On the Undecidability of Materialism vs. Idealism

Is mind an emergent property of matter or is matter an emergent property of mind?

According to Douglas Hofstadter

What is a self, and how can a self come out of the stuff that is as selfless as a stone or a puddle? What is an "I" and why are such things found (at least so far) only in association with, as poet Russell Edison once wonderfully phrased it, "teetering bulbs of dread and dream" .... The self, such as it is, arises solely because of a special type of swirly, tangled pattern among the meaningless symbols. ... there are still quite a few philosophers, scientists, and so forth who believe that patterns of symbols per se ... never have meaning on their own, but that meaning instead, in some most mysterious manner, springs only from the organic chemistry, or perhaps the quantum mechanics, of processes that take place in carbon-based biological brains. ... I have no patience with this parochial, bio-chauvinist view...

According to the Bible

In the beginning was the Word, and the Word was with God, and the Word was God. ... And God said, "Let there be light"; and there was light.

I believe that computability theory, particular, the lambda calculus, can shed some light on this problem.

In 1936, three distinct formal approaches to computability were proposed: Turing’s Turing machines, Kleene’s recursive function theory (based on Hilbert’s work from 1925) and Church’s λ calculus. Each is well defined in terms of a simple set of primitive operations and a simple set of rules for structuring operations; most important, each has a proof theory.

All the above approaches have been shown formally to be equivalent to each other and also to generalized von Neumann machines – digital computers. This implies that a result from one system will have equivalent results in equivalent systems and that any system may be used to model any other system. In particular, any results will apply to digital computer languages and any of these systems may be used to describe computer languages. Contrariwise, computer languages may be used to describe and hence implement any of these systems. Church hypothesized that all descriptions of computability are equivalent. While Church’s thesis cannot be proved formally, every subsequent description of computability has been proved to be equivalent to existing descriptions.

It should be without controversy that if a computer can do something then a human can also do the same thing, at least in theory. In practice, the computer may have more effective storage and be much faster in taking steps than a human. I could calculate one million digits of
𝜋, or find the first ten thousand prime numbers, but I have better things to do with my time. It is with controversy that a human can do things that a computer, in theory, cannot do.4 In any case, we don't need to establish this latter equivalence to see something important.

The lambda calculus is typically presented in two parts. Lambda expressions and the lambda expression evaluator:


One way to understand this is that lambda expressions represent software and the lambda evaluator represents hardware. This is a common view, as our computers (hardware) run programs (software). But this distinction between software and hardware, while economical and convenient, is an arbitrary distinction which hides a deep truth.

Looking first at
𝜆 expressions, they are defined by two kinds of objects. The first set of five arbitrary symbols: 𝜆 . ( ) and space represent simple behaviors. It isn't necessary at this level of detail to fully specify what those behaviors are, but they represent the "swirly, tangled" patterns posited by Hofstadter. The next set of symbols are meaningless. They represent arbitrary objects, called atoms. Here, they are characters are on a screen. They can just as well be actual atoms: hydrogen, oxygen, nitrogen, and so on.


The only requirement for atoms is that they can be "strung together" to make more objects, here called names (naming is hard).


With these components, a lambda expression is defined as:


Note that a lambda expression is recursive, that is, a lambda expression can contain a lambda expression which can contain a lambda expression, .... This will become important in a future post when we consider the impact of infinity on worldviews.

With this simple notation, we can write any computer program. Nobody in their right mind would want to, because this notation is so tedious to use. But by careful arrangement of these symbols we can get memory, meaning, truth, programs that play chess, prove theorems, distinguish between cats and dogs.3

Given this definition of lambda expressions, and the cursory explanation of the lambda expression evaluator (again, see [3] for details), the first key insight is that the lambda expression evaluator can be written as lambda expressions. Everything is software, description, word. This includes the rules for computation, the rules for physics, and perhaps even the rules for creating the universe.

