How not to argue about the resurrection

Since it’s Easter, I’ve been having a few discussions around the resurrection of Jesus (see Luke 24 for one account). One of the discussions involved my interlocutor arguing that the resurrection would require complete suspension of the laws of physics, and thus must be discounted. His idea was that the best explanation was “mass delusions and a series of hallucinations”.

I think it’s important to distinguish in what capacity we make different statements. As individual human beings we tend to be multifaceted; within specific disciplines, we must narrow our range of possibilities. Science, for instance, explores natural phenomena within the known universe. History explores multiple strands of evidence (some scientific, some not) to investigate and understand events in the human past. Psychology tries to unravel the curious workings of the human mind. Each of these is limited in scope, but powerful within its field.

Grainge Clarke on the assumptions of science

There’s an excellent article by W. Grainge Clarke on the philosophy of science and how it relates to the Christian worldview.

On the topic of the underlying assumptions of the scientific method, he writes:

“These presuppositions are, by their nature unprovable, and some philosophers would consider them unacceptable. Behind the acceptance of these presuppositions lies the fact that modern science developed when the dominant worldview in Europe was Christian. If the Christian worldview is accepted they all make reasonable sense. However, on the atheistic worldview, that all is the product of matter-energy, time and chance, then none of these presuppositions are justifiable. To consider just one case: ‘The human mind is capable of rational thought’. If the human mind has been developed solely by non rational forces then there is no reason to believe that it can be rational and certainly it is not to be relied upon. Consider two computers one of which was designed and assembled by the IT staff at the local university and the other by the local kindergarten. Which is most likely to function well? Yet the kindergarten children have much more intelligence than blind chance.”

You can find the whole article here:

“Wrong fight, wrong concepts, wrong everything” by Grainge Clarke

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Related posts:

Hypothetically speaking

Maths, science and abstractions

Where God meets physics

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God and the “God particle”

The Telegraph has an interesting short piece from Alistair McGrath today. He looks at the parallels between the faith in the Higgs boson and faith in God, both based on explanatory power rather than direct experiemental observation. He concludes:

“Some tell us that science is about what can be proved. The wise tell us it is really about offering the best explanations of what we see, realising that these explanations often cannot be proved, and may sometimes lie beyond proof. Science often proposes the existence of invisible (and often undetectable) entities – such as dark matter – to explain what can be seen. The reason why the Higgs boson is taken so seriously in science is not because its existence has been proved, but because it makes so much sense of observations that its existence seems assured. In other words, its power to explain is seen as an indicator of its truth.

“There’s an obvious and important parallel with the way religious believers think about God. While some demand proof that God exists, most see this as unrealistic. Believers argue that the existence of God gives the best framework for making sense of the world…

“There’s more to God than making sense of things. But for religious believers, it’s a great start.“

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Read the rest of the article here:

Higgs boson: the particle of faith

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Doing a little mythbusting…

Hard to believe that in such an intellectually advanced age there are still some who cling tenaciously to the notion that “Jesus was not a real historical figure”, but apparently the light of education has still not penetrated all the deep corners.

Should be unfortunate enough to find yourself accosted by denialists, you may find this essay series by James Hannam useful. Hannam writes in his introduction:

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“The thesis that Jesus never existed has hovered around the fringes of research into the New Testament for at least a century but it has never been accepted as a mainstream theory. This is for good reason. It is simply a bad hypothesis based on arguments from silence, special pleading, and an awful lot of wishful thinking. It is ironic that certain atheists will buy into this idea and leave all their pretensions of critical thinking behind…

In this four-part series, it is not my intention to study the minutiae of the various arguments. Instead, I will focus on three central contentions often advanced in discussions about Jesus. These are 1) the lack of secular references,  2) the alleged similarities to paganism, and 3) the silence of St. Paul.”

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Hannam deals with each of these contentions in a highly readable and well-researched series of essays. Read the rest of Is Jesus Christ a Myth? here:

Part 1  |  Part 2  |  Part 3  |  Part 4

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Hannam holds degrees in physics and history from Oxford and London universities, and his doctorate in the history of science from Cambridge University, and recently published God’s Philosophers: How the Medieval World Laid the Foundations of Modern Science, the first history of medieval science written for the layperson. (You can also read more from him at Quodlibeta).

