Darrell Hougen

I don't think so. One can characterize a random process in terms of a probability distribution, but imagination is no substitute for empirical evidence. What do you mean by, "an empirically expanded version of the concepts of identity and causality?" That sounds a little wishy-washy. Darrell

That is a novel definition. Space is generally taken to be the absence of a thing, the absence of dirt in a hole, the absence of furniture in a room, the absence of a loved one in one's life. Space is a mental abstraction, not something that exists. Darrell

That is a very nice statement of the solopsist view. It ought to be taken as a model. However, it also reveals the weaknesses of that view. First, it is clearly necessary to redefine words such as "experience" in order to get away with your argument. The word "experience" implies experience of some thing. If there is no thing, there can be no experience. Now, you say that the solopsist will insist that "experience" actually has some other meaning than the one normally ascribed to it. But what is that meaning? If experience is generated externally, then what is the difference between experience of reality and experience generated by some external reality? If experience is something that is completely internal, then one has to posit the notion that people are completely incapable of knowing the states of their own minds. When I was a child I sometimes had dreams of being chased by monsters. Then I learned that I could tell myself before I went to bed that I was going to carry a blaster and blast the monsters my in dreams. It worked. I was actually able to affect my dreams and take control of them so that they were no longer as scary. But that doesn't work in reality. If I'm being assaulted by a criminal, I can't simply imagine that I have a blaster and blast the criminal. Or, if I'm about to have a car accident, I can't imagine that my car can fly and get away with it. Nor, can I keep myself from falling from a high place once I have actually started to fall. The problem with the solopsist point of view is that if the illusion is self created, then what is to keep the person having the delusion from controlling it? And, if it cannot be controlled, then what is the difference between the illusion and reality? I used to take your view that the solopsistic viewpoint is useless. That is one approach. But, I believe that it is worse than useless. It is fundamentally untrue. You say that you don't believe the solopsistic point of view. But the question is, why? Simply because it is useless or because it somehow fails to correspond to your experience? Although the first response is logically safe, I suspect that the true answer is really the second. The universe is not empty space, it is the total of all things that physically exist. How do you know that this total is finite? The usual reply that this total isn't a thing either doesn't hold. Consider a finite subset of the universe, this is definitely a "thing", with a finite number of particles. Now the question is: is there a maximal subset that does contain everything, so that there is no larger subset? In that case the subset is the universe itself and it is finite. If that is not the case, i.e. for every subset A we can find another subset B so that A is a proper subset of B (B contains at least one more element than A), then by definition the universe is infinite. Whether this is the case is an empirical question, which cannot be decided by playing with definitions.A set is not a thing. A set is a mental container with no physical reality. That is why I said that empty space is not a thing. I was viewing the universe as that which contains everything that exists. But, if you wish to call the universe the set of all things, my argument still holds because a set is a mental collection of objects. I agree that the number of objects in the universe is an empirical question but that is irrelevant to the identity axiom. The identity axiom states that everything that exists, exists in some quantity. It does not state that the collection of all things is finite. Some Objectivists may take that view, but it is certainly not my view nor do I think it is warranted. I agree. I just don't want to get into that debate right now. I guess I'm not aware of any evidence that causality is ever violated. Even the EPR/Bell experiments are consistent with causality. If you know of any conflicting evidence, please let me know. This is where I depart ways with Peikoff. In my view, the decay of a Uranium atom is causal in the Objectivist sense. The moment of its decay is not determinate, but the nature of the decay is still constrained. The Uranium atom still has an identity. Its behavior is not arbitrary. Darrell