But the second key insight is that the lambda evaluator can be expressed purely as hardware. Paul Graham shows how to
implement a Lisp evaluator (which is based on lambda expressions) in Lisp. And since this evaluator runs on a computer, and computers are logic gates, then lambda expressions are all hardware. With the right wiring, not only can lambda expressions be evaluated, they can be generated. We can (and do) argue about how the wiring in the human brain came to be the way that it is, but that doesn't obscure the fact that the program is the wiring, the wiring is the program. That we can modify our wiring/programming, and therefore our programming/wiring, keeps life interesting.

Therefore, it seems that materialism and idealism remain in a stalemate as to which is more fundamental. It might be that dualism is true, but I think that by considering infinity that dualism can be ruled out as an option, as I hope to show in a future post.

[1] Gödel. Escher, Bach: an Eternal Golden Braid, Twentieth-anniversary Edition; Douglas R. Hofstadter; pg. P-2 & P-3
[2] The Bible, New Revised Standard Version, John 1:1, Genesis 1:3
An Introduction to Functional Programming Through Lambda Calculus, Greg Michaelson
[4] This would require a behavior we cannot observe; a behavior we can't describe; or a behavior we can't duplicate. If we can't observe it, how do we know it's a behavior? A behavior that we can't describe would mean that nature is not self-describing. That seems impossible given the flexibility of description, but who knows?. There might be behaviors we can't duplicate, but that would mean that nature behaves inside human brains like it can behave nowhere else. But there just aren't examples of local violation of
general covariance, except by special pleading.


Aunt Katherine


My Aunt Katherine (my mother's sister) passed away on my mom's birthday. My mother would have been 91, she was senior to Katherine by 3 years. I made the six and half hour drive to Memphis on Thursday for the privilege of speaking at her funeral on Friday. Katherine was my "Mary Magdalene" - she was the first in my memory to tell me that the tomb was empty and that she had seen the risen Jesus. It took years and years for the seed that she planted to finally grow.


Epistemology & Hitchens

A little over two months ago I wrote "The Zeroth Commandment" about how I think attempts by Christian apologists to "prove" the existence of God are, not only ultimately futile, but are also fundamentally misguided. In that same spirit, I also proposed the "Spock-Stoddard Test". I followed both of these up with "On the Knowledge of God" where I quoted Berkhof, who cited Kuyper:

... Reformed theology regards the existence of God as an entirely reasonable assumption, it does not claim the ability to demonstrate this by rational argumentation. Dr. Kuyper speaks as follows of the attempt to do this: “The attempt to prove God’s existence is either useless or unsuccessful."

Let me now attempt to put some theory behind these musings.

A Twitterer
attempted to take Christopher Hitchens to task for his statement:

What can be asserted without proof can be dismissed without proof.

Hitchens isn't wrong, but his statement is incomplete. The corrected version should read:

What can be asserted without proof can be accepted or dismissed without proof.

Why is this so? Because reason has to start somewhere. It has to hold that some fundamental, foundational, things are true simply because they are true. They are the first stepping stone on what may be a long journey.

It may be that an axiom results in a system that conflicts with empirical measurement. In that case, the axiom can be rejected (or the measurement questioned). It may be that the axiom agrees with empirical measurement. In that case, it can continue to be provisionally accepted for as long as no other disconfirming empirical measurement is found. Note that empirical agreement with one axiom does not rule out other axioms that have the same empirical agreement.

It may be that an axiom conflicts with other axioms or statements derived from those axioms. In that case, something has to give. Knowing what has to give can be problematic.

But it may also be the case, thanks to Gödel and the universe, that we can never fully explore the consequences of the axiom either logically or empirically. In that case, you are free to accept it or reject it.

I submit for your consideration that the axiom of "God" is in the latter category. You are free to accept or reject as you will. It may be one of the few truly free choices you get to make in life. In thousands of years there has been no successful logical proof of God's existence, nor has there been a successful logical proof of God's non-existence. Neither is there any generally accepted empirical proof either way. Note that I put self-reflection in the category of empirical proof.

But this means I also have to finish my examination of the Warren-Flew debate to show why Flew ultimately failed.