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Related posts:

Faith: reflecting on evidence

A theoretical faith

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A theoretical faith

The title of this post contains a pair of words that can be difficult to nail down. Let’s take them one at a time:

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Theory

In common parlance the word “theory” is used to denote something purely conceptual, usually in contrast to something which has been implemented in the real world. This causes difficulty when referring to scientific theories, because in science, the word carries somewhat different implications. Scientific explanations for observed phenomena start as hypotheses, which are basically conjecture. After more testing and data collection, if the hypothesis appears to be useful in explaining the data and predicting results, confidence in the explanation increases. Once there is a strong weight of supporting evidence, we start to refer to the explanation as a “theory”.

The American National Academy of Sciences describes the distinction in usage thus:

“In everyday language a theory means a hunch or speculation. Not so in science. In science, the word theory refers to a comprehensive explanation of an important feature of nature supported by [data] gathered over time. Theories also allow scientists to make predictions about as yet unobserved phenomena…”

So it is understandable that scientists become frustrated with the dismissal of a scientific theory with phrases like, “oh, it’s just a theory”. This sort of language shows a grave misunderstanding of the subject.

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Faith

Likewise, in common parlance, “faith” is often understood to mean “a belief without evidence”. But in the Christian context, faith carries very different connotations. Theologian Tyron Inbody (in The faith of the Christian church: an introduction to theology) notes three uses of “faith” within Christianity:

• Assent: we believe that God has revealed Himself to us and can be known personally. This aspect of faith is largely intellectual: we are presented with God’s assertions about Himself (in the Bible, for instance), we decide that they are trustworthy and assert that they are true.
• Trust: we believe that God will honour His promises, and that He is reliable.
• Loyalty: we strive to ‘live out our faith’. In this context: “To have faith is… to obey Jesus; it is to be loyal in life and death to the God whom we meet in Jesus Christ.”

Although these three aspects of Christian faith are distinguishable, they are also inseparable. Christian faith is inextricably entwined with understanding: we have knowledge and understanding of God from personal experience, Scripture and the community of believers, and this forms the basis of our trust in God. Inbody writes:

“Faith in the New Testament means belief, specifically belief in God’s Word in Scripture. To have faith is to assent or to give credence; it is to believe. Faith refers to our acceptance of the message of the gospel… Faith means ‘belief in and acceptance of His revelation as true… an act of intellect assenting to revealed truth.”

The Christian faith is not divorced from reason: it is inseparable from reason. But as Thomas Aquinas explained, it is not just an intellectual exercise: it is also an act of will. I decide that certain things are true, and I choose to act on that belief.

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A theoretical faith

Now, why have I put these two difficult words together?

Well, my personal exploration and acceptance of the Christian faith was similar in many ways to the development of a scientific theory. From the tentative hypothesis that Christianity is true, I sought more data with which to test this conjecture. The central elements of Christianity are the claims about the life, death and resurrection of Jesus. I found the evidence of his death and resurrection convincing enough to explore further.

A scientific theory is a framework which helps to explain observed phenomena. What about Jesus’ life and teachings? Do they make sense of the world I experience?  The framework of Christianity explains the world that I see around me more coherently than any other.

Of course, we should seek to challenge any theory to test its robustness, so I do this with my faith. The “problem of evil” is often considered the biggest counter to Christianity: Given that we observe evil in the world, how can we believe in the existence of a God who is both loving and all-powerful? I explore this question, and I come to a remarkable conclusion: Firstly, I find in Christianity a compelling and convincing framework to explain the coexistence of evil in this world and the Christian understanding of God. Secondly, if I try to remove God from the picture, I don’t even know what the word “evil” means. It turns out that the “challenge” becomes still further support for my beliefs. And so my faith grows. The more that I test it, the more compelling it becomes.

Christianity also claims that we can experience God personally. Here we must move to the “belief in”. I move from a position of intellectual assent and step out: I seek to meet with God through prayer and personal experience. He meets me. The God I encounter personally resonates completely with the God of my intellectual assent. My faith grows.

From my experience, my belief in God, comes my loyalty to God. I have found that if I seek to live my life in accordance with His will and listening to Him, my life is a much better place. He has shown Himself to be faithful and good.

