Sunday, November 23, 2008

Mathematics and God


My interest in this piece is the fact that I am gathering information from various sources in order to validate the work of Cornelius Van Til. Van Til is recognized as formulating a defence of the Christian faith variously known as the Transcendental Argument or (more broadly) Presuppositional Apologetics.
Presuppositional Apologetics recognizes that people come to various truth claims with a readymade worldview through which all truth claims are interpreted. Therefore a persons epistemological background is seen to play a crucial part in what is recognized as true or not true (or whether "truth" is even a valid category!). It is therefore the presuppositions a person holds that determine how those claims are judged. The high claim of Presuppositional Apologetics is that unless one presupposes the existence of God, no other presupposition can logically account for anything. This claim is so profound that any other presupposition will, when pushed to ultimate conclusions lead to irrationality. This post and others like it is concerned to point out the validity of this extraordinary claim by pointing to other writers who have seen and logically laid claim to a) either show non-theistic accounts to be using faulty logic or b) where an expert in a particular field has come to admit that from their particular world-view a certain phenomena is inexplicable.

In this post we look at Mathematics. And we look at it through the eyes of research mathmetician Leland McInnes Phd. The point of interest in his blog is not only the inexplicable fact of maths, (from a presumed naturalistic worldview) but the extraordinary ability of mathematics to correspond to the problems of physics sometimes even finding a mathematical solution to a "real-world" problem before the problem is even raised in a maths-related context.


I was browsing the Internet the other day looking for materials to teach math to our twelve year old when I stumbled across this blog: The Narrow Road by Leland McInnes.

Leland McInnes is a mathematician who recently completed a Ph.D. in topological algebra at the University of Western Ontario. He lives in Ottawa.  


http://en.wikipedia.org/wiki/User:Leland_McInnes

Now if math for you was anything like it was for me when I went to school you probably wouldn’t have given the blog another look, but for reasons unknown to me I stayed awhile and wandered down the paths that the author obviously found so intriguing and beautiful.


All that is in blue Italics comes from “The Narrow Road” by Leland McInnes or green italics from the book “Orthodoxy” by G.K. Chesterton. Anything in Bold I have added to make a point or emphasize. If you can wade through the lengthy logic of 1+1=2 given below you will pan out nuggets further on but otherwise don't be to daunted by it all! (Actually the length of the explanation serves well even if you don’t understand it, it is merely there to give weight to the point that maths actually makes complex logical operations palpable to elementary school kids.)

One of the first things I learned from McInnes is that what is seemingly basic and obvious is not necessarily so:






Natural numbers (also known as counting numbers) are one of those remarkable abstractions, like objects falling to the ground, that we take for granted. Natural numbers are, however, a very abstract concept - they simply don’t exist in the external world outside your own head. If you think otherwise, I challenge you to show me where the number 3 exists. You can point to some collection of 3 things, but that is only ever a particular instance that possesses the property common to all the particular instances from which the number 3 is generalised. Because we take natural numbers for granted we tend to make assumptions about how they work without thinking through the details. For instance we all know that 1 + 1 = 2 - but does it? Consider a raindrop running down a windowpane. Another raindrop can run down to meet it and the separate raindrops will merge into a single raindrop. One raindrop, plus another raindrop, results in one raindrop: 1 + 1 = 1. The correct response to this challenge to common sense is to say “but that’s not what I mean by 1 + 1 = 2″ and going on to explain why this particular example doesn’t qualify. This, however, raises the question of what exactly we do mean when we say that 1 + 1 = 2. To properly specify what we mean, and rule out examples like putting 1 rabbit plus another rabbit in a box and (eventually) ending up with more than 2 rabbits, is rather harder than you might think, and requires a lot of pedantry. I’ll quote the always lucid Bertrand Russell** to explain exactly what we mean when we say that 1 + 1 = 2:


The reader who is not especially interested in mathematics per se is cordially invited to skip the lengthy explanation given below, but note the paper saving properties of maths when we realize just how lengthy the proposition (1+1=2) is when we use language instead of numbers! It may be helpful to take up the comments beginning with the words:  "
As you can see..."

Omitting some niceties, the proposition ‘1 + 1 = 2′ can be interpreted as follows.
We shall say that φ is a unit property if it has the two following properties:
1. there is an object a having the property φ;
2. whatever property f may be, and whatever object x may be, if a has property f and x does not, then x does not have the property φ.
We shall say that χ is a dual property if there is an object c such that there is an object d such that:
1. there is a property F belonging to c but not to d;
2. c has the property χ and d has the property χ;
3. whatever properties f and g may be, and whatever object x may be, if c has the property f and d has the property g and x has neither, then x does not have property χ.
We can now enunciate ‘1 + 1 = 2′ as follows: If φ and ψ are unit properties, and there is an object which has property φ but not the property ψ, then “φ or ψ” is a dual property.
It is a tribute to the giant intellects of school children that they grasp this great truth so readily.
We define ‘1′ as being the property of being a unit property and ‘2′ as being the property of being a dual property.
The point of this rigmarole is to show that ‘1 + 1 = 2′ can be enunciated without mention of either ‘1′ or ‘2′. The point may become clearer if we take an illustration. Suppose Mr A has one son and one daughter. It is required to prove that he has two children. We intend to state the premise and the conclusion in a way not involving the words ‘one’ or ‘two’.
We translate the above general statement by putting:
φx. = .x is a son of Mr A,
ψx. = .x is a daughter of Mr A.
Then there is an object having the property φ, namely Mr A junior; whatever x may be, if it has some property that Mr A junior does not have, it is not Mr A junior, and therefore not a son of Mr A senior. This is what we mean by saying that ‘being a son of Mr A’ is a unit property. Similarly ‘being a daughter of Mr A’ is a unit property. Now consider the property ‘being a son or daughter of Mr A’, which we will call χ. There are objects, the son and daughter, of which (1) the son has the property of being male, which the daughter has not; (2) the son has the property χ and the daughter has the property χ; (3) if x is an object which lacks some property possessed by the son and also some property possessed by the daughter, then x is not a son or a daughter of Mr A. It follows that χ is a dual property. In short … a man who has one son and one daughter has two children.