Warren-Flew Debate, Part 2

I considered devoting the second part of this review to further examination of Warren's points. But that is such an unappealing task that I'm going to just skip on to Flew's positive argument for atheism.

In my
previous post, I lamented that neither side addressed what it means to know. Still, Flew made some observations which deserve comment.

On Knowledge

That is to say we have to start from and with our common sense and our scientific knowledge of the universe around us.

Yes, we all have to start somewhere. But we need to establish criteria on how we know we've arrived. With common sense, Flew fails to establish whether the majority view (theism) or the minority view (atheism) is the "common" one. One can do an internet search for "humans hardwired religion" and see the arguments for and against. The argument against says that humans are hardwired for pattern recognition, but this misses the point. After recognizing patterns, we seek teleology. And we are wired for teleology - we have to be - but
atheists suppress this aspect of being.

As to scientific knowledge, scientific knowledge is incomplete and sometimes wrong. This is not to disparage science; it's just the nature of the thing. Too, scientific knowledge contains descriptions based on empirical induction, and descriptions from empirical induction are probabilistic. That means that there is some point where we consider a probability high enough to be trustworthy - whether it's 50.1%, 75%, or 99.9999%. And this leads to the necessity of what it means to trust Nature and whether or not Nature is trustworthy. Note that the same considerations apply to questions about God.

Of equal importance is the trustworthiness of our intuitions. Feynman gives an idea of inability of intuition to grasp quantum mechanics. In his hour long lecture "
The Character of Physical Law - Part 6 Probability and Uncertainty", he begins by saying that the more that we observe Nature, the less reasonable our explanations of Nature become. "Intuitively far from obvious" is one phrase he uses. Within the first ten minutes of the lecture he says things like:

We see things that are far from what we would guess. We see things that are very far from what we could have imagined and so our imagination is stretched to the utmost … just to comprehend the things that are there. [Nature behaves] in a way like nothing you have ever seen before. … But how can it be like that? Which really is a reflection of an uncontrolled but I say utterly vain desire to see it in terms of some analogy with something familiar… I think I can safely say that nobody understands Quantum Mechanics… Nobody knows how it can be like that.

Neither Flew nor Warren acknowledged the problem of intuition getting in the way of apprehending truth, nor possible approaches for dealing with it. We'll see how this problem affects Flew's Euthyphro argument.

About the law of the excluded middle: in general surely it can only be applied to terms and contrasts which are adequately sharp.

This is quite true. Logic, and computation, are based on objects that are distinguishable. This means that if two things can't be distinguished, then we can't accurately describe them. This means that God is beyond reason and logic, because He is not made of distinguishable parts, yet we talk about Him as if He is. At the heart of the Christian concept of God is what is to us a paradox: what God says is the same as what God is (because both are immaterial and unchanging), yet what God says is somehow different from what God is. Flew doesn't mention if this difficulty - that God is beyond reason - is one of the things that enters into his affirmation that there is no God.

My first and very radical point is that we cannot take it as guaranteed that there always is an explanation, much less that there always is an explanation of any particular desired kind.

Bravo, except that this shouldn't be radical. We know that empirical knowledge is incomplete (we'll never experience the interior of a black hole, at least not in any way we can talk about it) and, ever since G
ödel, we know that knowledge based on self-referential logic is incomplete.

You can not argue: from your insistence that there must be answers to such questions; to the conclusion that there is such a being.

This. A thousand times this. Explanations are "just so" stories of which there can be no end. "Just so" stories that actually describe reality are much harder to devise.

For in the nature of the case there must be in every system of thought, theist as well as atheist, both things explained and ultimate principles which explain but are not themselves explained.

Note that Warren says the same thing: "God is the explanation which needs no explanation." In the final analysis, both sides end up with
what they start with! Flew starts with "no god" and ends with "no god"; Warren starts with "god" and ends up with "god". Everything else in between are flawed arguments. I hope that once you see this happen, time and time again, that you see that what passes for a lot of "apologetics" are vain attempts to prove what has been assumed as true!

