Introduction: The question of the existence of free will acquires great philosphico-religious importance in its relation to the concept of human moral responsibility, which in the religious and some philosophical or metaphysical contexts assumes that:
we possess a free will so that we can choose our actions (ie we could have acted differently than we did)
· there is a "good" and an "evil" way of acting,
· one "should" ("ought to") be good.
#2 & 3 generally assume some sort of 'beyond-personal' level of existence, an absolute or objective realm. On the other hand, if there is no good or evil apart from one's own judgement of good and evil, and if there is no "should" apart from what one feels one "should" do, then good, evil, and should are 'simply' personal emotions - however generally shared. In such a case, one cannot speak of "moral responsibility" in a 'super-personal', or absolute, objective sense - one can only speak of "actions in accordance with one's own moral feelings", or "actions in accordance with the moral feelings of others".
To many people, certainly to materialists, the notion of a transcendent realm - whether Platonic or of the Biblical type of otherwise - is nonsensical, not just 'unscientific'. However to many people the notion has intuitive meaning, and whether or not it is believed depends on various factors and considerations, rather than being dismissed out of hand it is by materialists. For our discussion we will speak within the context of this intutive understanding common among non-materilaists, and limit consideration to a hypothetical scenario in which there exists some super personal non-physical realm which gives definition to the concepts "good", "evil" and "should", and that humanity is connected to this realm in the sense of knowing of these concepts "intuitively". Since this is basically the Biblical scenario, for shorthand we'll use the term "God, creator of the universe" rather than some unspecified "super-personal non-physical realm granting objective status to good/evil and "ought", so that the context of our discussion is structurally identical to the Biblical one presented in Genesis's description of the creation, and the Eden account, where there exists a God, who created humans, and who expects them to live according to some moral code, and that humans have a "moral responsibility" to do what is "good".
One issue which we will explore in this article is the question of whether the type of free will required for this scenario is compatible with quantum theory. It is not.
We'll discuss briefly the ramifications of this incompatibility, and then we'll present an alternative.
Quantum Physics, Intuition, and Free Will - The Role of Quantum Physics in the Free Will Question
As a phenomenon in itself, quantum processes are unsufficiently radical to allow the operation of free willed activity. However, the very existence of quantum processes shatters the myth that all physical processes must be deterministic, and thus opens the door to acausal processes such as 'free will'.
Although it is easy to imagine deterministic processes, quantum physics teaches us that these are really random at their most fundamental level. The fact that this result is violently counterintuitive merely indicates to us that our intuition regarding what is and what is not physically possible is inadequate. Thus, although the extreme acausality required from free willed processes is also violently counterintuitive, the fact that it is so cannot be accepted as a disproof of free will. Instead, one can rely on one's intuition that one does possess a free will - a direct intuition - and ignore the already-proven fallible indirect intuition regarding what is physically possible.
[footnote 1: re Bell]
However, the problem is deeper than merely a conflict between current physics and our intuition and beliefs, it also involves a contradiction with logic.
The Objection from Logic
Even if we are prepared to rely on our intuition and to accept a limited form of quantum physics - limiting its validity to non-free willed processes - there remains a very serious objection to the existence of free will, not from physics itself, but from logic and the nature of causality.
Regardless of whether or not mental events are dependent on individual quantum processes, and whether or not these processes are random, free or determined, the very idea of free will seems logically impossible:
If a person decides to act in a specific way [even though he could have acted otherwise] then we could say he has exercised "free will" only if he acted this way for a reason. If he chose this specific action random, without reasons, then it is not a 'free willed' choice, but a random one. On the other hand, if there is a reason/motive for his choice, then this choice was determined by the reason/motive. Since this motive was in turn determined by his prior mental states etc., then his action is actually determined by these prior mential states, etc. E.g., why did you do that action rather than another? Because it was the right thing to do. Why did you do the right thing? Because I feel one must do the right thing. Why did you feel that? Because I believe in God. Why do you believe in ...? Because ... Why...? Because ... One can see that there must always be a "why" question which always leads to a "Because" answer: if there is no answer then the act is the result of a random process; if there is an answer to every question, then this shows that the action was determined.
It is impossible to understand how a decision can be rational and deliberate without being determined as well! This is the central paradox of free will: if a choice is to qualify as free will it must be rational, which implies it is determined - but if it is determined it is not free. Nevertheless, people firmly believe they have free will. Thus, at the core of the free will issue there lies the very fundamental issue of the logical/rational vs. the intuitively believed. In addition, as we saw previously, at the outer level lies the issue of free will indeterminary vs. the indeterminancy of quantum physics.
