The first question has to do with how Mr Hawking's world view could escape the self-defeating problems of a deterministic Grand Unified Theory of Everything, or GUT, as we described it in the previous report. One reader pointed out that Mr Hawking is certainly an adherent of Heisenberg's uncertainty principle, and as such, the uncertainty principle affords him a way out of the self-defeating situation we described last time. Moreover, it even leaves plenty of room for free will so that our beliefs can still be the result of rational and epistemic relationships. This is a popular method for avoiding the problems with a deterministic, purely physical universe and so deserves to be examined in some detail. Let's do that and let's begin by examining exactly what the Heisenberg uncertainty principle is.

     Mr Hawking devotes an entire chapter of his book to this principle, so there's no denying that he believes it to be true. The principle begins by noting a simple fact about measurements done on subatomic particles, particles like electrons, protons, neutrons, etc. Any time someone tries to measure some attribute of such a particle, such as its velocity, the measurement ends up seriously altering or even destroying the particle. That's because some detector must "touch" the particle in some manner. Because the particles are so small, any attempt to "touch" the particle through a detection apparatus can't help but change or annihilate the particle. This becomes a problem when we would like to measure more than one property of the particle at the same time. After the first measurement, the particle just isn't there any more in anything like its original state. So, when the second measurement is taken, it's just not clear at all what we are measuring.

      It's a lot like this following problem. Suppose you want to take a picture of the Capitol building in Washington, D.C., but all you have are one ton rocks and a large catapult. Your technique is to hurl the rocks in a huge mass at the building. The building will block some of the rocks, and those it doesn't will land on the other side of the building. You will then assemble a silhouette picture of the building by noting where rocks don't fall on the other side. In effect, the building creates a shadow of itself using a pattern of rocks. Let us suppose you've taken the "picture" in the requisite way (preferably while Congress is in session). Obviously, as a result of your efforts, the building will be badly damaged. Any other measurements you now wish to take of the building will certainly not reflect its original condition. The second measurement will now reflect a good deal of "uncertainty" as to its accuracy in telling you anything about the original structure. This is exactly what happens with subatomic particles, because we are using objects in the same order of magnitude as the particles to do the measuring/detecting of the particle. The problem is still there at our normal macro sized everyday level, but because we use, say, photons of light to see a normal sized object, the change in the object produced by the miniscule photons is negligible.

      As a result, when we measure one property of a subatomic particle very accurately, the remaining properties either can't be measured, or they are measured only very inaccurately. So, let's take two properties of a subatomic particle, its velocity and its momentum. The more accurately we measure the particle's velocity, the less accurately we can measure its momentum and vice versa. If we can measure the velocity of the particle with 100% accuracy, then our ability to measure its momentum is zero. So, in one sense, we can't measure both properties at the same time. This means that as far as our measurements of the two properties are concerned, one of the properties will always be indeterminate to the extent the other is determinate. Some properties of subatomic particles will, therefore, always be indeterminate to some degree, either a very great degree (complete indeterminacy) or a small one. Because some measurements will always be indeterminate, the argument goes, human actions find room for freedom in that space allowed by the indeterminacy. Into that space falls the human search for truth, including the search for the GUT. As a result, The search for the GUT avoids the self-assumptive incoherency we mentioned last time.

     There are two reasons why this reply is unsatisfactory and I will discuss both in turn. In the first place, the "uncertainty" or indeterminacy we are discussing applies to entities at the bottom level of reality, the subatomic level. The everyday macro level of reality that we are familiar with on a day to day basis is a composition of objects at the lower level. Things that compose larger objects do not necessarily transmit their properties to the higher level objects. Take the following example, the set of grey squirrels. Each individual squirrel weighs less than 20lbs. But that property, weighing less than 20lbs., is not a property of the set as a whole, which weighs considerably more.

      If you are of a more mathematical bent, we can consider a different example. Take a set that has exactly three members. Each of these members is, in turn, a set itself. Suppose the members are the set of rational numbers, the set of real numbers, and the set of even numbers. Each of these sets is infinite in cardinality, which is to say they have an unending set of members. They are infinite sets. Yet, that set to which they belong, the set that contains them, is not infinite. It has exactly three members, so it's a finite set. The fact that its component members are each infinite has no bearing on the size of the more inclusive set that contains them, which is limited to 3 objects. As a result, just because the component members of a set have a given property, one can't conclude--on that alone--that the more inclusive set has the same property as well. To argue that the more inclusive set must have a property because its members do, is a fallacy long known to logicians as the Fallacy of Composition.

     Applying what we've just learned to the matter at hand, one cannot argue that because particles at the subatomic level of reality exhibit indeterminacy, the macro objects that comprise them must exhibit indeterminacy as well. To argue that there must be macro level indeterminacy simply because objects at the subatomic level exhibit indeterminacy, is to committ the Fallacy of Composition. Subatomic indeterminacy is no guarantee of macro level indeterminacy nor of "space" in which human free will can exist.

      Let me move on to the second problem with the reply from indeterminacy. Let us suppose the first problem could be overcome, and a connection made between indeterminacy at the subatomic level of reality and indeterminacy at the everyday macro level, such that the latter could be clearly seen as a species of the former. By its nature, indeterminacy at the subatomic level of reality is statistical chance. This is part of what has made quantum mechanics famous. It attempts to handle the behavior of subatomic particles through statistical processes applied to random or chance events. If free will actions at the macro level of reality are of a species with atomic level indeterminacy, then free will actions are the result of statistical chance, not physical cause and certainly not the result of weighing evidence and using reason. So, now, the things you come to believe, and the actions you take, you believe and take due to PURE CHANCE. Why does the scientist believe the GUT? Answer: Pure Chance. Why do you decide to have oat sticks for breakfast? Answer: Pure Chance. Why do you believe anything that you do? Answer: Pure Chance. Again, there's nothing that you believe because it's true, simpliciter, including the uncertainty principle and the GUT itself!! You believe it because of...well...a lucky chance!

      Once again the connection between what you believe, on the one hand, and truth and knowledge on the other is severed. So, once again, if the Grand Unified Theory of Everything, including the uncertainty principle is true, you could never know the theory to be true. You believe it because, by chance, it's just there, in your head.

      I conclude that the appeal to Heisenberg's uncertainty principle, and the statistical elements of quantum mechanics to save Mr Hawking's program from self-assumptive incoherency, fail. Maybe this will satisfy my critics, maybe not. If you have more to say, please feel free to email me. We'll see what comes of it.

      In our next Special Science Edition, I will continue with what I promised last time--an examination of Mr Hawking's attempt to give time a purely physical explanation.