I have taken a look at coherentism and so far I am unimpressed. If you would like to enlighten us further, I would be happy to listen. However, I have a few comments to make about axioms, lest we talk past each other because of a misunderstanding of the nature of axioms in Objectivism. This is from a previous post to another forum: Axioms are commonly understood in common usage and in mathematics as being synonymous with assumptions --- statements that are taken to be true for the sake of argument or before any arguing or discussion begins. The fact that mathematical axioms, for example, happen to correspond to facts of reality is taken to be coincidental and of limited interest once the debate has begun. This, unfortunately, is a completely inverted and irrational view of the true nature of axioms, both in mathematics and philosophy. An axiom is actually a summary of a large number of facts which is implicit in those facts. The Peano Axioms, for example, are a summary of arithmetic facts. It is a concise statement of infinitely many true statements such as 1 + 1 = 2, 2 + 1 = 3, 2 + 3 = 5, etc. The fact that such statements are true does not depend upon the Peano Axioms, the truth of such statements is an observational fact. If one has 2 oranges and brings in 3 more oranges, then one has 5 oranges. The statement, 2 + 3 = 5, abstracts away the oranges and the Peano Axioms summarize many such statements. Similarly, the Objectivist statement that existence exists, is simply a summary of facts of the form, an orange exists, a car exists, I exist, etc. The axiom, existence exists, does not cause all of the observational facts to be true, but it is implicit in them. The point can be further illustrated by reference to the program of David Hilbert in 1900 to axiomatize all of mathematics. He, and many other mathematicians, believed that we would eventually discover a set of axioms that would capture all mathematical knowledge. Thereafter, discovery of new mathematical truths would be a simple matter of applying the axioms to known true statements in order to deduce new ones. However, in 1931 Kurt Gödel proved that no finite set of axioms could ever summarize all mathematically true statements. In fact, he showed that there would always exist infinitely many mathematical truths that were not implicit in the axioms, no matter how large the set. Gödel's proof makes sense if axioms are viewed as summarizing statements, rather than starting points. If axioms are viewed as starting points, then it is tempting to think that the only true statements are the ones implied by the axioms. But, if they are viewed as summary statements, then it is not surprising that it is impossible to give a concise summary of all possible knowledge. The conclusion is that the axioms are not starting points. They are statements that are taken to be true because they are implicit in all knowledge. Any attempt to refute them, requires their use, as does any attempt to justify them. Because they are implicit in all knowledge, they are inescapable and irrefutable. Darrell

I don't see how my usage differs from Michael's usage. Darrell

Hmmmm. I must resist the urge ... Seriously, you should ask yourself whether that is a meaningful question in the context of the current discussion. Darrell

This is not just the opinion of some Objectivists, it is the official doctrine, and it is one of the big holes in Objectivist theory.I won't disagree with you here, although it appears that some big name Objectivists hedge. They don't come right out and say that the world is deterministic because they know what that would imply for the concept of free will. Again, I agree. However, no one has ever produced a satisfactory explanation of free will, so I have to give them credit for at least defending the empirical evidence. It would be easy to give up free will because of its apparent contradiction of the laws of physics, whether they be deterministic or random, except for the fact that free will evidently exists. If volitional consciousness were not possible, the debate that we are having right now would be completely meaningless because neither of us would have any choice about it. The fact that the law of identity does not say what anything is, does not make the concept meaningless. What the law of identity says is that everything has a specific nature. That may seem so obvious as to not be worth mentioning, but let's consider the history of philosophy. Both the mystics and the subjectivists ignore the law of identity. The mystics believe in certain supernatural beings. The implication of "supernatural" is that the being is above nature or that the being has no particular nature. The being is capable of defying the laws of nature and is sometimes said to have the ability do anything, to know everything to see everything, etc. The subjectivists, on the other hand believe that existence is dependent upon consciousness. That something is so just because someone wants it to be so. The naming of things is an arbitrary social convention. Nature has no identity outside of the human mind. It could all be a figment of the imagination, etc. These considerations might seem rather far removed from the modern scientific world, and to the degree that they are, it only serves to prove the efficacy of the law of identity. However, much of the "mystery" surrounding modern physics is evidently a result of the temporary abandonment of the law of identity. It is the result of a lapse into subjectivism --- the notion that the state of a physical system depends upon the performance of a measurement or even the observation of a conscious mind. The law of identity is a subject of metaphysics, not physics. It tells you nothing about any particular physical system. It only informs you of the possibility of understanding that system. It tells you that the system has specific properties and that, if you are sufficiently clever, those properties can be identified. It doesn't tell you how to identify them or what they will be. Just that they will be something --- that they can be specified. Existence is identity. Consciousness is the faculty of identification. Darrell

