Wisdom from Tertullian et al.

Among the blogs I follow is one called Resurrection Orthodoxy, written by Joel Edmund Anderson.


He recently had a post that I thought was a good accompaniment to my own last blog post on probability and theology. The post describes the philosophy of two early Christians, Tertullian and Irenaeus. I am reposting (with Joel’s permission, part of the post related to Tertullian. After a brief introduction we are told that Tertullian is often quoted as saying  “I believe because it is absurd.”

The post continues:

Ever since the time of Sir Thomas Browne (1605-1682), this quote has been held up as an example how Christianity is, at its very foundations, irrational, and how, in their stupidity, Christians actually hold up such irrational faith as a virtue. The fact, though, is that Tertullian never said such a thing. What he said was part of a larger argument regarding the truthfulness of Christianity. He said:

“The Son of God was crucified: I am not ashamed – because it is shameful.
The Son of God died: it is immediately credible – because it is silly.
He was buried, and rose again: it is certain – because it is impossible.”

What Tertullian said was not “I believe because it is absurd,” but rather, “It is certain, because it is impossible.” But what does that mean? Well, Tertullian was actually using an argument that he borrowed from, of all people, Aristotle. In Rhetoric 2.23.21, Aristotle says this:

“Another line of argument refers to things which are supposed to happen and yet seem incredible. We may argue that people could not have believed them, if they had not been true or nearly true: even that they are the more likely to be true because they are incredible. For the things which men believe are either facts or probabilities: if, therefore, a thing that is believed is improbable and even incredible, it must be true, since it is certainly not believed because it is at all probable or credible.”

Simply put, the argument is that if something according to convention is considered impossible or ridiculous, but people claim that they actually experienced that supposedly impossible thing occur, one must strongly consider the fact that what they’re claiming really is true, despite what convention accepts.

Convention says, for example, that dead people do not resurrect. If one person came out of Judea, claiming to have spoken to a resurrected Jesus, it would be reasonable to assume that person was insane. But if 5, 10, even 500 people claim to have witnessed the crucifixion, death, and resurrection of Christ, then it would be reasonable to pause and consider the fact that perhaps such an “impossible” thing really, in fact, happened. That was what Tertullian was saying….

That ends the fragment I wanted to repost here. (Please take a look at the rest of the post for more insights).

In my previous post I said that believing in something that is impossible (with a probability = 0) is a sign of insanity. But Joel, (and Tertullian and Aristotle) make a very good point here. If many people witness something that was deemed impossible (or, if scientists do controlled, well-conducted experiments repeatedly showing the same thing) there is another alternative to insanity:  what was previously deemed impossible, is  actually possible. This has happened in science numerous times.

I will follow up on this theme in the future.

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Reason, Freedom and Doubt

I was quite pleasantly surprised when I became a Christian to find that there is a great deal of rational and logical analysis in Christian theology. Reading or listening to people like NT Wright or John Walton is not at all different in this regard from listening to a good physicist describe evidence for a theory. How far can we go in the application of logical tools to issues in theology? Let’s find out.

We can consider some theological ideas in terms of probability. Probability notation describes the likelihood of something happening. For almost all applications of probability theory, that likelihood is unknown and is somewhere 0 and 1.

Sometimes the use of probability is extended to truth statements, which are binary – they are either true or false. This allows us to include all statements under the general umbrella of probability. In this way, we can define three categories of probability P. P = 1 is a statement of certainty of truth, while P = 0 is a statement of certainty of falsehood or impossibility. For P = anything else (0<P<1), we have a statement of uncertainty.

As examples, the probability that the USA is a nation, P(the United States exists as a nation) = 1. That is a statement of certain truth.  P(the moon is made of jello) = 0. That is a statement known to be factually false. But for many interesting questions, like what is the probability that the stock market will rise in value tomorrow?  P(the stock market will rise tomorrow) >0, <1. For some things, we can calculate the probability – for example, we know the probability that a flipped coin will land on heads  is P(heads) = 0.5. This still doesn’t tell us how a particular coin toss will turn out, but it does tell us the likelihood of getting a head.

How does belief connect with probability? We have free will to believe in anything. We can believe in God, in Allah, in Christ, in aliens, in conspiracy theories, in a flat earth, or that we are Napoleon. However, there are limits to belief. It is not possible to believe that something is true if the P = 0, nor is it possible to believe that something is false if the P = 1. Such beliefs might claim to be held by some people, but this is the definition of insanity. For example a belief that you are in fact a dead historical figure like Napoleon violates the impossibility of believing that something with P = 0 (which is the P that you are in fact Napoleon) can be true.

As a corollary, it also makes no sense to say that we believe in things that are factually true. It doesn’t make sense to say “I believe in the existence of France”, unless of course, we were in a period where the existence of France as a nation were not a certainty.  We do not have the freedom to believe that the IRS exists, because we know that “the IRS exists” is a demonstrably true statement.