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I do not think that my personal experiences are unusual: in fact, I would say that the process I have described is analogous to the faith of most any Christian. The details will be a bit different, of course. St Paul had a rather more dramatic starting point for his faith, but he still based it on beliefs about God: specifically, beliefs that Jesus was God and that he was resurrected from the dead. Paul’s belief in and loyalty to God were a response to this.

Christian faith intrinsically contains a rational and evidentiary basis. N. T. Wright, the bishop of Durham, writes:

“I cannot… imagine a Christianity in which the would-be Christian has no sense, and never has had any sense, of the presence and love of God, or the reality of prayer, of their everyday, this-worldly life being somehow addressed, interpenetrated, confronted, embraced by a personal being understood as the God we know through Jesus.”

For a final description of faith in a Christian context, I close – as is often the case – with C. S. Lewis. In Mere Christianity, Lewis writes:

“Faith, in the sense in which I am here using the word, is the art of holding on to things your reason has once accepted, in spite of your changing moods.”

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Related posts:

Faith: reflecting on evidence

Believing and understanding

Chesterton on Miracles

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Maths, science and abstractions

I attended a forum last week entitled “Is there certainty beyond science?”. As one of the speakers pointed out, perhaps a useful starting question would be, “Is there certainty within science?”, but the title did raise some interesting questions about what we mean by the words “certainty” and “science”.

Certainly (see what I did there?) there seems to be a common assumption that science at least aims to find certainty in the midst of confusion. The general perception is that science rigorously follows a trail of evidence to reach conclusions which can be claimed with a high degree of confidence. And there are even mechanisms to try and assess the degree of uncertainty in a given scientific theorem (although the willingness of adherents to acknowledge that uncertainty may be somewhat hit-and-miss).

What is often missing from the conversation is the impact of methodological assumptions on the usefulness of the conclusions which result from a particular methodology. Let’s look at mathematics as an extreme example.

Maths operates within the ultimate abstraction. It is a realm of pure ideas. This has advantages: because the system is entirely conceptual, the laws can be rigorously defined. This allows us to “prove” mathematical theorems by conclusively demonstrating a logical consistency. But to apply a mathematical concept to anything real, we must project from the abstraction back to the real world, where we cannot rigorously define the laws. Some of the projections are useful: arithmetic operations are easily projected onto everyday objects (so “3 bananas + 4 bananas” can easily be understood as seven actual bananas). Some projections are less straightforward: the relationship between a second-order differential equation and the acceleration of a car under constant force is not quite as intuitive.

Science also operates within an abstraction. The realm of science is limited by its methodological assumptions, such as philosophical naturalism and the regularity of nature. These assumptions are useful in that they allow us to limit the potential interactions that we investigate to those which are amenable to the tools of science. In other words, we limit what we will accept as an explanation of phenomena, and this allows us to define our area of investigation. But in making these assumptions, we have created an abstraction of the real world, and it is this abstraction that we investigate rather than the real world itself. As in the case of mathematics, the conclusions may or may not be readily suited to being projected back into our understanding of the real world.

It is worth noting that any of our abstractions are only definable from outside the system. We say that mathematics operates within a logically consistent and rigorously defined framework, but its logical consistency cannot be proven mathematically. (This isn’t a case of “It hasn’t been done yet”, this is a case of “It’s impossible even in principle”). We make a working assumption of methodological naturalism when we engage in scientific research, but we cannot scientifically demonstrate the validity of such an assumption.

Perhaps more interestingly, this also implies that we cannot fully define the operational parameters of the real world from within the system.

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Related posts:

On Spherical Cows and the Search for Truth

Believing and understanding

Chesterton on Miracles

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Chesterton on Miracles

Another excerpt from G. K. Chesterton’s Orthodoxy, this time on the subject of miracles:

But my belief that miracles have happened in human history is not a mystical belief at all; I believe in them upon human evidences as I do in the discovery of America. Upon this point there is a simple logical fact that only requires to be stated and cleared up.  Somehow or other an extraordinary idea has arisen that the disbelievers in miracles consider them coldly and fairly, while believers in miracles accept them only in connection with some dogma.  The fact is quite the other way. The believers in miracles accept them (rightly or wrongly) because they have evidence for them.  The disbelievers in miracles deny them (rightly or wrongly) because they have a doctrine against them. The open, obvious, democratic thing is to believe an old apple-woman when she bears testimony to a miracle, just as you believe an old apple-woman when she bears testimony to a murder … If it comes to human testimony there is a choking cataract of human testimony in favour of the supernatural.  If you reject it, you can only mean one of two things … you either deny the main principle of democracy, or you affirm the main principle of materialism — the abstract impossibility of miracle.  You have a perfect right to do so; but in that case you are the dogmatist.  It is we Christians who accept all actual evidence — it is you rationalists who refuse actual evidence being constrained to do so by your creed. But I am not constrained by any creed in the matter, and looking impartially into certain miracles of mediaeval and modern times, I have come to the conclusion that they occurred.  All argument against these plain facts is always argument in a circle.  If I say, “Mediaeval documents attest certain miracles as much as they attest certain battles,” they answer, “But mediaevals were superstitious”; if I want to know in what they were superstitious, the only ultimate answer is that they believed in the miracles … Iceland is impossible because only stupid sailors have seen it; and the sailors are only stupid because they say they have seen Iceland.

The sceptic always takes one of the two positions; either an ordinary man need not be believed, or an extraordinary event must not be believed.

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Related posts:

Believing and understanding

Faith: reflecting on evidence

Plus ça change…

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On Spherical Cows and the Search for Truth (Part II)

Update:

This post and Part I have been edited and combined into a single essay. The full version can be found here.

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Part I of this essay was an overview of how models (and scientific inquiry in general) actually work.

Let’s have a quick recap of the key points:

• Explanations should be as simple as possible, but no simpler.
• We make sense of complex systems by building models.
• Models are built for specific objectives and incorporate assumptions.
• The usefulness of a model depends on the validity of those assumptions.
• We cannot modify our objectives without re-examining our assumptions.
• Models can never be verified (shown to be true), only confirmed (shown to be useful).
• Scientific theories are models.

In this section, I want to explore the role of science in the search for ultimate truth.

We need to recognise the limitations of science as a method of pursuing truth, and with our newly-acquired understanding of models I hope that it will be clearer what those limitations are.

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Methodological naturalism and the limitations of scientific models

Science, as a collection of models (termed theories or hypotheses according to their level of confirmation), is built on a set of assumptions. These are broadly grouped under the philosophy of methodological naturalism, and could be summarised as:

• The world we observe actually exists and is consistent.
• We can use our reason and senses to explore it.
• The material world is all that there is.

So we must ask ourselves: how useful is naturalism as an assumption?

The general opinion amongst philosophers of science is that it is a useful simplification. That is not to say that it is true, only that it is useful. Steven Schafersman, a geologist and prominent advocate against Creationism, writes that:

“… science is not metaphysical and does not depend on the ultimate truth of any metaphysics for its success … but methodological naturalism must be adopted as a strategy or working hypothesis for science to succeed. We may therefore be agnostic about the ultimate truth of naturalism, but must nevertheless adopt it and investigate nature as if nature is all that there is.”

Philosopher of science Robert Pennock, also a prominent voice against Creationism (and Intelligent Design), is more explicit. In his 1997 paper for a conference on “Naturalism, Theism and the Scientific Enterprise”, he states that science “makes use of naturalism only in a heuristic, methodological manner.” He also argues against even the theoretical possibility of using scientific methodology to explore supernatural issues:

“Methodological naturalism itself … follows from reasonable evidential requirements in science, most importantly, that hypotheses be intersubjectively testable by reference to law-governed processes.”

Why does this preclude the supernatural? In the same essay, Pennock writes:

“Experimentation requires observation and control of the variables. We confirm causal laws by performing controlled experiments in which the purported independent variable is made to vary while all other factors are held constant and we observe the effect on the dependent variable. But by definition we have no control over supernatural entities or forces.”

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The pursuit of data

Assumption are fundamental to understanding the usefulness of the outputs of a model. But the assumptions underlying the scientific method will also influence the data that we subsequently look for. This limitation has been noted by philosopher Karl Popper and historian of science Thomas Kuhn, who notes that the “route from theory to measurement can almost never be traveled backward”. Theories also tend to build on each other, usually without revisiting the underlying assumptions.