No, it doesn't. We may have good reasons to think that reality is independent of consciousness, but this tautology won't tell us. Every thing could in principle be a figment of the imagination and still be itself.Lets look at the Objectivist definition of consciousness. Consciousness is the faculty of perceiving that which exists. In order for there to be a consciousness, there has to be some thing to be conscious of. Therefore, something must exist apart from consciousness. If you disagree, posit a meaningful definition of consciousness that we can debate. The question is: what is a "property" of a system? Atomic systems may have an infinite number of bound states for example. You can't say a priori that the universe isn't infinitely large.I do not consider the universe to be a thing. Empty space is not a thing. We can certainly debate what a property is. However, that does not eliminate the obvious usefulness of such a concept. Why can't causality be violated? That is an empirical question that cannot solved by a tautology.I do not see how such a question could be answered empirically. How could you ever know whether an apparent violation of causality was a real violation of causality or just the result of a logical error? In Objectivist thought, an object has a specific nature and acts in accordance with it. That is the law of identity. In order for the law of identity to be violated, there would have to be some object that did not have a specific nature --- it could be one thing today and another thing tomorrow. No measurement would ever be stable, no characteristic ever the same. And, if such were the case, it would be impossible to reason about it because no conclusion could ever be validated. Empirical evidence would be impossible and would mean nothing. Causality is a corolary. It is the application of the law of identity to the possible actions of an object. If an object has a nature that can be specified, then its possible actions can also be specified. If it violates causality, that means its scope of action is unlimited and nothing can ever be known about it. Darrell

Can we kick this dead horse any harder? Identity is a totally empty and meaningless concept. "consistent with its nature" means nothing. This constrains the properties of something how? This guides our thinking how? It is equivalent to saying that "anything can be anything but it can't be what it's not". There is no context where the concept has any teeth. An empty tautology is worthless. In fact it's worse than worthless when it's used to defend a position (causality for one). In fact, this empty idea POLLUTES thinking. First of all, my comments were directed mainly at other Objectivists, some of whom seem to labor under the assumption that the physical world must behave deterministically in order for the identity axiom to be true. That is, if a particle has a certain identity, then it must behave in a particular manner. That statement may appear to imply that the behavior of a particle must be deterministic. It appears to imply that if it is possible to determine the initial state precisely, then that information must be sufficient to predict the exact trajectory of the particle forever afterward (unless it interacts with another particle whose initial state was not known). However, I am arguing that that is not the case. What I am saying is that if a particle is governed by a well defined probability distribution, then its behavior is still constrained in a manner consistent with the identity axiom. Its trajectory is not fully determined, but it is not completely arbitrary either. The particle still has a specific nature. The identity axiom has several important consequences. It implies, for example, that reality is independent of consciousness. Therefore, the state of a physical system is independent of whether anyone performs a measurement on that system or whether any conscious being sees the result of that measurement. The act of measurement only alters the state of the system in the sense that any interference with the system alters the state of the system. The fact that one kind of interference is called a measurement and another kind of intereference is called something else is completely irrelevant to the state of the system. The identity axiom implies that every property of a system is finite. It implies that causality cannot be violated. I would like to think that this is merely a semantic disagreement and therefore give you the benefit of the doubt on this issue, but it appears that it is your failure to grasp the existence/identity axiom that is at the root of your own confusion. In another post, you stated: You are right in stating that the notion that reality depends upon observation is an extreme violation of Objectivist principles. It is also not true. Nothing in QM demands that reality depend upon observation or even the possibility of observation and such interpretations should be avoided. Logic is impossible if existence does not have primacy over consciousness. Darrell