Thus, a belief in the existence of free will implies a belief that not only is physics as we know it incomplete (since it rules out non-random 'free' choice) but logic itself is flawed since it does the same.
A Radical Solution
Clearly, the only mechanism which can allow a free willed process is one which does not rely on quantum/macroscopic processes but instead on some hitherto unknown-to-science acausal 'free' process which goes beyond determinism and beyond P/D randomness. Once this 'free' process decides 'freely' show to react no problems remain. Indeed, if such free process exists the remaining steps can be taken on the macroscopic level: in fact quantum effects would only interfere since they would introduce an uninvited element of randomness into a carefully arrived at 'free' decision.
Thus, quantum physics alone is not radical enough to encompass free will. In order for it to allow free will, we must postulate a new 'free' 'acausal' process [footnote2]. Of course we still require the basic postulate of quantum physics which allow a multiplicity of choices. However, we no not need to consider the quantum physics and our new phenomena as separate laws; instead we can consider our new 'free' process to be a fundamental phenomenon in nature with quantum physics a special limited case of this phenomena where the decision between options is not 'free' as it is in its general form, but is instead P/D random: we can then consider determinism to be a further special even more limited case, where the decision occurs not freely, and not P/D/R/, but rather with 100% probability in one set way, so that effectively no choice exists.
We are essentially left with three options:
Option A
Science/logic as presented today are essentially correct. The universe arose by itself. All events including mental events occur in a P.D.R. way, and thus free will is physically impossible. In addition, if causality is valid, then free will is logically impossible. Therefore, man has no control over his actions and thoughts and cannot logically be held responsible for them. Of course people are not logical, and thus many people feel that they are responsible for their actions, and have invented the words "moral responsibilities" to describe this emotion. This of course does not mean that one should reject science: on the contrary, one is simply clearing away what is not science - using scientific reasoning to show that certain assumptions are invalid, unproven, and removing them from the category of science.
In this way, by removing the unscientific assumption that there is no Gd, purpose, free will, etc., that man is not unique, one prevents the pseudo-scientific circular logic of using the assumption that these do not exist to prove that they do not exist.
Option B
Gd created the universe and instituted a system of "natural law" to run it. All events occur in accordance with this natural law, except when Gd intervenes in nature. If quantum physics is correct, then the state of the universe at any time follows in a PDR way from the initial created state of the universe. Therefore, everything that occurs does so as a direct result of some combination of Gd's choice of initial state, this choice of system of natural laws, and randomness. Clearly, Gd cannot expect man to act other than he does act, since man has no control over his actions - all man's actions are determined/random results of Gd's initial act of creation. As a result, Gd cannot hold man responsible for his actions. Of course, many men, not realising that they really do not have free will, will believe that they are responsible, i.e., that they do have free will; however, they are wrong. Man has free will and is responsible for his actions because:
1. Quantum physics (P.D.R.) does not hold in the realm of human mental processes
2. A causality-defying process allows man to freely choose his actions without this choice being either determined or random.
Option C
God created the universe in such a way that it follows the P.D.R. laws laws of quantum physics - except for consciousness, which is a higher-level phenomenon. Humans are moral responsibile for their choices/actions due to their possession of a true free will.
Conclusion: If one believes deeply in free will-based moral responsibility we are led to the conclusion that science/logic as it is presented today is incomplete in a basic sense - we must reject the universality of quantum physics and the seemingly logical demands of causality. This basic incompleteness of science is due to the incorrect assumption that consciousness is a physical phenomenon as any other, and the often-accompanying implied assumptions that humanity is a purely physical being essentially a product of chance in a purely-material universe which arose by chance.
……………
Footnote 1: re BELL: We can evade problems of "hidden variables", Bell's inequality, etc. by pointing out that even in the free willed case where the event is not random, this is only due to the effect of some outside cause which forces the quantum event to occur in a specific way - there are no hidden variables within the system itself which determines how it will occur: rather, it is another system outside which "imposes its will" on the quantum event.
Footnote 2: However, once this process is allowed, there is no need for quantum physics at all. Instead, we can say that once the decision is made by the 'free' process, the rest can occur in a deterministic way: the decision is carried out deterministically with 100% probability rather than the 99.9999% probability supplied by quantum physics.
.......................................................................................
For other discussions of the connection between moral choice, free will, consciousness and quantum physics, see the article "Quantum Physics and Halacha" and the author's book "And God said: "Let There Have Been a Big Bang".