Popper examines this problem of nested assumptions in his critique of naturalism:

“I reject the naturalistic view: It is uncritical. Its upholders fail to notice that whenever they believe to have discovered a fact, they have only proposed a convention. Hence the convention is liable to turn into a dogma. This criticism of the naturalistic view applies not only to its criterion of meaning, but also to its idea of science, and consequently to its idea of empirical method.” (The Logic of Scientific Discovery)

Note again the emphasis (in the second sentence) on the problem of confusing model confirmation with verification. This self-reinforcement of theory dominates most of science. Kuhn writes:

“Once it has been adopted by a profession … no theory is recognized to be testable by any quantitative tests that it has not already passed.” (The Structure of Scientific Revolutions)

We will never find what we do not seek and are unwilling to see.

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The usefulness of models

In their correct place, of course, models are very useful. The great French mathematician Pierre-Simon Laplace used Newton’s model of gravity to calculate the motion of the heavens (as well as for predicting ballistics) in his masterpiece Mécanique céleste. Napoleon asked to see the manuscript, being greatly interested in ballistics. According to the story, after perusing the equations Napoleon turned to Laplace and asked, “Where is God in your book?” To which Laplace famously replied, “Je n’avais pas besoin de cette hypothèse-là.” (“I had no need of that hypothesis.”).

Laplace was perfectly correct. He was using calculus to predict the motions of celestial bodies and bodies moving through air, and it is not useful to incorporate theological complications into that  prediction. Remember: as simple as possible, but no simpler. Of course, Laplace also didn’t include gravitational attraction from other stars in calculating the orbits of the planets. In the real world, we believe that other stars do exert gravitational attraction, but it is a useful simplification in our model that we ignore them at the scale of our solar system.

Laplace’s model does not correspond perfectly to reality, but it does allow us to make sense of data and make predictions, provided that we stay within the limits of its assumptions. Popper comments on the usefulness of the Darwinian evolutionary synthesis, despite the great limitations of that theory:

“Darwinism  is not a testable scientific theory, but a metaphysical research program … And yet, the theory is invaluable. I do not see how, without it, our knowledge could have grown as it has done since Darwin …  Although it is metaphysical, it sheds much light upon very concrete and very practical researches … it suggests the existence of a mechanism of adaptation, and it allows us even to study in detail the mechanism at work.”

But let us never confuse useful with true.

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Science and truth

So what can science really tell us, if not truth? Well, within the limitations of its assumptions, it can give us great insight into process and the nature of the material universe. But it cannot, by definition, tell us anything about the immaterial: including the supernatural, philosophical reasoning and morality.

The great Stephen Jay Gould, in his essay Nonmoral Nature, commented thus on the limitations of science:

“Our failure to discern a universal good does not record any lack of insight or ingenuity, but merely demonstrates that nature contains no moral messages framed in human terms. Morality is a subject for philosophers, theologians … indeed for all thinking people. The answers will not be read passively from nature; they do not, and cannot, arise from the data of science. The factual state of the world does not teach us how we, with our powers for good and evil, should alter or preserve it in the most ethical manner.”

Indeed, science cannot even comment on the validity of its own assumptions: they must simply be accepted at face value for any science to be done at all. As per Gödel’s Incompleteness Theorem, they are postulates which cannot be proven by the system itself.

In our search for insight into the supernatural, we’re out of the territory of science. And recall the fundamental principle of modelling: we cannot change our objectives without re-evaluating our assumptions. So we can’t even adapt any current science to deal with these questions: science is simply not equipped for the task.

I do not propose allowing supernatural explanations into science. But I do suggest that it is very misleading to imply that science in any way supports a materialist worldview. This is mere question-begging: scientific theory, by its very assumptions, operates within a materialist worldview.

But we do not live in “science”. We live in reality.

Are we searching for truth, or are we searching for a theory nested in unprovable assumptions?

If the supernatural exists, it is beyond the tools of science. But if we have a supernatural aspect to our existence, it is not beyond our experience. To limit ourselves wholly to a materialist view may deprive us of fully experiencing a part of ourselves.

Philosopher Alvin Plantinga argues strongly for this line of thinking. He wrote:

“If you exclude the supernatural from science, then if the world or some phenomena within it are supernaturally caused – as most of the world’s people believe – you won’t be able to reach that truth scientifically.”

Are you missing out on something important by clinging to rigid materialism, perhaps because of a mistaken belief that such a worldview has scientific justification? Is there anything more to life?