I am using the term "logic" in the Objectivist sense (this being an Objectivist forum), namely, "the non-contradictory identification of the facts of reality." You are free to develop whatever logic you like, so long as it does not result in the assertion of a contradiction. Whether your logic is efficacious or you end up with a lot of "don't know" answers is another issue. Now, are you saying that you wish to employ a method of reasoning in which you leave some states of your knowledge as "indeterminant"? --- In other words, is this an epistemological issue? Or are you saying that reality may itself be indeterminant? If the latter, then this isn't really a question of epistemology and therefore not an issue of logic. It is an issue of metaphysics. I do not believe that an indeterminant physical theory is required. However, I would be happy to debate that question. I'm not sure exactly what the Copenhagen Interpretation says, but I don't think I'm arguing against the modern interpretation of QM, at least as far as I can tell by reading Wikipedia articles. I know that at some point in the past, physicists used words like "measurement" or "observation" in their theories. However, a simpler explanation that appears to be consistent with QM is that the system in question must interact with one or more outside particles --- particles that are not considered part of the system under consideration. It is that interaction that causes the collapse of the wavefunction. So, for example, in the double slit experiment, it is the interaction of the electron with the slit detector that causes the collapse of the wavefunction. In the EPR/Bell experiments, it is also the interaction of the particle pair with the detectors on either side that cause the wavefunction collapse. Now, I realize that QM sometimes describes a particle or pair of particles as existing in a superposition of states so that it isn't really in either state, it is in some indeterminant state. But that is not a philosophical requirement. I would prefer to say that the particle(s) exist in a definite state described by a linear combination of wavefunctions. The idea that a particle or particles could exist in a compound state may be counterintuitive, but that is a more philosophically satisfying position than the assertion that the the state is indeterminant. The problem with stating that the state of a physical system is indeterminant is that it confuses metaphysics with epistemology. It confuses what is, with what we know about it. Hence, all the confusion about consciousness, measurements, and cats. If our experiments seem to indicate that particles are simultaneously in multiple states, then they are simultaneously in multiple states. They are not in some indeterminant state that only resolves itself when you look at it. Then I would throw out locality. According to the, "No Communication Theorem," a non-local interpretation does not violate causality. The other two cannot be escaped. Darrell

Hi Judith, Nice to make your acquaintance. Darrell

Hi Chris, it is a shame that that opportunity slipped by. I just wasn't paying attention to this group at that time. Hopefully, we'll all get a chance to meet some time. Also, I'm not opposed to meeting individuals that live in the area. Darrell

I liked Paul's response to your first point, but let me answer it another way. Information, in the mathematical sense, can be stored in a physical system. It is in that sense that every physical system can be said to possess information about its past states and, in a closed system, information about its future states. There was a mind bender going around at the time I was in college that stated that all of the information in the Library of Congress could be stored in a single block of aluminum. Simply convert all of the words in all of the books into numbers, string them out to create a single large number and put a decimal point in front of that number. Then, cut the block of aluminum to that length in inches. To recover the information, simply measure the block. Now, clearly that is not possible, for any number of reasons. But, fundamentally, there is a limit to the amount of information that can be stored in any device because no physical system can possess an infinite amount of information about its state. As far as analog versus digital goes, the argument is a red herring that has been refuted long ago. A digital system can approximate an analog system to any desired degree of accuracy and in light of the above argument, there is a limit to the number of digital bits required to represent all of the information contained in an analog system. Besides, who says AI is impossible? As to your second paragraph, are you saying that all of the elementary particles can be created by repeatedly blasting an atom? Of course, blasting the atom requires energy at the very least and one could say that all of existence is present in a sufficient amount of energy. I view particles as being stable energy states (in some sense). Matter and energy are interchangeable. Of course, the reality that emerged from another big bang might be very different from the current one, especially if one believes in fundamental randomness. Darrell

Thanks for the catch and the fix, or the fix and the catch. I'll examine my qoutes more closely next time. :-P Darrell

The problem with this approach is that philosophers such as Kant have created vast philosophies for doubting the efficacy of the human mind based on their interpretation of the physical world. If man's mind is not competent to know anything about the natural world, then how can be competent to inform man's moral choices? If man cannot be sure of the identity of anything or even sure that anything exists, how can he make moral decisions? If a thing behaves one way today and another way tomorrow, how can man know the effects of his actions and which are the proper ones to take? That is why this discussion of constrained randomness is so important. It appears that some physical system behave in a random way, but that action is still consistent with the nature of the entity in question. The entity still has an identity. It still behaves in a manner that is consistent with its nature. So, man's mind is still efficacious in understanding its behavior. And, man can still make value judgments about things that exist. Darrell