As you can see, once we try to be specific about exactly what we mean, even simple facts that we assume to be self-evident become mired in technical detail. For the most part people have a sufficiently solid intuitive grasp of concepts like “number” and “addition” that they can see that 1 + 1 = 2 without having to worry about the technical pedantry. The more abstractions we pile atop one another, however, the less intuition people have about the concepts involved and it becomes increasingly important to spell things out explicitly.



We can see from the above that math is about logic or reasoning that otherwise would be very involved if it weren’t for the “shorthand” system of numbers. It was when I understood the idea that logic was endemic to math that my ears pricked up. Also when he talks about the “beauty of math”. I had not long ago written about beauty in the eye of the beholder (see
http://struth-his-or-yours.blogspot.com/2008/05/yes-this-is-true.html) I repeat the Albert Einstein quote from that piece-

"The eternal mystery of the world is its comprehensibility"


One of my pet subjects is the veneration of science in our day so when he started speaking of maths as being the foundation of modern science this also interested me.


The discovery and development of mathematics is one of the great achievements of mankind — it provides the foundation upon which almost of all modern science and technology rests. This is because mathematics, as
the art of abstraction, provides us the with ability to make simple statements that have incredibly broad application. For example, the reason that numbers and arithmetic are so unreasonably effective is that they describe a single simple property that every possible collection possesses, and a set of rules that are unchanged regardless of the specific nature of the collections involved. No matter what collection you consider, abstract or concrete, it has a number that describes its size; no matter what type of objects your collections are made up of, the results of arithmetic operations will always describe the resulting collection accurately. Thus the simple statement that 2 + 3 = 5 is a statement that describes the behaviour of every possible collection of 2 objects, and every possible collection of 3 objects.

In the above we see something of the universality of mathematics and the unity in diversity that philosophers have for ages attempted to comprehend, we can understand a little of McInnes’s (and our own?) fascination and awe of it all.

And again when he started talking about logical paradoxes and the philosophical considerations and arguments currently taking place amongst the mathematician elite I began to see a familiar pattern somewhat akin to the conspiracy of facts that G.K. Chesterton speaks of in his book Orthodoxy:

The Paradoxes of Christianity.

The real trouble with this world of ours is not that it is an unreasonable world, nor even that it is a reasonable one. The commonest kind of trouble is that it is nearly reasonable, but not quite. Life is not an illogicality; yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in wait. I give one coarse instance of what I mean. Suppose some mathematical creature from the moon were to reckon up the human body; he would at once see that the essential thing about it was that it was duplicate. A man is two men, he on the right exactly resembling him on the left. Having noted that there was an arm on the right and one on the left, he might go further and still find on each side the same number of fingers, the same number of toes, twin eyes, twin ears, twin nostrils, and even twin lobes of the brain. At last he would take it as a law; and then, where he found a heart on one side, would deduce that there was another heart on the other. And just then, where he most felt he was right, he would be wrong. It is this silent swerving from accuracy by an inch that is the uncanny element in everything. It seems a sort of secret treason in the universe. An apple or an orange is round enough to get itself called round, and yet is not round after all. The earth itself is shaped like an orange in order to lure some simple astronomer into calling it a globe. A blade of grass is called after the blade of a sword, because it comes to a point; but it doesn't. Everywhere in things there is this element of the quiet and incalculable. It escapes the rationalists, but it never escapes till the last moment. From the grand curve of our earth it could easily be inferred that every inch of it was thus curved. It would seem rational that as a man has a brain on both sides, he should have a heart on both sides. Yet scientific men are still organizing expeditions to find the North Pole, because they still organizing expeditions to find a man's heart; and when they try to find it, they generally get on the wrong side of him. Now, actual insight or inspiration is best tested by whether it guesses these hidden malformations or surprises. If our mathematician from the moon saw the two arms and the two ears, he might deduce the two shoulder-blades and the two halves of the brain. But if he guessed that the man's heart was in the right place, then I should call him something more than a mathematician. Now, this is exactly the claim which I have since come to propound for Christianity. Not merely that it deduces logical truths, but that when it suddenly becomes illogical, it has found, so to speak, an illogical truth. It not only goes right about things, but it goes wrong (if one may say so) exactly where the things go wrong. Its plan suits the secret irregularities, and expects the unexpected. It is simple about the simple truth; but it is stubborn about the subtle truth. It will admit that a man has two hands; it will not admit (though all the Modernists wail to it) the obvious deduction that he has two hearts. It is my only purpose in this chapter to point this out; to show that whenever we feel there is something odd in Christian theology, we shall generally find that there is something odd in the truth.