Not to science. To life.

C. S. Lewis, certainly, had no doubt about the importance of our supernatural aspect. In Mere Christianity he described the human condition thus:

“You don’t have a soul. You are a soul. You have a body.”

What are you missing out on?

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Related posts:

On Spherical Cows and the Search for Truth (Part I)

Faith: reflecting on evidence

Believing and understanding

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On Spherical Cows and the Search for Truth (Part I)

Update:

This post and Part II have been edited and combined into a single essay. The full version can be found here.

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Science is great.

It lets me play with cool toys, it pays my bills, it helps me understand the world.

But I have to phrase that last part carefully. It doesn’t completely explain the world, it helps me understand the world.

That’s because science deals with models.

And models have assumptions.

And assumptions lead to limitations.

This may not be a bad thing. Depending what we are trying to understand, and the level of detail at which we are trying to understand it, the assumptions may greatly simplify our work without interfering with our objectives. But a clear statement of the assumptions is vital for anyone trying to assess the usefulness of a model in addressing a particular question.

Let me illustrate all this with cows.

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Modelling a cow

Suppose we need a quick estimate of the mass of a cow. (Imagine we’re in a rural setting far from a WiFi signal and can’t use Google). With just a pencil and piece of paper, how would we get a quick first-order approximation?

Well, we can’t lift it up, so we have to come up with an indirect route to get the mass. We know that:

Mass = Volume x Density

…and we know that most animals are approximately the density of water (hence the fact that they float at the surface of water but are mostly submerged). And we know from school that water is 1000kg per cubic metre. (For the USA readers, sorry, but I’m going to use SI units for this. One of the beauties of a rational measurement system is that it makes this mental arithmetic a lot easier).

So all we have to do is estimate the volume of a cow and we’re home free.

Now, since a cow is an awkward shape for which we can’t calculate a volume, we’ll approximate it to something simpler. Such as a sphere:

Or, if that seems a little too abstract, try a cylinder:

Better? OK.

You’ll note that the legs, tail, ears and head and neck are all drawn in lines: that’s because we’re going to ignore them in our calculation. If we make the cylinder a little bigger than the cow’s body, we’ll be able to safely assume that the “small skinny bits” could fit in the left-over spaces, and the overall volume will be about right. Remember this is just a first-order approximation.

So now we walk over to the cow, and try and gauge the dimensions of our cylinder.

We’ll assume an average-sized cow, and let’s approximate it at maybe 1m in diameter, and about 1.5m long. For a cylinder, volume is given by:

V = π × r² × l

Crunching the numbers, (and assuming π=3.2 to make the maths easier), this comes out at 1.2m³. Recalling the density of water, our final estimate is 1.2tonnes for the mass of a cow. Which is actually pretty decent: steers are about 750kg, the heaviest bulls are about 1750kg, so 1200kg is the right ballpark.

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The modelling process

Note what we did in the exercise: we built a model to organise our thinking, and we did it in following way:

1. Define your objectives. (Give a rough estimate the mass of the cow).

2. Make assumptions in light of the objectives. (The skinny/pointy bits can be ignored. The body can be represented by a cylinder. The density can be approximated by water).

3. Build a model incorporating those assumptions. (A simple cylinder of density 1000kg/m³)

4. Extrapolate from the model results back to the real world. (Our cylindrical model weighs 1.2 tonnes → we estimate that an actual cow weighs approximately 1.2 tonnes).

Thus our model of reality helps us to understand reality by simplifying it and then extrapolating the results back to reality.

Einstein famously said that an explanation should be as simple as possible, but no simpler.

How do we decide how simple to make it? By understanding our objectives and making assumptions in light of those objectives. The assumptions are all valid based on the starting objective that we only need a rough estimate. If we need an accurate mass (ie., our objectives change), those assumptions don’t hold anymore.

Now let’s watch it all go wrong.

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Tripping on the next step

Suppose we now ask ourselves: “What is the surface area of a cow?” (Don’t ask why we’re pondering mathematical questions in a cow paddock, just run with it).

Well, we think to ourselves, we have a model of a cow. We know how to calculate the surface area of a cylinder:

A = 2 × π × r × (r + l)

…so we’ll take our cylinder and crunch the numbers again. This is easy!