I am trying to develop an Objectivist argument that is non-classical. I do not believe that determinism is required by Objectivism. In fact, I have argued that it is incompatible with Objectivism because it requires the existence of a physical system capable of storing an infinite amount of information, which contradicts the identity axiom. Neither logic nor reality are on the table. Existence has primacy over consciousness. Nothing in QM, properly understood, requires an actual conscious observer. The behavior of electrons in the double slit experiment is independent of whether anyone is actually watching them. Moreover, no contradictions can exist in reality. Reality simply is what it is and it could not be otherwise. It is not contingent on any observation. I'm not saying what I'm saying just because Rand said it. What you are basically advocating is an anything goes philosophy. If logic is on the table, then I can say anything I want and you cannot refute it. You cannot debate anyone. You cannot know anything at all. You cannot even know that you cannot know anything. You are verging on the embrace of a contradiction. People attempt to make things more "profound" than they are in order to make them sound mysterious, that is mystical. There is nothing mystical about the laws of nature, even if they involve randomness. Darrell P.S. I cannot seem to fix the quotes in this post. Sorry for the appearance. (Note from MSK: Sorry to intrude, but I fixed it. You had misspelled one of the code words - quote was spelled as qoute.)

I have been trying to come up to speed on the current understanding of quantum mechanics, at least in a philosophical sense, so that I can understand how it relates to Objectivism. I took one class in quantum mechanics as an undergrad, so I know something of the theory, but we never discussed interpretations of QM or Shrodinger's cat, or the Bell inequalities, so I apologize for any ignorance of the subject. First, let's start with the Bell inequalities. My understanding is that a Bell inequality should hold for any system in which a pair of particles act independently. There is a limit to the correlation between sets of particle pairs that is a simple result of the assumption of statistical independence. Consequently, in any situation in which the states of two particles depends only upon a hidden variable, there is also a limit on the correlation. However, the quantum mechanical description of a pair of particles that form a singlet state implies that two such particles are not independent, at least until they interact with the environment. Therefore, they may be more highly correlated than is permitted by a hidden variable theory. Let me be more specific. If a pair of particles forming a singlet state are emitted in opposite directions, and the state of one is measured by a detector, then, according to QM, that measurement affects the measurement of the other particle by another detector some distance away. Moreover, that effect is instantaneous. In any theory in which one measurement is not allowed to instantaneously affect the other one, a Bell inequality must hold. However, Bell inequalities are violated by actual experiments. The reason that no information is communicated by this process is that only the correlation of the measurements is affected. However, to determine the correlation, one must compare the states of the two particles which requires communicating information at a speed that is less than or equal to the speed of light. So far so good? I'm not sure I stated everything perfectly. The next question is, what is the physical reality of the wave? In QM, the wave is often described as a probability wave. But the double slit experiment implies to me that the wave has actual physical existence. There is clearly something that goes through both slits. It may be that at any one time, the mass and charge of the electron only goes through one slit, though we don't know which one, but some aspect of the electron goes through both. The same thing could be said of the two-particle-singlet. It appears that the two particles actually share something in common that stretches between them until at least one of them interacts with another particle. At that point, the connection is severed. But is that connection something that actually exists? Another question is whether a system exists in a specific state at every moment in time. The usual interpretation of QM seems to imply that it doesn't, but I find that philosophically unsatisfying. In fact, I don't know of any physical evidence that a system doesn't exist in a particular state. With the double slit experiment, we can imagine that the mass and charge of an electron goes through one slit or the other on every trial and that it is just the wave that goes through both. That does not appear to contradict any of the evidence. The Bell/EPR experiments could be interpreted in a similar light. Another question: Is randomness physically real? I would say that it is. All of the experimental evidence seems to be consistent with that notion. Moreoever, I don't think this causes any conflicts with Objectivism. An electron must still behave in accordance with its nature. Its randomness is limited. It can't spontaneously turn into a physics professor lecturing at Cal Tech. It can only hit the screen at some point allowed by its probability distribution. But, that leads to Schrodinger's cat. Although the original description makes no sense in that there isn't a simple wave function with one degree of freedom describing the state of his cat, it is still disturbing that QM allows for the possibility of very low probability events. For example, all of the air suddenly rushing to one side of the room because all of the air molecules just happened to be going the same direction at the same time. (I guess that is classically allowed too). The fact that the probability is very low is not that comforting. Rather, I would suspect that beyond some point, the probability is identically zero. Perhaps something like Shannon's cummunication theorem holds --- if the information transmitted is less than the channel capacity, then the probability of error goes to zero. Or, perhaps it is the phenomenon of wave function collapse. At least wave function collapse seems to imply that the system can't be infinitely entangled. Only certain limited entanglements are permitted. Darrell