McInnes pays tacit approval to Chestertons appraisal of reality with the following lines, in effect saying just when you think your math is able to explain reality down to the last dotted “i” and crossed “t” it all goes to custard and challenges the very roots of logic.
As an example he waxes lyrical about the impossibility of expressing the square root of 2 as a fraction.(See
http://jedidiah.stuff.gen.nz/wp/?p=14 )

Paradoxes of the Continuum, Part II



Mathematical arguments can be very persuasive. They lead inexorably toward their conclusion; barring any mistakes in the argument, to argue is to argue with the foundations of logic itself. That is why it is particularly disconcerting when a mathematical argument leads you down an unexpected path and leaves you face to face with a bewildering conclusion. Naturally you run back and retrace the path, looking, often in vain, for the wrong turn where things went off track. People often don’t deal well with challenges to their world-view. When a winding mountain path leads around a corner to present a view of a new and strange landscape, you realise that the world may be much larger, and much stranger, than you had ever imagined. When faced with such a realisation, some people flee in horror and pretend that such a place doesn’t exist; the true challenge is to accept it, and try to understand the vast new world. It is time for us to round a corner and glimpse new and strange landscapes; I invite you to follow me down, in the coming entries, and explore the strange hidden valley.
As we noted at the start of this post, when a mathematical argument leads you somewhere you don’t wish to go you are left having to challenge the very foundations of logic itself. Surprisingly, that turns out to be the resolution: smooth infinitesimal analysis rejects
the law of the excluded middle.

So that while celebrating- if you like- the exquisite logical nature of maths at the same time when we come across these paradoxes we have to embrace either our inadequate grasp of higher logic or “challenge the very foundations of logic itself”
This reminds me of the Christian paradoxes like the Trinity, which is, after all a mathematical expression.
Now thus far you may be piqued at my attempts to elucidate a conspiracy of facts which, to my mind point to not a little evidence that all of these things are in fact the orchestration of an extraordinary, dare I say supernatural mind. But here it gets even more interesting. Given that McInnes is just an ordinary if somewhat brilliant mathematician not having any particular interest or view on metaphysics, or perhaps being even unabashedly secular in his thinking, the following observation of his becomes even more astonishing.


So far we’ve been discussing the completely abstract. We’ve climbed up a path of increasingly theoretical constructions built one atop the other to reach a point of potentially perilous irrelevance. Now it’s time to step into the concrete world. Our universe can be thought of as a space with some structure - the laws of physics. We can ask what functions or transforms of space and time will preserve certain structures (like, say, Maxwell’s equations). This leads us to a group of transformations of space-time that preserve desired properties - as I said, groups, once you know to look for them, crop up everywhere. Now something intriguing happens: the internal structures of the group correspond in a natural way with physical conservation laws, such as the law of conservation of energy, or the law of conservation of momentum. Things get really interesting, however, when we realise that, given the group, each irreducible representation of the group very naturally corresponds to a different fundamental particle, with force-carrying and non-force-carrying particles neatly delineated from one another according to the degree of the irreducible representation!



Now I do not lay claim to completely understand what he’s talking about here but you will no-doubt get the gist of it. Especially from what follows:


All of a sudden what had seemed like a little axiomatic game that mathematicians were off playing by themselves is having very real impacts on the world in which we live. All of a sudden we’ve come crashing back down into relevance. Which brings us to the start of the truly hard questions: why does it work?!



I like to compare his expression here with that of a person doodling with pen on paper. All sorts of lines, shapes and concepts are produced, which although interesting, were thought to bear no relation at all to reality other than the paper and ink they are created on. Suddenly and inexplicably (at least in the naturalistic world-view) someone has made the connection realizing that his or her creations are in fact a reinterpretation of the real world. That is what mathematics  is all about.


Mathematics works. That much is obvious to anybody - mathematics is essentially the language of much of science, and is seemingly unendingly applicable to the real world. The problem is that it is not at all obvious why this should actually be the case. Philosophers have struggled with this question since Pythagoras, all to no avail. It is entirely all too common for mathematicians to embark on a purely theoretical exploration of the truly abstract and abstruse as a mental game, only to have, decades or centuries later, their work prove stunningly applicable to some very real world problem. The mathematics that laid the foundations for General Relativity began with mathematicians wondering, purely hypothetically, what would happen if they ignored Euclid’s fifth postulate; much of the work of G.H. Hardy, who famously claimed no discovery of his would ever make a practical difference in the world, has found considerable application in cryptology. To explain its effectiveness it seems we need first to explain what mathematics actually is.


So why does it work? If your worldview precludes the existence of anything greater than the human mind then it would seem your explanation would inevitably fall short!


If mathematics is simply the abstraction of our intuitions about the physical world, then why is it so universal? Surely each mathematician would then develop a personal mathematics from their own intuitions and claims of mathematical objectivity would become muddied. Equally one can ask why it is that a rejection of intuition on purely logical grounds, such as the rejection of Euclid’s fifth postulate, should lead to mathematics that is surprisingly more applicable rather than less.

The same problem has been touched on in the issue of the universal human apreciation of beauty, and also exists in the universality of moral order. As McInnes so rightly points out if it was merely an arbitrary human construct why should a Japanese mathematician find just the same applicable way of doing math as someone from Lithuania? And again why should it then "lead to mathematics that is surprisingly more applicable rather than less" ? These "coincidences stretch the credibility of the naturalistic mindset to breaking point- who then has more "faith" ?




The following comes from Wikipedia articles:
Eugene Paul "E. P." Wigner, November 17, 1902 – January 1, 1995), was a Hungarian American theoretical physicist and mathematician.

