indeterminacy is the absence of microscopic information in the initial conditions of the universe. Conventional statistical mechanics describes a system as in some unknown microstate, one of many compatible with the given macrostate. Layzer's SCP says that a complete description provides only a probability distribution of microstates.
These probability distributions are conventionally viewed as incomplete descriptions of systems in definite though unknown, or even unknowable, microstates. Layzer's account interprets them as complete descriptions. Because microstates evolve deterministically, the conventional interpretation implies that macroscopic systems evolve deterministically. In Layzer's view, by contrast, a macroscopic system’s initial state need not uniquely determine its subsequent states. He describes the critical difference between the statistical entropy of Ludwig Boltzmann and J. Willard Gibbs.
Boltzmann’s theory applies to ideal gases; Gibbs’s statistical mechanic applies not only to samples of an ideal gas but to any closed system of N particles governed by the laws of classical mechanics. Its quantum counterpart, quantum statistical mechanics, preserves the overall structure of Gibbs’s theory and its main theorems. Like Maxwell and Boltzmann, Gibbs identified thermodynamic equilibrium with statistical equilibrium. Boltzmann’s theory reproduces the classical thermodynamic theory of an ideal gas, with the statistical entropy of the probability distribution of a single molecule’s microstates in the role of thermodynamic entropy and a parameter that characterizes the maximum-statistical-entropy probability distribution in the role of absolute temperature. Gibbs’s theory reproduces the whole of classical thermodynamics, with the statistical entropy of the probability distribution of a closed macroscopic system’s microstates in the role of thermodynamic entropy and a parameter that characterizes the maximum-statistical-entropy probability distribution in the role of absolute temperature. So Boltzmann’s theory may appear at first sight to be a limiting case of Gibbs’s. But Boltzmann proved that the statistical entropy of the single-molecule probability distribution increases with time (unless it has already reached its largest admissible value), while Gibbs proved that the statistical entropy of the probability distribution of the microstates of the sample as a whole is constant in time. The resolution of this apparent contradiction is unproblematic. It hinges on a mathematical property of statistical entropy. The statistical entropy of an N-particle probability distribution can be expressed as the sum of two contributions. The first contribution is N times the statistical entropy of the single-particle distribution. The second contribution is associated with statistical correlations between molecules of the gas sample. The constancy of the N-particle statistical entropy is consistent with the growth of the single-particle contribution. Taken together, Boltzmann’s H theorem and Gibbs’s proof that the statistical entropy of the N-particle probability distribution is constant in time imply that the second contribution – the contribution associated with intermolecular correlations – decreases at a rate that exactly compensates the growth of the first contribution. In terms of information: the decline of single-particle information in a closed gas sample is matched by the growth of correlation information. Although Boltzmann correctly identified the thermodynamic entropy of a closed gas sample with the single-particle statistical entropy, his derivation of the H theorem – the statistical counterpart of the Second Law as applied to an ideal-gas sample – had a technical flaw. The derivation rests on an assumption (known as the Stosszahlansatz) that cannot in fact hold for a closed gas sample. A stronger form of this assumption states that correlation information – the amount by which the information of the single-molecule probability distribution, multiplied by N, falls short of the information of the N-molecule probability distribution – is permanently absent. As we’ve just seen, this assumption cannot be true, because the decay of single-molecule information creates correlation information at the same rate. So even if correlation information is initially absent, it cannot be permanently absent. The persistence of correlation information in a closed system poses a threat to the very notion of thermodynamic equilibrium. Free Will as a Scientific Problem
In his second recent paper on free will, Layzer says that "for reasons that have little to do with quantum indeterminism we have the capacity to shape the future through our choices, plans, and actions...quantum indeterminism is not the only form of indeterminism. A variety of
macroscopic processes, I will argue, have indeterminate outcomes; chance is endemic in
the macroscopic domain." (p.1)
Layzer criticizes quantum mechanics, reviewing the superposition principle (quantum wave functions are probability amplitudes with non-zero values for different states and in different positions at the same time), the axiom of measurement (expectation values predict the outcomes of many experiments), and the projection postulate (measurement collapses the wave function to a single state or location). He describes alternative interpretations for quantum mechanics that avoid the non-intuitive "collapses," by Eugene Wigner and by Hugh Everett (many-worlds).
He also discusses statistical mechanics, with the intractable problem of microscopic reversibility but macroscopic irreversibility.
Layzer then introduces his Strong Cosmological Principle, the idea that local physical variables are random probabilities dependent on the frequency of occurrence of given properties in distant similar places in the infinite universe.