……………
Appendix: Background Explanation
The Universe as God's Machine
Assuming that a God created the universe and natural law, then any act/event which follows automatically from the initial state of the universe itself is an "act of God". In order that man be responsible for his actions it must be true not only that it was physically possible for him to act otherwise than he did but also that he was free to choose his actions from among these available alternatives. Under these conditions, we can say that free will exists. If on the other hand it was not physically possible for him to choose any of the other alternatives, or if there were no other alternatives to choose, then his act is an automatic one, and is caused by the conditions of the universe as Gd created it. As such, it is an act of Gd, and not an act for which man can be said to bear responsibility.
One of the fundamentals of Judaism is that man is commanded by God to shun certain actions and to actively pursue others and that man is responsible for his actions. This implies that it is up to man whether or not he will do these actions, i.e. that man has a free will. Science on the other hand, has raised a number of objections to the idea of free will.
According to the philosophy of scientific Determinism, all phenomena are governed by natural law: ie, all events always occur in accordance with certain cause-effect relationships , and only in accordance with them, as though they were following some obediently all powerful set of laws. We thus call these regular cause-effect relationships "natural law". As a result, if one possesses all the relevant information characterizing a system (any system) at any one point in time, then since event must follow event in accordance with natural law, if the natural law is known it is possible to compute the exact state of that system as it would be at any other time, past or future.
Since event follows event in a way initially set by natural law, we say that events are determined by prior events, and thus we say that the state of the system at present is determined by the state as it was at a previous time. Implicit in this philosophy is the belief that all observed phenomena are subject to natural laws. For example, although thoughts, emotions, and decisions are mental phenomena, they are detectable by the humane consciousness and are therefore considered to be operating subject to some (albeit as yet unknown) natual law.
Since our minds, thoughts and emotions are part of the physical universe, thus and since by knowing the state of the entire physical universe at any given time one could predict its state at any future time, emotions, thought, etc. would be predictable as well.
Of course, the necesssary calculations might well be so long and difficult that the entire human race with all its computers might not be able to complete such a prediction. Nevertheless, the problem is at least theoretically "solvable". That is, given all thoughts, emotions, actions, motions, positions ... of all the particles/entities in the universe, as they are/were at any one point in time, their future thoughts, emotions, actions, motions, positions could be exactly specified: ie, for example, your thoughts at the very moment were determined by the previous state of the universe (which includes the previous state of your brain and of your surroundings, etc.). That state is determined in turn by the previous state, etc., so that your thoughts are actually determined by the very first state of the universe.
The possibility has been raised that even were such a calculation to be made, the amount of information to be processed would be so vast that even in theory the result could be obtained only after the predicted event already occurred. For example, a prediction of the universe-state one year in the future would take a minimum of two years to calculate.
However, in our case, this is irrelevant: when we say that the future can be predicted, we mean that it is determined - even if the prediction of events requires a longer amount of time than the actual occurrence of the events, if they can be predicted at all, then this is proof that the events are determined.
Thus, if the exact state of the Big Bang were known, one could (in theory) predict all the actions, thoughts, works of art and philosophy and science, all acts and words of kindness and brutality, love and hate, of all humanity for all time.
Thus, if the theory that the universe is (totally) deterministic is correct, then every act that we consider to be spiritual, good, meaningful, or beautiful is merely an inevitable, automatic consequence of the Big Bang.
It is not even necessary that it is possible for man or any physical being in our universe to be able to predict the unfolding of the universe in order for this to be true. Obviously, if a God created the universe with its physical laws in such a way that it would develop in one and only one way, then everything that occurs in that universe is an automatic result of God's creating the universe - whether or not we can predict events, they are nevertheless determined.
Causality and Determinism
The "law of gravity" as it was formulated before the modern period stated that all things tended to fall to the earth. This was based on observation, not on some brilliant theoretical deduction. If rocks fell but wood rose to the sky, the "law of gravity" would say "rocks fall and wood rises". If on Sundays and Tuesdays rocks fell but other days they stayed where placed, the law of gravity would say " .........." Even in such a universe, this law of gravity would be "prescriptive" because it could predict what would happen to rocks and wood if the day of the week were known. However, if every few minutes there was a change, sometimes rocks fell, sometimes not, sometimes water flowed sometimes not, etc., then a complete description of events could be made only after they had occurred. However, once a complete list is made, one could say that this list is "the law of gravity"; i.e. the law of gravity states that last Tuesday at 9 a.m. .... and at 9:05 ... and at 9:08 .... etc. This is however a descriptive "law", not a prescriptive law since it describes but does not predict. However, it is a fact of mathematics that no matter how complex this law would be, it would be possible to express it mathematically so that one would have a formula, a mathematical law of nature, to describe the entire history of the universe.