However, the exercise of free will does apply  to when it comes to belief in a statement for which P is greater than 0 and less than 1.  For example, we have free will to believe that God exists (or not) because P(God exists) > 0, but < 1. I know of no proof that God exists or does not exist. Atheists are fond of saying that there is no evidence for God’s existence, which may or may not be true, but it doesn’t matter, because evidence does not prove a proposition, and lack of evidence does not disprove it.

Since the probability of the existence of God is neither 1 nor 0, belief in God is subject to free will. Turned around, if we assume that belief in God is always subject to free will, then P for God’s existence can never be 1 or 0, meaning that God’s existence can never be proven to be true or false. What this is saying is that if free will exists, the existence of God can never be proven beyond doubt. If it were, then only insane people could not believe (or believe) in God, and therefore there could be no free will to believe. If our theology requires free will, which it does, then the existence of God cannot ever be proven.

We can use evidence for God’s existence (some of it scientific, some not) to allow us to assume that that P is large. This evidence can allow us to feel comfortable with the assumption that God exists. The more evidence for or pointers to God’s existence, the more likely it is that God exists. But there will always be room for doubt – there MUST be room for doubt. While there are pointers that increase the P of God (such as the fine tuning of the physical constants), it is to be expected (and welcomed) that atheists can find ways to demonstrate that such evidence is not conclusive and that alternative theories, such as the multiverse, are at least possible.

These alternatives allow an element of doubt and therefore allow free will to remain a reality. The same arguments apply to any attempt to scientifically prove the existence of the Creator. So that when some creationists say that life’s diversity is proof of God, because there is no other way to account for it, they are trying to prove the wrong thing. If they were successful, they would have destroyed the possibility of doubt, and with it, free will. God’s gifts to us of faith and freedom are precious. So is His gift of reason and logic. Let us not hesitate to accept them all with gratitude and humility.




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Intelligent or Divine Design?

The appearance of design suggests a designer. But how can we define the appearance of design? William Dembski, one of the founders of the Intelligent Design movement (ID), has subjected this question to some rigorous statistical treatment, with the intention of showing that biological creatures fit the definition of designed objects and therefore were specifically designed.

I don’t think there can be much argument with the idea that biological entities show evidence of design. Darwinian theory of natural selection agrees that all living creatures appear to be designed, and provides a mechanism for how this design appearance came to be.

The ID argument goes that if the probability of such characteristics arising without any intentional (or intelligent) input is sufficiently low, then it will have been proven that some form of design that does not use chance processes must have been involved. If you find a sandcastle on a beach, it is safe to presume that the structure was designed and built by some form of intelligence, simply because the alternative, that the windblown sand formed what we recognize as a sandcastle by chance, seems to be impossible. (Now we know that in fact it isn’t impossible, but the probability of this happening is extremely small, and therefore it is as good as impossible.)


The difference between the sandcastle example (and its relatives, like the famous tornado blowing through the junk yard and building a 747 airplane) and Darwinian evolution is that with evolution, chance is only involved in the first step, the production of genetic variation. The enormous power of natural selection (as described by Dawkins in Climbing Mount Improbable) can indeed allow unexpected, very low-probability events to happen. But ID does have a valid point in focusing on the genetic variation part. Selection needs to have something to select. And it is not always clear how some biological structures or functions arose from previous forms simply by blind mutational chance. Some of the newer ideas in evolutionary theory (see previous posts on the EES) might go a long way to explaining this. In fact, the ID proponent Michael Denton acknowledges this in his latest book (see previous post on my review of the book at Biologos). So some parts of the ID worldview are not without merit.

In fact, and I don’t know if ID folks have used this argument, there is no question that ID exists in the world and has played a role in evolution. Nobody argues with this, and Darwin used it as the basis of his theory. Yes, I am talking about selective breeding for a purpose, and the intelligent agent in this case is us. We deliberately designed wine grapes, seedless watermelons, tasty tomatoes, faithful dogs, docile cattle, and so on. We haven’t created new species this way, nor whole new body plans, but we haven’t really tried to do that. With new genetic engineering techniques, we might get there. And of course, if we are believers, we know that whatever we can do, God can certainly do. But did He?

I think the real problem with ID is theological. It makes two assumptions about the nature of God that I believe are contrary to Christian (and other religious) thought. The first is that the existence and majesty of God as creator of everything is subject to scientific proof. I think that is a theological and scientific fallacy. The fact that ID has failed to convince most scientists that it has proven the existence of God is therefore beside the point, because such proof should in fact be impossible.