He received a share of the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles". Wigner is important for having laid the foundation for the theory of symmetries in quantum mechanics as well as for his research into the structure of the atomic nucleus.

In 1960, Wigner published a now classic article on the philosophy of mathematics and of physics, which has become his best-known work outside of technical mathematics and physics, The Unreasonable Effectiveness of Mathematics in the Natural Sciences is the title of an article published in 1960 by the physicist Eugene Wigner. In the paper, Wigner observed that the mathematical structure of a physics theory often points the way to further advances in that theory and even to empirical predictions, and argued that this is not just a coincidence and therefore must reflect some larger and deeper truth about both mathematics and physics.
"It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of laws of nature and of the human mind's capacity to divine them."
The miracle of mathematics in the natural sciences

Wigner begins his paper with the belief, common to all those familiar with mathematics, that mathematical concepts have applicability far beyond the context in which they were originally developed. Based on his experience, he says 
"it is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena." 
He then invokes the fundamental law of gravitation as an example. Originally used to model freely falling bodies on the surface of the earth, this law was extended on the basis of what Wigner terms "very scanty observations" to describe the motion of the planets, where it "has proved accurate beyond all reasonable expectations."

Another oft-cited example is Maxwell's equations, derived to model the elementary electrical and magnetic phenomena known as of the mid 19th century. These equations also describe radio waves, discovered by David Edward Hughes in 1879, around the time of James Clerk Maxwell's death. Wigner sums up his argument by saying that 
"the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it." 
He concludes his paper with the same question with which he began:

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning."

What if- just supposing (and I know nothing of of Euclid’s fifth postulate!)- Humans were made in the image of a "super-being" who designed and brought into being the universe- and therefore were able to think his thoughts after him? Would it then not be "natural" that mathematics developed because of a conformity to a pattern of intelligibility that was in fact stamped on the whole universe, and us included being part of that stamp? 


Does mathematics fit so well because it does in fact comport with the language by which all of the creation exists?


Does this explanation possibly answer what otherwise is just amazing coincidence. What if these sort of things don't just happen in mathematics but in all areas of human endeavour? Ask Doctor Michael Behe what questions he has raised about the evolution debate, what about the language of dna? Or the issues raised by Guillermo Gonzalez and Jay W. Richards in their view of astro-biology and earths place in the universe, the happy "coincidence of the Goldilocks theory, the anthropic principle?


Can it then be argued that mathematics is simply logic? This would explain, to some degree, its applicability: mathematics would simply be the expression of fundamental eternal universal truths.

Here we must commend McInnes for his objectivity and intellectual honesty, there is a real contradiction here which he is really struggling with. Because in fact he is conceding- if mathematics is simply logic, and it is universal - it has therefore existence in its own right independent of mankind- How does it have this independence from mankind when we know that maths is strictly a mind thing? In other words it only takes place on a mental level. And how come it does apply so well to the universe if after all the universe is a completely random accidental cataclysm of circumstances? It shouldn't fit at all to the degree it does. The difference in the basic presupposition between say Einstein and McInnes is that for his worldview Einstein was a deist, that is he believed in (at the very least) the existence of a unifying, ordering entity over and above all that we call nature. Whereas McInnes is struggling to find within the closed order of nature an explanation for all the order and universality both in logic, specifically mathematical logic, how it works in our minds, is applicable to our world and does in fact transcend them both.

McInnes is struggling in fact with the skeptical mantra of the likes of Carl Sagan from whom this quote comes:

Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves."—Pale Blue Dot: A Vision of the Human Future in Space,

Carl Sagan was hugely popular in his time, and in some ways resembles the crusader for naturalism of recent times- Richard Dawkins. But I think even the most sceptic reader would have to think twice about his statement-
 "in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves." 
in the light of Eugene Wigner's statement from above- 


"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."


To continue with McInnes interesting journey....

Unfortunately, despite truly heroic efforts by some of histories greatest mathematicians and logicians (Frege in “Foundations of Arithmetic” Russell and Whitehead in “Principia Mathematica”) the reduction of mathematics to pure logic failed. While Russell and Whitehead managed to construct a remarkable edifice out of pure logic, introducing along the way many new concepts such as Type theory which is now of great importance in computer science, they fell short of building mathematics as we know it: their system was too weak and required extra axioms (the axiom of infinity and the axiom of reducibility) which cannot reasonably be called purely logical principles.
Can we not, then, define our base set of rules and proceed by logic from there? This was the approach to mathematics favoured by Hilbert and his formalist school. While this approach did much to shore up the shaky foundations of pure mathematics before running afoul of Gödel’s Incompleteness Theorems, it simply sidesteps our initial question. Mathematics, in this line of thought, becomes reduced to a game played with symbols on paper and an arbitrary set of rules (we ask only for consistency). Why should such an arbitrary game apply to reality? That is not at all clear.
The debate as to what mathematics actually is continues, mostly in philosophic circles - No school of thought has yet given a satisfactory answer. Personally I lean towards a more recent view that mathematics is about structure and can be grounded best in a structure oriented language such as that of Category Theory. However, Category Theory does not yet provide a sufficiently rigorous foundation to make that claim truly defensible. Only time will tell.
Thus we began wondering what there is in mathematics that we don’t know, and conclude realising that we don’t even know what mathematics is.


"No school of thought has yet given a satisfactory answer."

One wonders what would count as a satisfactory answer for McInnes- only one that proceeded from a naturalistic worldview?