We can see that if we take any universe's history, even if the laws changed chaotically every minute, we could write the entire history of the universe, even express it mathematically, and call it the "natural laws" of that universe; we would be right in calling it this because every event could be derived from the "natural law" ... However, this would be a descriptive rather than prescriptive law. In contrast, imagine a universe in which prescriptive natural laws are available, and in which these laws maintain their validity always and everywhere, and where only a very few basic laws are needed to predict any event anytime anywhere. In such a universe, rather than considering natural law merely as a "description" of events, as it would be in a chaotic universe, we are tempted, after meditating on this regularity and encountering it everywhere and always, to consider that events must occur in accordance with natural law.
What we are actually saying is that "causality" is not a priori truth: if effect Y always has followed from cause X, we do not say that if X occurs then Y must occur following it, but rather that so far, Y has been observed to follow X.
If in a chaotic universe, Mr. X commits a certain act in certain circumstances, and claims that he acted in accordance with his "free will", then although we could say that it was "natural law" acting rather than free will, we would probably conclude that since the universe was so chaotic that obviously no law is acting that there is a good chance that Mr. X's act was not determined, but was rather voluntary, as he claims. In contrast, in an ordered universe, with prescriptive laws, we would probably say that just like all events in the universe are determined, so too X's act was also a direct consequence of natural law. Thus it would be difficult in such an ordered universe to assume that X was acting 'voluntarily'. Nevertheless, since as we have seen causality is not a priori, we can say that even in an ordered, apparently causal universe, no events 'must' occur (in any determined manner) and thus human activity cannot be 'determined', and can therefore be free.
Despite all this however, the fact is that all common, familiar events do seem to show a very strict adherence to physical law, and thus although one cannot ever be forced to conclude that causality is valid, of necessity nevertheless it does seem (at first) so indispensible to the intuition that it seems impossible for acausal event to occur.
In the following we will begin by assuming that although acausality is logically possible all events are constrained to occur in accordance with 'natural law'. After exploring the ramifications of this approach i.e. the exclusion of acausality, to the question of free will we will show that acausality is not only a logical possibility but is a physical fact. This of course would seem to open the way for free will. However, we will then show that the problem with free will. However, we will then show that the problem with free will exists nevertheless.
Determining Free Will
Now, if men's acts are truly automatic results, we can neither claim credit for our meritorious deeds, nor be held responsible for even the most reprehensible crimes. Rather, since Gd created the Big Bang, and all our actions follow inevitably from it, then Gd is the direct cause of all that "we" do. Humanity and the rest of nature are merely the puppets through which the universe acts out the drama programme into the Big Bang by Gd.
Indeed, if the universe actually does develop in this totally automatic way, then it is in reality merely a very large machine of which we are simply a small part. Like the motions of a machine, our actions are devoid of any moral or spiritual meaning. The motions of a machine cannot be "good" or "evil" - they just "are". Determined, automatic events, our actions thoughts and emotions, are thus neither "good" or "evil" - they just are.
Yet we all feel very deeply that our actions do possess meaning and that there does exist a distinction between right and wrong, good and evil. Is there any way to overcome this paradox? Can our actions have meaning?
Clearly, in order that we could consider our actions to have any meaning, we would have to believe that in some way we could control what we do. That is, we would have to believe both that alternative possibilities exist, and that man can choose freely from among them.
If we control our action, then at least to some degree we are neither puppets or machines. Our actions carry with them a measure of "responsibility", and they therefore have the potential to be meaningful. However, both these possibilities were negated by physics: it was an accepted doctrine in physics that each event occurred as a direct inevitable result of other events - there are no alternatives possible. The event occurs as it does because it cannot occur otherwise.
The idea of unpredictable processes seemed contrary to the spirit of science, and of physics in particular. Thus, many people ceased to believe in free will so that they would not be forced to give up a belief in science and predictability. Thus, it was postulated that our feeling that we possess a free will is only a fantasy (caused perhaps by that strange phenomenon we call consciousness).
And then came quantum physics ...