Unfortunately, it’s also incorrect.

In using the cylinder, we are mistaking our model cow for an actual cow.

In modelling terms, we have modified our objectives without revisiting our assumptions.

The assumption that “all the pointy bits don’t make much difference” is true for volume, but it is not true for surface area: they make a very significant contribution to that value. Thus our cylindrical cow is a very poor model for estimating surface area.

Modifying the objectives of a model will generally require a new model. At the very least, all the assumptions must be revisited and evaluated if our model results will retain any relevance in the real world.

This is also true, of course, of any unconscious assumptions we may have made.

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The verification problem

Science is basically a giant collection of models. The process that I’ve just described is analogous to the entire scientific method.

What we do in science is look at data, try and imagine an underlying process which could explain it, and then build a conceptual model. (The models are often mathematical – but not always – because mathematics allows us to express concepts simply and clearly in a well-defined system). We then try and imagine what other observations would be consistent with that model, and we look for support for it. If it reliably predicts actual observations (or in scientific jargon, if it has good explanatory power), we might regard the model as having been confirmed. This is the stage at which we may move from regarding it as an hypothesis to calling it a theory.

What we cannot do in science is verify a model. Verification (from the Latin “verus”, meaning “truth”), implies that the model is actually the truth.

A classic paper by Naomi Oreskes, Kristin Shrader-Frechette and Kenneth Belitz in the journal Science phrased this point particularly succinctly:

“Verification and validation of numerical models of natural systems is impossible. This is because natural systems are never closed and because model results are always non-unique. Models can be confirmed by the demonstration of agreement between observation and prediction, but confirmation is inherently partial. Complete confirmation is logically precluded by the fallacy of affirming the consequent and by incomplete access to natural phenomena. Models can only be evaluated in relative terms, and their predictive value is always open to question. The primary value of models is heuristic.” (“Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences”, Science 263 (5147), 1994)

Models are useful. The whole point of a model is to help us understand what is otherwise incomprehensible. But at all times we must remember that any model (including a scientific theory) is not truth.

Oreskes et al. continue:

“A model, like a novel, may resonate with nature, but it is not a “real” thing. Like a novel, a model may be convincing – it may “ring true” if it is consistent with our experience of the natural world. But just as we may wonder how much the characters in a novel are drawn from real life and how much is artifice, we might ask the same of a model: How much is based on observation and measurement of accessible phenomena, how much is based on informed judgment, and how much is convenience?” (Ibid.)

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We’ll look at the implications that all this has for science and the search for truth in Part II.

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Related posts:

On Spherical Cows and the Search for Truth (Part II)

Faith: reflecting on evidence

Believing and understanding

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Faith: reflecting on evidence

Update:

This post has been edited and expanded. The full version can be found here.

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There seems to be a great deal of confusion among non-Christians about the meaning of the word “faith” in a Christian context. The prominent atheist evangelist Richard Dawkins writes that: “Faith, being belief that isn’t based on evidence, is the principle vice of any religion.” And further: “[whereas] scientific belief is based upon publicly checkable evidence, religious faith not only lacks evidence; its independence from evidence is its joy, shouted from the rooftops”. And thus we see that for Dawkins (and many atheists), religious faith is blind faith.

But such a view is totally at odds with the view of faith presented in the Bible and maintained throughout mainstream Christianity. The biblical narrative is full of references to faith based overwhelmingly on evidence. This was the whole reason that the apostle John wrote his gospel: “these are written that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name” (John 20:31, NIV). Francis Collins, former head of the Human Genome Project, says that Dawkins’ definition of faith “certainly does not describe the faith of most serious believers in history, nor most of those in my personal acquaintance.” Throughout the Bible we see this theme: you have been given evidence, so believe.

On the topic of evidence, we often see the charge that “Faith is opposed to science”. As both a scientist and a Christian, I find that to be patently false. Firstly, we must understand the rightful position of science on the topic. The great evolutionary proponent T. H. Huxley coined the word agnostic to describe not only his own personal philosophy, but also the necessary stance of science. He wrote,

“Agnosticism is of the essence of science, whether ancient or modern. It simply means that a man shall not say he knows or believes that which he has no scientific grounds for professing to know or believe. Consequently Agnosticism puts aside not only the greater part of popular theology, but also the greater part of anti-theology.”