Hi Martin, here is a link to a paper that describes a non-deterministic physical system: http://www.citebase.org/fulltext?format=ap...o-dyn%2F9402004 Of course, the equations only describe a model of the system. It may be that a more refined model would not be non-deterministic in the classical sense. However, I think it is instructive to examine what the paper actually says: First, it should be noted that, according to the paper, the time evolution of a system is not completely determined in the classical sense if the differential equations describing the system fail to satisfy the Lipschitz condition. Second, although the behavior may only be indeterminant if the system actually passes through the singular point, it will be nearly indeterminant near the singular point. Classically, that may not amount to indeterminism, but it would appear to be a route for quantum randomness to affect the behavior of a macroscopic system rather directly. As a side note, I will try to address everyone's responses to my earlier posts as I have time. Darrell

How? In common usage they certainly cannot. The electromagnetic waves transmitting information to my television set don't transmit an infinite amount of information and I don't think it is fundamentally possible for them to do so. I do, but I am racking my brain to find a way to communicate it.Well, as you can see, I'm very interested in this topic so I'd love to hear your explanation. Metaphysical randomness won't get you there. Stepping outside of the action-to-action causal paradigm is the first step. I guess I don't see myself as stuck in that paradigm. Maybe you can help me see why you think I am. Darrell

That would true only if an ensemble of particles behaved as a collection of independent particles. If the joint probability distribution were non-trivial, some sort of epiphenomenal behavior might arise. Darrell

Michael, I'm not sure I understand the fundamental problem here. There is quite a bit of science dedicated to learning how constructive forces create macroscopic entities in certain cases. For example, astronomers seek to explain how the sun and stars were created from hydrogen atoms. Biologists seek to understand how trees grow and take the shapes that they do. There are many unexplained creation processes, and perhaps some philosophical issues that need to be resolved, but I'm not sure what you're driving at. The idea of top-down contruction seems backwards to me. However, I could imagine forces that only become apparent when an entity has reached a certain size or mass or level of complexity and that those forces could shape the final creation. For example, I'm pretty sure that gravity plays a role in shaping a developing person. At small scales, electronic forces are probably much stronger than the pull of gravity and the development of an embryo in the early stages is largely unaffected by it. However, the length of a person's legs, thickness of their bones and strength of their muscles is undoubted affected by gravity. Gravity is an external effect, but one might imagine that the shapes of various parts are affected by fluid pressure which, again, is negligible at a small scale but becomes more pronounced as the organism grows. So, there could well be "forces' that shape mental development that only become apparent at later stages of development. In my opinion, for metaphysical randomness to be possible at the higher stages, it must be possible at the lower. I don't think I have contradicted what I said above because none of the forces that I mentioned above were non-existant at the microscopic level, they just didn't have a significant effect until the higher levels of development. Randomness, in my view, must be the same. Darrell

So, Dragonfly, I would like to know what you think the difference is between predictability and determinism. Is a system, in your view, unpredictable simply because it is impossible to measure the initial conditions with perfect accuracy? Or is there a deeper dichotomy? Darrell