Explanation of Quantum Physics
According to quantum physics, events at the most fundamental level are not determined but can instead occur in more than one way. In order to know how an event will occur, one must use the quantum formulas to determine both which are the different ways the event can occur, and also the relative probability of each such different way of occurrence. Then nature rolls the dice and chooses one of these ways: for example: assume there are five ways for an event to occur, A B C D E; assume further that way no. A has a 10% probability, B a 5% probability, C has 35%, D a 27%, and E a 33% chance. Nature then constructs the following table in its mind and then rolls a one hundred-sided die. If the number on the die is e.g., between , and 10, then event X occurs in way A. If the number is e.g., between 51 - 77, it occurs in way D, etc.
Way No. Code Nos. Relative Probability
A 1 - 10 10%
B 11 - 15 5%
C 16 - 50 35%
D 51 - 77 27%
E 78 - 110 23%
A 100-sided die: each number has an equal chance
in each throw
Every physical process is governed by physical law, and every event occurs in some specific circumstance. By combining a knowledge of the relevant physical law and the relevant circumstances with the rules of quantum physics, one can exactly determine the relative probabilities of each "way of occurrence" for every type of physical process, under any circumstance.
Since the relative probabilities are exactly determined, we call quantum processes "probabilistically determined" processes. However, to stress the fact that since the actual choice is made using a random procedure we call quantum events "probabilistically determined random events" [P/D/R events].
Free Will: To many people, this weakening of determinism seemed to up the possibility that free will does indeed exist; since there is indeed a multiplicity of options available at each decision point, our decisions are not uniquely determined.
However, it would seem that this was a misplaced hope - it became clear that although there are indeed a multiplicity of physically possible options for each event, the choice of which possibility to select is not up to us, but is rather up to pure chance. We now explain this further.
Quantum Physics and Free Will
According to quantum physics, the universe is governed by probabilistically determined randomness (P.D.R.). We can imagine the development of the universe in the following way: outside the universe there is a "random number generator", and every time a quantum process is to occur in the universe in one of X number of ways, the universe picks a random number between and X from the generator, and causes the events to occur in accordance with the chosen random number. Thus all events occur in a random way selected from among the various possible automatic results of prior events. Therefore, any event in the universe [results either automatically from the initial state of the universe, or] is a P.D. random event. Nothing within the system, i.e. within the universe, is partially predetermined by the initial universe-state, and partially random, i.e., it is P.D.R. People are part of the universe, as are their thoughts, emotions, decisions, etc. As such, all actions, thoughts, emotions and decisions of all people of all time are partially predetermined automatic events, and partially random ones, i.e., they are P.D.R. events.]
Obviously the thought "I am dead" does not reflect reality; nor does the thought "the world is flat". However, one can imagine circumstances which would lead to the arising of such thoughts. Thus, although all thoughts always result automatically randomly from the initial state of the universe, the contents of a thought need not be true. Thus, even though thoughts such as "I have a free will" or "this thought is neither determined nor P.D. random" will exist in the universe even though deeply held beliefs in free will exist, this does not change the fact that - if quantum physics is correct - there is actually no free will, and that all thoughts are determined/P.D. random.
Since science today postulates that the universe is P.D.R. , it would seem that free will is physically impossible.
However, certain modifications to quantum theory have been suggested which would not affect the contradicting experiment, but would make it compatible with free will. We now consider this modified form of quantum physics.
Probabilistic Quantum Free Will
Since free will assumes that more than one option is available at each decision, free will is not compatible with determinism. However, free will seems to conflict with quantum physics as well, since according to quantum physics, events are decided by a random process, while free will requires a very non-random, very deliberate, choice.
One can, however, get around this difficulty as follows:
Very little is known about the human mind/brain. It is quite possible that if the laws of the mind were known, it would turn out that when quantum physics was applied to them, the result would be that the relative probability of a quantum event in the brain's decision center occuring as the mind wishes it to occur is 99.99%. That is, decisions are based on quantum processes, so that there UareU options available to choose from, and yet the choice process, although random, is so heavily weighed in favour of occuring as the mind wishes it to occur, that affectively events follow the mind's will: i.e., it is if one has a 100,000 sided die, and each time a free willed choice is made, the die is flipped: if it lands on any number between 1 - 821,367 or 821,369 - 1,000,00, then the free willed choice is acted upon. If it lands on 821,368, it is not acted on. Thus, in only one out of 1,000,000 choices will the event not occur as desired.