This is not to say that science can never contribute to faith. Among the central issues of the Christian credo are belief in the historical truth of certain events. I believe that Jesus was a real person, that he lived around 2000 years ago, that he was crucified under the orders of Pontius Pilate, then the Roman Procurator of Judea. I believe that God raised him from the dead, and that he appeared physically to hundreds of people after his resurrection. There are many other things that I believe about Jesus, but I offer these as a starting point, not only because they are all verifiable by historical and archaeological evidence, but because all my other beliefs about Jesus hinge on his death and resurrection. The apostle Paul, preaching to the gentiles in Athens, explains that the resurrection of Jesus was “proof to all” of God’s plans. In his letter to the church in Corinth, Paul is even more explicit: “if Christ has not been raised, then all our preaching is useless, and your faith is useless.” (1 Cor. 15:14, NLT). But the scientific contributions to the question of the death and resurrection of Jesus, principally through archaeology and textual criticism of the historical records, overwhelmingly endorse the beliefs I have stated above. There is evidence, so I believe.

On broader issues, such as the existence of a God who created the universe, science is in a far more difficult position. I have already discussed in a previous post how Stephen Jay Gould articulated so clearly that:

“Science simply cannot (by its legitimate methods) adjudicate the issue of God’s possible superintendence of nature. We neither affirm nor deny it; we simply can’t comment on it as scientists.”

The tools of science are unequipped to deal with the supernatural and the unobservable. Sir Peter Medawar, Nobel laureate in Medicine, noted that:

“The existence of a limit to science is, however, made clear by its inability to answer childlike elementary questions … such as ‘How did everything begin?’; ‘What are we all here for?’; ‘What is the point of living?’”

Furthermore, for any postulated experiment to determine God’s existence, we have what I would term the isolation problem. That is to say, scientific experiments rely on experimental controls: if we wanted to determine the existence or lack of existence of God in an experiment, we would need another experiment in which God didn’t exist, to which we could compare our results. But God is present in the entirety of existence. He is not just the Creator but the Sustainer of the universe. Imagine a creature which lived its whole life under water and could not exist without water, attempting to eliminate “wetness” from an experiment.

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Acceptance of evidence: the real issue

In fact, the perceived lack of “evidence” for the Christian faith generally arises from an a priori decision that any evidence pointing towards the truth of Christianity must automatically be rejected. When the “Big Bang” theory was first proposed, it was met with staunch opposition from atheists on principle, rather than on scientific grounds, because it would lend support to the idea that the universe had a specific beginning, and thus force the issue of God’s creation into the picture. An endless universe could ignore the need to explain its beginning, but a universe with a definite and identifiable starting point could no longer bypass this issue. When the cosmic microwave background was discovered, the validity Big Bang theory was accepted as being conclusively demonstrated, but the same objectionists simply moved on to other semantic arguments and ignored the theological implications.

Jesus himself referred to this phenomenon: in chapter 16 of Luke’s gospel, he tells the story of a man who has died and is suffering in hell, and he begs that someone rise from the dead to go and warn his brothers of the truth. He is told that the prophets and the scriptures already give all the information his brothers need. But, he says, if someone from the dead goes to them, then they will believe. To which the reply comes:

“If they do not listen to Moses and the Prophets, they will not be convinced even if someone rises from the dead.” (Luke 16:31, NIV)

For those less insistent on keeping our eyes closed, every facet of the universe is a glorious testament to God’s creation. Even T. H. Huxley acknowledged that:

“… true Agnosticism will not forget that existence, motion, and law-abiding operation in nature are more stupendous miracles than any recounted by the mythologies, and that there may be things, not only in the heavens and earth, but beyond the intelligible universe, which ‘are not dreamt of in our philosophy’.”

Or, as the psalmist phrased it:

“The heavens declare the glory of God; the skies proclaim the work of his hands.” (Psalm 19:1, NIV)

Is that a statement of science? No. But so much of what makes life glorious is inaccessible to science, and it really would be a shame to just ignore it all.

As for me, I do not take a blind leap of faith. The path ahead is thoroughly illuminated by historical evidence, scientific insight and personal experience, and I see clearly where I am choosing to walk.

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Related posts:

Believing and understanding

On Spherical Cows and the Search for Truth

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