A satisfactory argument has been given, but it appears not to be satisfactory to many even though logically tenable. This is somewhat surprising  and unfortunate-  when the logicality of it appears to be not  ground enough for intellectuals. Positing a supernatural being is both logically and experientially justifiable. This naturalistic bias is strongly evident here. What are the reasons for it? We turn to Vern Poythress.

Vern Poythress earned a B.S. in mathematics from California Institute of Technology (1966) and a Ph.D. in mathematics from Harvard University (1970). After teaching mathematics for a year at Fresno State College (now California State University at Fresno), he became a student atWestminster Theological Seminary, where he earned an M.Div. (1974) and a Th.M. in apologetics (1974). He received an M.Litt. in New Testament from University of Cambridge(1977) and a Th.D. in New Testament from the University of Stellenbosch, Stellenbosch, South Africa (1981).

 In 1974 Poythress published in The Journal of Christian Reconstruction an article entitled:


Here is a short extract from this paper:

 "The Reformational expression “total depravity” of man is used to say that no area of man’s nature and no area of his involvement with the world is left untouched or undefiled by man’s rebellion (Rom. 3). For an exposition of this, one could not do better than turn to the second book of Calvin’s Institutes. “The whole man, from the crown of the head to the sole of the foot, is so deluged, as it were, that no part remains exempt from sin, and therefore, everything which proceeds from him is imputed as sin.” Therefore, we now expect mathematical truth also to be misunderstood and perverted by fallen man."

Remember some of the prior observations and remember also that the words in blue are actual quotes from McInnes:


  • Mathematics is a mind matter: Natural numbers are, however, a very abstract concept - they simply don’t exist in the external world outside your own head.

  • ·Mathematics is intrinsically logical: Mathematical arguments can be very persuasive. They lead inexorably toward their conclusion; barring any mistakes in the argument, to argue is to argue with the foundations of logic itself

  • While essentially logical, current understanding of logic fails to give a complete explanation of some problems including what constitutes mathematics. Some problems in mathematics are greater than logic, or beyond our grasp of logic: we don’t even know what mathematics is.

  • Mathematics is universal: If mathematics is simply the abstraction of our intuitions about the physical world, then why is it so universal?

  • Mathematics bears an astonishing relationship to the real world- it explains the world: mathematics is essentially the language of much of science, and is seemingly unendingly applicable to the real world.
    McInnes asks all the right questions the most important being: Why does it work?!

    Being abstract it exists only in our heads, but on the other hand it is both logical and universal and it relates perfectly to the real world. (And in all the right places as Chesterton would affirm it goes wrong!) While it is inextricably logical, on certain occasions it defies logic. We didn’t invent it so much as discovered it.

    Mathematics- as the art of abstraction- exists, that is certain. It exists independently of human minds as its universality and its relationship with the real world verifies, we didn’t invent it. We did not invent the world. To say that math is a man-made entity when mathematical exercises which are happening purely on a theoretical level and then repetitively shown to bear amazing relevance to real world problems which are beyond the scope of human influence, is irrational. Its logic confirms that it is a matter of intelligibility, that the world may be explained in its (relatively!) simple terms also testifies to this. Some of it is not explained adequately or entirely by logic.

Let's summarize even more briefly-

  • Universal

  • Existence

  • Independence

  • Immaterial

  • Intelligible

  • Logical

  • Mysterious

Does that sound like the attributes of something (someone) else you’ve heard about? Go figure!

 It was Einstein who said- 
"The eternal mystery of the world is its comprehensibility." and also "I have deep faith that the principles of the universe will be both beautiful and simple  
It was his firm belief that the universe was intelligible and his deistic outlook encouraged him to attempt to comprehend the universe in such broad swathes with such little formulas.  

 has stood the test of time for over a hundred years but is now beginning to be questioned by the apparent discovery of Neutrinos, (See article Neutrinos News and Neutrality) sub-atomic particles travelling at greater than the speed of light. If this is verified then much of modern physics will have to be rewritten. This may further exemplify what G.K. Chesterton was meaning when he said :
The real trouble with this world of ours is not that it is an unreasonable world, nor even that it is a reasonable one. The commonest kind of trouble is that it is nearly reasonable, but not quite. Life is not an illogicality; yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in wait.

The real question is are these quirks attributable to divine personality? to G.K. Chesterton, the "not quite" symmetry of the universe was one of many evidences of intelligent design.



Richard Polkinhorne who worked for many years as a theoretical elementary particle physicist, from 1968 to 1979  was Professor of Mathematical Physics in the University of Cambridge, before resigning to train for the ministry of the Church of England. He is an Anglican priest and a Fellow of the Royal Society and was knighted by the Queen in 1997.

John Polkinghorne: The Friendship of Science and Religion

In this video he shows how compatible Science is with belief in God. In fact he shows how the two disciplines overlap on certain questions and how they can indeed be informative to each other across those boundaries. In case you missed it he is a distinguished Quantum physicist. Among some of the comments he made is this:


You can say that the physical Universe is rationally transparent to us. We're able to look into its workings, not only the vast curved structure of space/time, but also into the strange counter intuitive quantum world of the atom and things smaller than the atom, the sort of physics I myself worked in. The regime which, if you know where something is- you don't know what it's doing, if you know what it's doing- you don't know where it is. That's the quantum world, Heisenbergs Uncertainty Principle, totally different from the world of everyday, but nevertheless a world we can explore and to a very large degree understand.
So, why is science possible?....Not only is science possible but it turns out that it is mathematics, it is mathematics, which is the key to unlock the secrets of the physical Universe, the actual technique in fundamental physics to look for equations which are characterized by the unmistakable quality of mathematical beauty. Not all of you perhaps, will know about mathematical beauty, some of you undoubtedly will, it's a fairly er, er, rarified form of aesthetic pleasure...but, but it is one for those of us who are privileged to speak that language, can recognize and agree about. And we've found time and again in the history of physics that it's only... only equations that have that character of mathematical beauty which will prove to be convincing, by their long term fruitfulness of results and insights that they yield. So if youve got a friend, who is a theoretical physicist, and you want to upset him or her, then just say that "that latest theory of yours, looks rather ugly and contrived to me" and they will be very upset.
I suppose the greatest theoretical physicist I have ever known personally, was somebody called Paul Dirac. You may not, all of you, heard his name, but he was one of the founding figures of quantum theory and unquestionably the greatest British theoretical physicist of the 21st century. He was not a religious man, and he was not a man of many words, and he was once asked, "What is your fundamental belief?" And because he was not a man of many words he went to a blackboard, and he wrote on the blackboard: "The Laws of Physics Are Expressed In Beautiful Equations"

This lecture is well worth listening to in its entirety. It is a bigger picture of science and mathematics. Two of the points that he makes reference to are- quite apart from the inexplicable character of aesthetic beauty that epitomizes good formulas- that mathematics is a universal language but it was not invented so much as discovered, and it has an uncanny ability to anticipate how the Universe is put together. It is a reflection of the inherent underlying mathematical principles by which the Universe appears designed.


Tuesday, October 14, 2008

Response To An Atheist




Letter To The Editor Whangarei Leader
I write in response to A.L Brett

It was written some thousands of years ago that it is a foolish thing to say (even to yourself) there is no God.

Firstly the word "atheist" is the description of one who holds that there is no God. It is an untenable position for this reason- It is an ultimate definitive or exhaustive statement, an absolute statement if you like. It is foolish for the simple reason that a mere man (or any number of mere men) would claim infinite and infallible knowledge of all that exists, which is what you must assert in order to say God does not exist. This is what you are claiming if you are an atheist. You are in fact claiming by implication an attribute or power that has been reserved for God alone- that of infinite knowledge.
Whether or not you believe in his existence you surely would see the absurdity of claiming absolute knowledge. No Mr Brett all you can really say is “I do not believe such a God exists” in which case your view becomes an opinion more or less developed from evidence you may or may not have. And I for one will defend your right to an opinion, which I might reasonably expect you to do for me.



“atheists don’t preach from 1000 year old writings” (abridged) What is that to the point? How long ago did Isaac Newton “preach” about the law of gravity, is it still relevant today? Would it have been relevant a thousand years ago? Truth by its very nature is timeless, lets have no more of this new versus old stuff, what people really want to know is “Is it True?” Bell bottomed trousers and hoop skirts are in and out of fashion like politicians, but should we deal with truth this way?


“Atheists don’t go on healing and worshipping crusades to obtain donations…” Donations are given freely as a question of conscience, you pay taxes whether you would like to or not, even whether they are justified or not. I will grant you that there may be odd cases of manipulation for financial gain but greed is a vice of human nature found in any sphere of society and if religion were to be free from it then you would have to abolish all human involvement! But to be fair and consistent you would need to abolish every other human institution also, including atheism. An old sage (whom I have a great respect for) once said “should men ban rope because some will hang themselves with it?” To castigate Christianity because some abuse it is to mask the point. (I mention Christianity here since a Christian minister has been taken to task on his letter.) In other words don’t throw out the baby with the bathwater. Surely you aren’t trying to tell the public that atheists are without exception pillars of society where avarice is never to be seen! This and other evils are why Christianity exists, but it does not guarantee that it cannot be abused by the very evils that are the reason for its existence.


“Atheists don’t start holy wars…” Let’s dispense with this foolish talk of “holy” war, war is anything but holy and I would venture to say that word has only ever been used to rope in the religious for political ends or used in discussion against religion. As for atheists not starting wars, more blood has been shed in the last hundred or so years than the previous 1000 put together. And that happens to coincide with the fact that atheism has never, in the history of mankind been the driving force in any civilization except in these last hundred or so years. Stalin for example killed millions of his own people in just a few years, and communism is at its heart atheistic by definition. Communism is the child of an atheistic worldview. Chairman Mao said religion is the opiate of the people and his regime has waged war on millions. The Khmer Rouge- another horrific slaughterhouse scene following the existential ideologies of atheistic philosophers. Hitler enlisted Nietzsche a philosopher who coined the phrase “God is Dead” and wrote of a superman by whom Hitler promulgated the idea of a super race, the Arian. And this by no means diminishes the list. Nope, waging war is the human struggle for power to dominate and merely enlists the “God” word for enlarging the power base when it suits. It is unfortunately true the human propensity for self-deception is such that no one relishes doing evil (and justifies it) so much than when he does it in the name of God.