How often and when, when you make a claim to know something or other, do you undertake or expect to be construed as undertaking to provide a supporting demonstration of the kind which Dr. Warren so vigorously and so often challenges me to provide? Certainly when we claim to know anything, we do lay ourselves open to the challenge to provide some sort of sufficient reason to warrant that claim. But that sufficient reason can be of many kinds. And, although it may sometimes include some deductive syllogistic moves, the only case I can think of offhand in which a syllogism is the be-all and end-all of the whole business is that of a proposition in pure mathematics. Clearly that is not the appropriate model in the present case.

Again, Flew is right. The problem is that he doesn't say what the appropriate model is. He doesn't provide the testability criteria that he demands must be present (covered in the the
next post).

The other way, which is the interesting one which I want to consider, is to urge that whereas we who have not enjoyed the revelatory experiences vouchsafed to the believer cannot reasonably be required to accept his claims, this believer himself is in a sure position to know.

Flew is basically saying that the "deaf" don't need to trust the "hearing". Here, Flew says "I haven't heard". Later, he will say, "I don't see." While he admits these things, he then needs to show that the theist is hallucinating and examine whether or not his presumption of atheism is the cause of his not hearing or seeing. As anyone who does puzzles knows, changing how you look at the puzzle can enable you to see things previously missed.

Flew gets positive marks for trying to lay a foundation of what it means to know; but negative marks for the incompleteness of his presentation. Having reviewed these points, the next post will examine Flew's three arguments.

Warren-Flew Debate, Part 1

In my post "On the Knowledge of God", I wrote: "I have come to the conclusion that neither side [theist and atheist] has any arguments that aren't in some way fundamentally flawed. One day, I will make this case in writing." I guess today is the day to get started (but not, yet, to finish). One problem, of course, is which side to address first and which arguments within each side to address. I could, for example, consider the debate between Richard Dawkins, the author of The God Delusion, and John Lennox of which a transcript of the debate is here. I could, for example, cover Feser's "Five Proofs of the Existence of God". I could review "On the Existence of Gods" by Saltarelli and Day. I could ignore what everyone else is saying and present my own case. But even when I do get around to that, I'll still want to include answers to objections, which means covering the traditional arguments.

Somewhere, in a place that I can no longer find
1, I remember reading that Antony Flew was the "most important atheist you've never heard of." On the other hand, Flew may have abandoned atheism in favor of deism in 2004, six years before his death. One side says the switch may have been the result of senility - a charge which Flew denied2. Still, up until that point, he had an impressive pedigree. And in 1976, he debated Thomas Warren over a period of four nights in Denton, Texas where he argued for the affirmative position that there is no God. The debate is available on Youtube and in print.

My primary goal will be to examine Flew's arguments. My secondary goal will be to dissect Warren's responses to Flew. I have to admit that my sympathies -- but not my worldview -- are with Flew in the debate. My impression is that, of the two debaters, he is the more careful craftsman. He is trying to paint a picture with careful brush strokes while Warren is firing a paint gun. Flew is wielding a scalpel, while Warren is using a chain saw. Both have their uses, even though Flew removes the wrong organ and Warren cuts down the wrong tree.

Because my sympathy is with Flew I will deal with his arguments last. First, I want to show where Warren's responses to Flew fall flat. First, Warren makes the claim that Flew has to hurdle seven walls; escape seven cages, to "know" that God does not exist. Warren presents his chart number 9 (manually recreated with minor edits):

Note that, with one exception, Warren is in the same place. Where Flew must show the eternality of matter, Warren must show the creation of matter. After that, at least according to Christianity, Warren must answer the same questions. Genesis says that we are made from "rocks and dirt" (Gen 2:7). Since the "dust of the earth" is unconscious, the same transition must be made. Conscience, i.e. morality, must also enter into the picture. And so on. If Warren could go back in time, what would he see? Would he see dust forming into a human shape which then begins to move? If so, what would intermediate shapes, if any, look like? How long would it take? Would it happen in an instant? Would it happen in minutes? Would it happen over millions of years? How long would the operation to make Eve take? Seconds? Minutes? Hours? What does Warren think he would see? The only difference between Warren and Flew's position on "life from rocks and dirt" is time scale and the presence, or lack thereof, of agency. Since Warren can't go back in time, how does he know what he claims to know? He may answer, "because the Bible says so," but that is an appeal to authority which, in any other undertaking, would require additional support.