I'm not sure I understand this. It appears that you are saying that action-to-action causation is necessary for metaphysical randomness but yet that randomness is not caused by the actions of other things. How is that possible? It appears that you are contradicting yourself. In my view, metaphysical randomness is more fully consistent with an entity-to-action view of causality exactly because a random behavior is a behavior that cannot be predicted from knowledge of the behavior of the other entities with which an object interacts. The behavior comes from the entity itself. This naturally leads to a question about how such behavior can be consistent with the laws of physics such as conservation of energy, conservation of momentum, etc. But this can be handled if we assume that a particle, for example, transfers some of its momentum and energy to another particle when it changes course. For example, in the thin slit experiment in which electrons are beamed at a target on the other side of a grating, the electrons can be assumed to transfer some momentum to the grating as they pass through, thereby conserving momentum within the system. Darrell

Actually, it turns out that there are some systems that are governed by non-deterministic sets of equations. There are infinitely many solutions at a single point so that it doesn't matter whether infinite accuracy is possible or not. The solution at the singularity cannot be resolved. In my post, I sort of glided from that observation into an information theoretic argument which is, in some sense, an argument of modern rather than classical physics. However, I would argue that the notion that particles exist with mathematically exact parameters (location, momentum, etc.) and that have perfectly deterministic trajectories violates the law of identity. If we view a particle or system of particles as a system possessing a certain amount of information about its state, then, because it would require an infinite amount of information to give the particles mathematically precise locations and trajectories, the system would be required to possess an infinite amount of some quantity (namely, information) which violates the law of identity. Now, it could be argued that I am mixing the epistemological with the metaphysical because information content is not really a property of a physical system. However, I would disagree with that assessment. As we know, living in the modern, computer age, physical systems can be used to store and transmit information, e.g., disk drives and communications links. Slightly more broadly, any physical system can be used to store information. Indeed, every physical system stores information about its state. Some systems store a lot of information about their past states, but are very hard to predict. Other systems are easy to predict, but store little information about their past states. Still other systems are somewhere in between. That is part of Chaos theory. But, in the end, the amount of information that a system is capable of storing is finite. That is a physical fact which is predictable from the law of identity. On this view then, the classical notion of metaphysical determinism is inconsistent with the law of identity. I do not believe that living things, and humans in particular, have some quality that is unexplainable in terms of the fundamental constituent parts of which they are composed. I do believe that this leads to some type of metaphysical dualism. I do not, at this point, have a good explanation of free will, but I do not see how to get there without the use of some notion of metaphysical randomness. A system is random if there is no strictly mechanistic explanation possible for its behavior. Darrell

Hi Paul, I have given this topic a bit of thought, so let me give it a try. This will be brief as I don't have time to write a proper response. Also, I have not read every single entry in its entirety (though I did skim the entire list). Simply put, randomness (non-determinism) is a fact of existence and it is a requirement of free will (proactive behavior). To begin, non-determinism is consistent with classical physics. There are some classical physical systems that have non-deterministic solutions. Some physical systems have equations with infinitely many solutions at some point. (Such equations often have a square root, for example). I had a physics professor (Alfred Hubler) that actually created a non-deterministic device. In it, a ball rolled down a slope of a particular shape in a bath of castor oil. Roughly, there was a downward sloping hill that leveled out at a single point and then sloped downward again. Watching the ball roll down the hill was amusing because it would stop at the level point for an indeterminant amount of time before proceeding down the hill. It sometimes rested for less than a second and sometimes for several seconds. Now, someone might object that, being an experimental setup, it couldn't perfectly implement the equation which was supposed to govern its behavior so it might actually be deterministic. However, the problem is much deeper than that. The fact is that any physical system can represent only a finite amount of information at any moment in time and the amount of information it can represent depends upon the "size" of the phase space region through which its trajectories pass. Therefore, if the trajectories of a system pass through a very small region of phase space, information must be lost. But, the trajectories must re-emerge on the other side of the singularity (or near singularity) and must go somewhere. Therefore, information must be added to the system to describe the system parameters. I will assert, for the time being, that the source of the information is randomness. All physical systems are random to some degree. Therefore, all physical systems are proactive to some degree --- ever wonder where the wind comes from? Randomness does not require the injection of energy into the system and, therefore, proactive systems are consistent with the laws of physics such as the conservation of energy. Living things and humans in particular have evolved to control and make use of this randomness. As an aside, statisticians have learned that some randomized algorithms are more effective than deterministic algorithms at solving complex problems. Darrell