The Basic Problem
It would then seem that FW is compatible with quantum physics. However, in actuality it is not. The problem lies in the causal chain leading to the decision to act, i.e., in way no. C. Even if we say that once the decision is made to do "C", the relative probability of C accuracy becomes 99.9999%, nevertheless, we must examine how it came about that C was decided upon rather than A,B,C,D, or E. Whatever process it was, it was either random or determined and thus not free. That is, once the free decision is made, we can use quantum physics to say that it is indeed possible that there are options available, and that one can force events to occur in accordance with the choice. However, it is still impossible to understand how the choice itself can be arrived at except via physical processes, all which are necessarily random or determined.
In other words: it is true that when making a decision, various options are open, as postulated by quantum physics (rather than there being only one inevitable 'option' as per classical determinate physics). It is also true that once the mind decides which of these options to choose, that it can ensure that its choice is followed - with a degree of certainty of 99.9999% - since the physical laws of consciousness and of free will taken together with quantum physics determine that the relative probability of events occuring as decided by the will is 99.9999%. What still remains an unsurmountable difficulty is the question of how the decision itelsef is taken - i.e., what is the procedure whereby the mind chooses its desired option. The decision will involve quantum and macroscopic processes, and will thus also be either random or determined; there is no way to exit from this loop: if the only processes involved can only be either quantum or macroscopic ones, then at the most fundamental level all is random and/or determined, not 'free'.
So we can see that though quantum physics does solve the problem of the multiplicity of options necessary to free will, and it can allow decisions to be carried out with arbitrary precision by appropriate manipulation of the relative probabilities, it is nevertheless unable to solve the basic problem of how the actual choice is arrived at.
GODEL
One of the most surprising and significant mathematical results ever arrived at is that formulated by Kurt Godel in 1930.
Roughly speaking, Godel's "first incompleteness theorem' states that in mathematical systems, there are true statements which cannot be proven. That is, a system generates equations which we can see are true, using our common sense and mathematical intuition, but which cannot be proven to be true by using only the rules of the system itself. Instead, one can prove the truth of these statements only by adding on new components to the system. However, although it would now be possible to prove those intuitively true but unprovable statements, the new enlarged system would itself generate new statements which were also intutively clearly true, but not provable within the newly enlarged system. Of course one could add on yet additional components to allow a proof to be formulated, but then the newer system would generate true but unprovable statements ... etc., etc.
Thus, mathematical systems are "incomplete".
This astonishing theorem, which was rigorously proven by Godel, destroyed the hopes of those who wished to reduce all of mathematics , and all of the physical universe, to only those concpets/entities directly provable. It was now evident that man's mathematical intuition was able to grasp truths not directly provable in any given system.
To quote Prof. R. Rucker: (P. 178)
"The Incompleteness Theorem shows that human beings can never formulate a correct and complete description of the set natural numbers, (0,1,2,3, ...), but if mathematicians cannot ever fully understand something as simple as number theory, then it is certainly too much to expect that science will ever expose any ultimate secret of the universe ..."
"...rational thought can never penetrate to the final, ultimate truth."
Godel even postulated that since man is able to grasp mathematical truths which are not rationally explicable - i.e. they are not provable within the relevant mathematical system - that perhaps "sets and concepts exist externally to any individual's activities" [Rucker, pages 175 - 6 referring to Godel's "What is ... Co. "].
Man can interact with these truths which (page 176):
"... may represent an aspect of objective reality, but, as opposed to the sensations, their presence in us may be due to another kind of relationship between ourselves and reality" [Godel ...].
Godel also wrote a paper discussing how one could (Rucker, page 177) "prove the consistency of mathematics by assuming that mental objects have an objective existence".
It is well known that science is not equipped to deal with questions such as "what should man do?", "what is good and who is evil?", etc. As a result, many people tend to denigrate these kind of questions and to claim that since science cannot encompass them, they are illegitimate.
However, when one considers that man is able to intuit(?) mathematical truths which are unprovable in any given mathematical system, it becomes much eåsier to claim that man can intuit(?) other unprovable truths as well, e.g., free will, the existence of Gd, Gd's omniscience, etc.
Similarly, even when some of one's intuitive beliefs seem to be conceptually conflicting, such as the idea of man's free will and Gd's omniscience, since both of these ideas belong to the extra-physical realm, one could postulate that the system of "physical universe plus logic" is not strong enough to prove their compatibility, but that in the higher realm, their consistency would be obvious.
Analogously, our example of how it is that Gd is both transcendant and immanent employed an analogy with spaces of differing dimensions: within the more limited system, appeared to the intuition which were troublesome to rational inquiry: however, when a more comprehensive system was employed, viz a higher dimensional space-time, the conflict disappeared.