And this leads to a fundamental problem. Neither side addresses what it means "to know". There is no mutual groundwork on the nature and limits of reason, empiricism, or self-evident knowledge. Warren has a way that he escapes the mutual prison cells, but I suspect he wouldn't permit Flew to use the same kind of tools. Warren says:

...the only way he can arrive at atheism is to come through all of these walls.

This simply isn't true. We know that knowledge obtained by empiricism is incomplete, if only because we can't experience everything. Thanks to Kurt G
ödel, we know that knowledge obtained by reason, if it is consistent, is incomplete3. Both Warren and Flew need to address what it means to know in the face of uncertainty.

There are some things that we just can't know. And some of the things we claim to know by reason are built upon statements that are taken to be true for no other reason than they are assumed to be true. These axioms, these presuppositions, these self-evident truths may, or may not, conform to external reality (whatever that turns out to be
4.) So while something might be logically true, it may not correspond to a correct description of Nature (cf. the "Stoddard" portion of the Spock-Stoddard Test).

Too, each system may give different answers to the same questions
5, and a question that has an answer in one system might not have an answer in another. It's important to watch for mental sleight of hand when someone argues the superiority of one system over another because their system has an answer to something the other does not. That's not necessarily a virtue. Their system will have unanswerable questions that might be answered in their opponents system.

Warren will use this technique ("my worldview has an explanation, but Flew's does not") as if this settles the matter. As above, it does not. Furthermore, wittingly or unwittingly, this leads to "God of the gaps" thinking. That is, the idea God has nothing better to do than to be an explanation for things where our knowledge is incomplete. While our knowledge will always be incomplete, the moment a particular gap in our knowledge closes, the need for God in that particular instance goes away. So much for an unchanging God.

Warren also seemed to refuse to accept the problem of the
Sorites paradox, that is, the lack of bright lines of demarcation between some objects. How many grains of sand comprise a pile? How many hairs on a head make the difference between bald and hirsute? In the theory of evolution, where did the difference between human and non-human occur? Warren states:

The truth of the matter is, the theist, who believes in Almighty God, has absolutely no trouble with the question of which was first--a woman or a baby.

Sure, but this is because Genesis gives an account where this question is answered. But, as stated before, just because there is an answer doesn't mean it corresponds to reality. The existence of an explanation is not evidence of the truth of the explanation. Warren then asks:

Have you ever seen anything that was neither human nor non-human?

Here, Warren is begging the question. What, exactly, does it mean to be human? That we have the form of a human? Clearly, the Sorites paradox comes into play, since a person who is missing limbs isn't less human than than someone who isn't. Is it based on behavior? If I lose my mind to dementia, does my humanity gradually fade? If something passes the Turing Test, can it be said to be human? Is humanity based on genetics? Neanderthal and modern humans apparently had a common ancestry. In practice, we find that the definition of human is fluid. It depends on form -- except when it doesn't. It depends on behavior -- except when it doesn't. It depends on genetics -- except when it doesn't. Warren ought to admit that our humanity is rooted in our being in the image of God -- but this has to be something non-physical. And since it's non-physical, it's hard to define. Warren is using a sharp line which his own theology has to affirm is actually ineffable.

To be continued...

[1] Possibly "
Did Jesus Rise from the Dead?: The Resurrection Debate", Habermas and Flew.
[2] Asking the senile if they're senile is like asking a drunkard if he's drunk, or an insane person if he's insane.
[3] G
ödel's first incompleteness theorem.
The Matrix
[5] Compare
Euclidean and non-Euclidean geometries.