The second theological quarrel is with the nature of God as pictured by ID. If you found a complex watch, you could assume that the maker and designer of the watch was an intelligent human being, and you would be right. But suppose what you found was a rabbit. Paley didn’t know much about biology, not even a fraction of what we know today. But even in his day it was known that rabbits reproduce themselves, react to their environment, grow, consume food, and undergo very complex metabolic chemical reactions.

A rabbit makes a watch look pretty simple. Certainly no human, no matter how intelligent, could design a rabbit. I agree that life is designed. But by calling this design “intelligent”, the way a human designer of watches or computers or aircraft is intelligent, we demean its nature. The more we learn about life, the more we understand that the design of life is far more than that. Life was designed by the creator. It is divine design, not intelligent design, and the mechanisms by which life was designed and created are not currently within our ability to understand.

I don’t know if we will ever get there, but I do think it is worth trying to find pointers to the actions of the living God, because doing so will help us reconcile our faith with the truths that we learn about the universe using scientific tools. But not to prove the existence or creativity of God. That is not provable, and needs no proof. We start with the premise that God exists and created the universe, and that His presence is real in the world and in our lives.


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Summer is over,  and the glorious month of September is here. Today marks the end of my long blogcation, and I welcome back any readers who were impatiently pining for new posts🙂. I think the coming year will be an exciting one. (Aren’t they all). 

The word “elegant” is the highest compliment in science.  The meaning of elegance is a bit shadowy. Simplicity may be part of it, but not necessarily. What makes something elegant is the sense one has, after reading it and understanding it, that it is of course the only and the perfect explanation. It is a solution that fits even more than the question originally asked, and its derivation follows naturally and in a pleasing way. E = mc^2 was elegant as was the double helix.

Stephen Hawking wrote in The Grand Design that “Ever since Newton, and especially since Einstein, the goal of physics has been to find simple mathematical principles of the kind Kepler envisioned, and with them to create a unified theory of everything that would account for every detail of the forces we observe in nature.” But Hawking admits that all simple and elegant Theories of Everything have failed, and the only candidates for theories that can include gravity are anything but simple or elegant. It seems that elegant solutions are becoming rarer as we probe deeper into the mysteries of nature.

Einstein and many who came after him were convinced that the final Theory of Everything, which would combine gravity and quantum theory, would turn out to be a simple, profound, and lovely equation. By now, it is safe to say that it isn’t going to be that way at all. String theory, the standard model of particle physics, and a good deal of the newest evolutionary biological theories, might be correct (or not) but nobody accuses them of being elegant.

I have read that some physicists are getting very frustrated with the results from the LHC, which are not helping resolve outstanding questions in particle physics. This reminds me of the sense I had later in my research career that whenever I did an experiment to try to find an answer to a specific question, I always got an entirely unexpected answer, one that actually raised many more questions. So what is our Book of Nature, our Book of God’s Works, trying to tell us?

I like the notion of a simple all-encompassing equation that explains a great deal. That is the holy grail of science, and it is wonderful thing to come across such elegant theoretical marvels. But the realist in me sees the contradictions, dead ends, and false starts, and concludes that the universe is trying to tell us something, something that we haven’t really wanted to hear. What it is telling us is “Sorry guys, the easy stuff is over. Nice work with classical mechanics and momentum and relativity and the Hardy-Weinberg equation and Mendelian inheritance. Great stuff. But now comes the hard part. And you are going to need a larger computer.” Or perhaps a whole different approach.

I wrote a post a while back about the stop signs of nature – those signals that indicate that we can go no further toward truth using our previously trustworthy vehicles on a well-known road. I believe we will come across more and more of these STOP, GO NO FURTHER signs as we struggle to make sense of an increasingly complex universe. With time, we have seen the likelihood of a simple understanding of everything recede with every new discovery. It’s possible that at some point, the famous New Yorker cartoon by Sidney Harris that shows the words “and then a miracle occurs” in the middle of a complex equation will become real. This is a very controversial idea, and I don’t expect much agreement, certainly not from fellow scientists.


Perhaps the message of that cartoon, not to mention of all the available scientific evidence, is that elegance is still a beautiful thing, but we are looking for it in the wrong places. It might not be found in an equation at all. It might not even be found using standard scientific, methodological naturalism approaches to reality. So what is our Book of Nature, our Book of God’s Works, trying to tell us? Maybe we need to check out some other Books more carefully, is one possible answer. Or maybe we need to write a new one.


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Over the past year I have very much enjoyed posting almost 70 articles on this blog. I have also been happy to see the comments, likes, and post reblogging, and want to say thanks to all of the followers and other readers of the Book of Works.

It is summer time, and though I am quite busy with some deadlines, and ongoing work on long term projects, I am hoping to take some time off soon. So from today I am on blogcation, and will not be posting here for a few weeks.