The classical variables that figure in Einstein’s description of the structure and contents of spacetime are to be interpreted as random variables – mathematical objects characterized not by a definite value at each point of space-time, but by a set of possible values and corresponding probabilities. We can interpret these probabilities as relative frequencies, or proportions, in infinite samples whose members are randomly distributed throughout space.He says that "this interpretation of Einstein’s description of spacetime and its contents resolves the prima facie conflict between the deterministic character of Einstein’s field equations and the fact that quantum measurements alter the macroscopic structure of spacetime unpredictably." (p.26) Layzer's account of chance resembles in important ways an account given a century ago by Henri Poincaré, who in the 1880's discovered the phenomenon now called deterministic chaos in his studies of planetary orbits for three-body problems. The outcomes of chaotic processes depend sensitively on their initial conditions. [James Clerk Maxwell similarly discovered chaos theory in hydrodynamic flows twenty years earlier.] Poincaré showed that if the initial values of the parameters that define an orbit are smoothly distributed over a small subrange of their possible values, the possible values of these parameters at a later time will be smoothly distributed over the entire range. A historical account characterizes the initial orbital state by a joint probability distribution of positions and velocities, which evolves into a distribution that characterizes a multitude of observationally distinguishable orbits. To accommodate such situations, Layzer says he needs to modify the rule that links probability distributions of (classical or quantum) microstates to classical macrostates. The standard rule equates the value of a macroscopic variable in a given macrostate to the result of averaging the corresponding microscopic variable over the probability distribution of microstates that represents the given macrostate. We modify it in three ways. First, we characterize macrostates by experimentally distinguishable ranges (or aggregates) of microstates, as in the above examples. A probability distribution of microstates may then represent two or more experimentally distinguishable macrostates. Second, we equate the result of averaging a microscopic variable over such a probability distribution to the result of averaging the measured value of the corresponding macroscopic variable over a “large number” of replicas of the measurement. Finally, to incorporate into our rule the fact that neither physical laws nor initial and boundary conditions that comply with the strong cosmological principle serve to define a particular position, we interpret the set of replicas mentioned in the preceding paragraph as a “cosmological ensemble” – a set of replicas randomly and uniformly distributed throughout an infinite space. (Like Gibbs’s ensembles, a cosmological ensemble is made up of imaginary replicas. But each replica in a cosmological ensemble is in a definite macrostate. And cosmological ensembles have a physical interpretation: they allow us to express the assumption that physics cannot make unconditional predictions about where in the universe given measurement outcomes are realized.) These rules enable us to calculate the probabilities of experimentally distinguishable measurement outcomes from measurements of mean values. (p.28)Layzer claims that his historical account of initial conditions offers a new view of the role of chance in macroscopic processes. Physicists have conventionally held that the outcomes of macroscopic processes other than quantum measurements are predictable in principle. Some, though not all, evolutionary biologists have taken issue with this doctrine, which also seems to be at odds with judgments based on ordinary experience. But physics as conventionally interpreted assures us that to a contemporary version of the omniscient mind posited by Laplace in his essay on chance, nothing except quantum measurement outcomes would be unpredictable. The historical account of initial conditions sketched in this essay supports the contrary view suggested by evolutionary biology and experience: much of what we observe in the world around us is influenced by chance. (p.31)Layzer is then prepared to address the problem of free will. The premise of physical determinism is false, he says. Defenders of libertarian free will usually grant at the outset that events other than the outcomes of quantum measurements are determined by universal physical laws and antecedent conditions. They must then explain how it can be that we are able to shape the future through our choices and decisions. In this essay I have argued that the premise is false: Events in the macroscopic world are not determined by universal physical laws and antecedent conditions; a wide class of macroscopic processes have indeterminate outcomes. And if the processes involved in reflective choice belong to this class, there is no scientific reason why we should not accept the proposition that we shape the future through our choices and decisions... (p.36)He asks "How does free will fit into a scientific picture of the world?" (p.38) Do conscious acts of will cause our voluntary actions? From a thorough examination of the evidence bearing on this question the psychologist Daniel Wegner has concluded that the answer is no. “Conscious will arises from processes that are psychologically and anatomically distinct from the processes whereby mind creates action.” This conclusion accords well with the arguments and conclusions of the present essay.To summarize his latest paper on free will, Layzer imagines that a large assembly of similar situations in different regions of the infinite universe can provide the source of the macroscopic indeterminism needed for free will, without depending on quantum indeterminism. In each individual system, everything appears determined, but in the assembly of all systems, the strong cosmological principle insures there will be a variety of objectively indeterminate outcomes. Layzer says that the fact that we don't know which of the many possible systems we are in means that our future is indeterminate, more specifically that our current state has not been pre-determined by the initial state of the universe. Layzer does not explain specifically how the abstract indeterminacy in "cosmological ensembles" affects the human mind/brain, nor how it does not entail that our choices and actions are random (the randomness objection in the standard argument against free will). As Arthur Stanley Eddington first did in 1927, Layzer finds that his objective physical indeterminacy withdraws the determinist objection to free will. However, where Eddington's indeterminacy came from the then-new quantum mechanics, Layzer's indeterminacy comes from his strong cosmological principle, the abstract notion that there are multiple similar situations for our decisions in other locations - a "cosmological ensemble" - in the infinite universe. Layzer's "objective indeterminacy" appears to provide no more basis for a free will model than Epicurus's "swerve," William James's "chance," or Werner Heisenberg's quantum indeterminacy, without a more careful explanation of exactly how his indeterminacy figures in the two stages of the decision process. Normal | Teacher | Scholar |