“Atheists don’t’ tell other non-believers…” Etc, etc. Really Mr Brett! What sort of people is it then who spend millions of dollars telling us what to eat, what to drink, where to eat it and drink it, what to wear, where to live and how to live, what to think and whether or not it is profitable to think at all. Atheism or to call it by its more covert name secularism is the most promulgated religion of the world. The atheistic worldview is the presupposition behind 90 per cent of every book, newspaper article,(letter to the editor), television series, movie, government policy etc, etc ad nauseum! And I must admit it has done a superb job Mr. Brett. Atheists keep to themselves? Do they indeed?
I go to the movies once in a blue moon and what do I find? I went recently with my wife and 10 year old son to the movies. We watched “Happy Feet” The penguin villains in the cast were the old, the religious, and the leaders. The particular emphasis of these “villains” was the use of Christian jargon like repentance and the derogatory use of Christian ideas. The audience would, I imagine be mostly young impressionable children. Is not this coercion? Whatever! And people begrudge the little time we may have on the blessed box. And not to put too fine a point on it, what exactly are you doing writing to the paper...? Looks like a soapbox to me!
All of this in the final analysis is beside the point. Whatever the worldview a person has, each believes in the reality of it or he/she wouldn’t hold it as his/her worldview and each in his/her own way preaches it as true, whether incidentally or by design. The real issues are, we both must defend each other’s right both to have the freedom to express our views, and to seriously question our own basis for believing either atheism or Christianity.
Is it true or is it not true?


If the claims of Christ are true then all these other things fall into their proper perspective. Would you not forgive a dog if you realized all he could do to alert you of danger were to tear at your trousers and pull you in the opposite direction? Some efforts are clumsy, some are insincere but can’t these be the faults of the messengers not the message? If the message is true then the incompetence or insincerity of the messenger is irrelevant.


"A thing is not necessarily true because badly uttered, nor false because spoken magnificently." St. Augustine



K A Campbell

Sunday, October 12, 2008

Human Heart Needs Belief

Click on newspaper clipping to read column
Human Heart Needs Belief
At last- something I can agree with in Joe Bennett’s column, (Northern Advocate, Sat. Oct 11) even if it’s only the header! I don’t have much objection to his appraisal of Hollywood’s cult status either, or the observations on fear.

I concede that he is right about human nature in so far as our need to believe in something; it’s endemic, it comes with the territory.

The acrid smell of falsehood really begins with the statement: “There is no joy in mere reason” Einstein would not agree with him, and I’m with Einstein.
[i]"The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed."
Sounds like good reason to me, and, by his own lips Einstein iterated the inspiration and beauty of the mysterious (his need to know) was only satiated by his reason (his ability to know).

[ii]"The further the spiritual evolution of mankind advances, the more certain it seems to me that the path to genuine religiosity does not lie through the fear of life, and the fear of death, and blind faith, but through striving after rational knowledge."

Again I’m with Einstein, firstly he finds no shame in assuming that ultimately the big questions are irrevocably metaphysical; matters of faith and reason. Second, blind faith- as he implied, is antithetical to reason, but that does not exclude a faith based on reason. This is the fallacy Bennett would have us believe (in common with all naturalistic thinkers) that faith and reason are like oil and water, mutually exclusive.

The “silly human heart” is not silly for its need of belief but silly for not being more careful in what it believes.

My hat goes off to you Mr. Bennett we are indeed creatures who need a belief system, the question is which one is the best and most suited to reason?

As a self-confessed “wordsmith” Bennett may find solace in a quote from an eminent wordsmith of another stripe. When asked by a journalist what is the most profound thing he’d ever heard, Malcolm Muggeridge replied (probably in a singsong voice): “Jesus loves me this I know ‘cause the Bible tells me so….”

Silly people believe that Muggeridge was a victim of circular reasoning and thereby invalidating his beliefs- not realising that reasoning on reason is equally circular. Muggeridge had faith in a transcendent reason- faith in reason per se is just mankind disguising that he has made himself God- whereby man becomes the measure of all things.
[i] Einstein quotes Copyright: Kevin Harris 1995,

Tuesday, September 30, 2008

The Language of Natural Selection



Natural Selection


From Wikipedia, the free encyclopedia


Natural selection is the process by which favorable heritable traits become more common in successive generations of a population of reproducing organisms, and unfavorable heritable traits become less common, due to differential reproduction of genotypes. Natural selection acts on the phenotype, or the observable characteristics of an organism, such that individuals with favorable phenotypes are more likely to survive and reproduce than those with less favorable phenotypes. The phenotype's genetic basis, genotype associated with the favorable phenotype, will increase in frequency over the following generations. Over time, this process may result in adaptations that specialize organisms for particular ecological niches and may eventually result in the emergence of new species. In other words, natural selection is the mechanism by which evolution may take place in a population of a specific organism.
Natural selection is one of the cornerstones of modern biology. The term was introduced by Charles Darwin in his groundbreaking 1859 book The Origin of Species[1] in which natural selection was described by analogy to artificial selection, a process by which animals with traits considered desirable by human breeders are systematically favored for reproduction. The concept of natural selection was originally developed in the absence of a valid theory of inheritance; at the time of Darwin's writing, nothing was known of modern genetics. Although Gregor Mendel, the father of modern genetics, was a contemporary of Darwin's, his work would lie in obscurity until the early 20th century. The union of traditional Darwinian evolution with subsequent discoveries in classical and molecular genetics is termed the modern evolutionary synthesis. Although other mechanisms of molecular evolution, such as the neutral theory advanced by Motoo Kimura, have been identified as important causes of genetic diversity, natural selection remains the single primary explanation for adaptive evolution. (Emphasis mine)


The above text as indicated has been taken from Wikipedia the free encyclopedic reference on the world wide web.




What I want to illustrate using this text as an example, is how certain forms of language are smuggled in and borrowed in subtle ways, and sometimes not so subtle which show the underlying presuppositions and assumptions of the writer and all who are influenced by him/her.