I hope everyone has a great and relaxing rest of the summer, and I hope to see you back here in September.   Peace and joy to all.

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The Reasonable Ineffectiveness of Mathematics in the Biological Sciences


(With apologies to Wigner)

The fact that biology is not rich in theory is well known. Of the theories that do exist (such as Darwin’s theory of evolution), many have never been formulated into mathematical laws. Physics envy is a well-known propensity of those biologists who desire to be working on a more general understanding of whole fields (like cellular biophysics or regulation of gene expression) rather than on uncovering details of particular subsystems.

I used to be certain that the lack of mathematical rigor in biology was the fault of biologists, who generally are unable to grasp the fundamentals of even simple math. But that canard may be less true than it used to be (if it ever really was). With the explosion of systems biology and the development of algorithms for data mining, there are plenty of biologists around who are perfectly familiar with the manipulation of equations and concepts of theoretical formulation.

Certainly for some areas of biological science, good mathematical minds (taking a break from physics) have attempted for quite some time to apply their skill to producing the kind of laws that are (as Wigner put it) “true everywhere on the Earth, was always true, and will always be true.” And yet, success in these attempts has been limited at best.

Evolutionary biology is a good example. We certainly have a wonderful theory, one that has been well formulated, improved upon and expanded over the years to include data and concepts from many disciplines, and that has been supported beyond question as to its truthfulness. And yet, where is the law of evolution? Why can we not formulate a mathematical treatment of the evolutionary process, including inheritance of genotype, selection of the fittest phenotype, and fixation of that genotype in the population?

Of course, there are equations that can approximate some of the steps fairly well, but not the whole process. Is this because biologists are too stupid or lazy to come up with the right answers? Of course not, and even if they were, physicists have fared no better at the task, and not for want of trying.

So, what is the problem? I think the answer might be that biology is, unlike physics, simply not amenable to mathematical description. This is certainly not a new thought; biologists have been saying this for generations, although I have never believed it. The whole point of making a theory is to tame what seems to be a wild, complex mess of unconnected data into a tidy manageable package. But what if tidy manageable packages are something alien to biology? What if there is a fundamental truth behind the enormous difficulty of reducing biology to math?

Of course, mathematics doesn’t describe the real physical world very well, either. What it does is describe models of the real world perfectly, and the best laws for the models are used for real-world calculations. If the model is very good, the laws work well in the real world also.

Perhaps this is the problem. Perhaps there aren’t any really good biological models. In evolution, for example, one can develop a model, but as soon as we have one that can be predicted by an equation, we run into major difficulties. How can we define fitness so that it can be mathematically described? We cannot say that we will determine fitness by the number of offspring produced, because that leads to a circular argument. Fitness is a characteristic that cannot be quantitated a priori . But if we cannot assign a value of fitness to a characteristic, how can we model the process of natural selection?

The fitness issue is only one example of the problems facing the theoretical biologist in the construction and use of models. Take the cell. Or better, any functional cellular component, like ribosomes or chloroplasts. We know a great deal of the detail of the molecular mechanisms of protein synthesis, and we can make impressive videos or elaborate cartoons, but how can such a process be mathematically modeled with any degree of accuracy?

Actually the problem is much worse. There are very few biological entities or concepts that can be defined mathematically with sufficient precision to allow for making models. Even the idea of a species turns out to be very fuzzy. One definition of a species is a group of animals that can produce viable offspring only by mating with each other. The problem is, there are too many exceptions to this rule to make it mathematically precise.  And what about the majority of living species that don’t actually mate (like all the bacteria, and other monists)?

Sharing the same exact DNA sequence doesn’t really work, because individuals within a species don’t share their exact complete sequences, and it is impossible to draw the line between who is in the species and who isn’t on this basis. It seems that the idea of species is useful, but not very exact, and very hard to pin down.

So, it might be necessary, in order to make any mathematically based theoretical progress in biology, to either: 1. Invent some new kind of mathematics or formalism that is conducive to describing biological reality (as was done a number of time for physics); or 2. Give up on a mathematical treatment, and use something completely different. And no, I do not know what that might be, but it might need to stretch what we call science and methodological naturalism a bit. We might even need philosophy to get somewhere!. I can write this scientific heresy here, because this is my blog, and I can write anything I want. If you are reading this, you can also, and I would love to read what you think about this idea.

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My Talk on Evolutionary Biology

Here is the link to my recent talk at the American Scientific Affiliation Washington DC Metro Chapter, on June 24, 2016. Its a bit dark, and its long, but about half of the video is discussion from the audience, which is worth hearing.

Among the voices in the Discussion (the camera didnt move, so you cant see them) are Mike Beidler, Keith Furman, Anna Rich, Tom Burnett, Paul Arveson, Langston McKee, and a number of guests whose names I didnt write down.


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