Remember although this is an elementary and basic piece of free information on what is an exceedingly widely accepted theory which in point of fact has gone well beyond the realm of theory in most peoples minds (scientific community especially), it is still an accurate reflection, and representative of what more sophisticated proponents of the theory espouse. I am sure the same tendencies would be apparent in more stringently edited scientific papers of the same ilk. Remember- this is science, neutral, objective,impartial, interested-only-in-the-facts-science.



In the first two words of the piece the underlying assumptions are immediately apparent.


Natural selection- how often has that phrase been bandied about! What is selection? How is the term ordinarily used? Ordinary people use the term when they describe how they might choose a watermelon at the supermarket. Some people check the withered stalk, you will find others smell it, yet others take to tapping it and listening intently. The one thing that all these methods have in common is: someone is distinguishing a valued one, from one to put back by using their minds in different ways to find how ripe it is and therefore its suitability to eat. What is important to notice is that "selection" is a value judgement- a function of a mind.

But of course we all knew that, that’s why the word Natural needed to be planted in front. The word natural dare I say naturally means: of nature. Its purported meaning may be more contextually gleaned from a bit further down the piece where we have a comparison with artificial selection.

Natural selection is one of the cornerstones of modern biology. The term was introduced by Charles Darwin in his groundbreaking 1859 book The Origin of Species[1] in which natural selection was described by analogy to artificial selection, a process by which animals with traits considered desirable by human breeders are systematically favored for reproduction


So Darwin intended, by introducing this phrase, to show that a process similar (by analogy) to that of human breeders was taking place all by itself, that is without a mind. I would venture to say that the really novel thing about this phrase is that never before had the word selection been used without reference to some mind except perhaps as a metaphor.
When human breeders of animals practice their skills they must start with certain things in mind- and I italicize those words deliberately and emphatically. They have in mind deliberate standards to which they are aiming. As cow breeders we were looking for and indeed aiming for by choosing, selecting bulls with certain favourable characteristics to breed with cows who had favourable characteristics that we wished to enhance or maintain. Now look at the words that have been used with reference to breeding. But not just my words, those that have appeared in the above piece also.
Favourable or favoured: again we see that this is a word borrowed from cognizant beings, never before used without reference to God or man. To favour means to look upon with favour, that is either to bestow some benefit with respect to and because of something that the recipient has done or because of what it is. Another form of favour is to bestow some benefit unconditionally, that is for nothing the recipient has done or not for any state of being in the recipient. Nevertheless favour is a word always (at least until Darwin) used in conjunction with reason- a faculty of mind.


Desirable: Here again the word is never ordinarily used without reference to a mind or at the least an animate being. But in Darwins terms an inanimate, mindless entity called nature is expressing not only an ability to select but desire and favour. It does not end here, these ideas are all tied up with a master plan, another term which goes hand in hand with a reasoning, cognizant mind.


Systematic: We have got so used to using these words in the context of science as in solar system but they have been divorced from their original context of a machine or process which stemmed from an idea or design from a designer in short from the workings of rational being or beings.


So we have these words and phrases used in the context of a mindless entity which in any other context are always used in conjunction with rational, reasoning minds.
· Selection
· Favourable
· Natural selection acts on the phenotype, or the observable characteristics of an organism
. Whatever acts as a response in the form of favour or selection is accorded under normal uses of language the dignity of rational mind.


All of this is ascribed in Natural Selection to a mindless entity called nature.

In plain language a mindless something had a plan and a goal for achieving better and better bred creatures and was achieving it by favouring creatures with survival as a reward for the recipient having certain desirable characteristics that the mindless thing could recognize and reward and favour. One wonders why Richard Dawkins used the analogy at all in his book the "Blind Watchmaker". After all if the watchmaker is blind as well as mindless he can hardly be called a watchmaker, why even the gender specific "he"? Oh that is just his point you say- Well why then is the language employed in Evolutionary Theory inseperable from the identical sort of language one ordinarily employs in the description of a complex goal oriented, rationally designed, mechanically orchestrated, purpose driven process or system? The short answer is because it cannot be seperated. The microsm as in the macrocosm is so complex and yet so accessible and intelligible because they have a common ultimate origin which is also (to a degree) intelligible- the Logos. And therefore we, endowed with intellect are able to know even as we are known. It takes one to know one.


Call it Darwinian Evolution or modern evolutionary synthesis, at bottom if people are going to use the terms: selection, favour, acting on observable behaviours, there is no getting away from the fact that these terms are all functions and capacities of a reasoning mind. How can non-mind reward, favour, or act on observable characteristics? If it is mindless nature then even if it had eyes to see observable characteristics it certainly could not reward them because it didn’t have a mind to! And if it didn’t have a mind how could it distinguish favourable from unfavourable characteristics. If it didn’t have a mind how could it even think of the term favourable? If it didn’t have a mind how could it (even over the sort of time frame commonly spoken of) reward favourable characteristics? These terms only have meaning within the context of reasoning minds.
No we have to look closer at the underlying reasons for the almost hysterical reactions from certain quarters when thoughtful people have attempted to offer another explanation for the vexed problem of origins. In a paper written by Alvin Plantinga ("When Faith and Reason Clash: Evolution and the Bible." University of Notre DameIN 46556) Plantinga relates this quote by the famous atheist Richard Dawkins-
"although atheism might have been logically tenable before Darwin," said he, "Darwin made it possible to be an intellectually fulfilled atheist."
Scientists with a naturalistic mindset have an axe to grind:
In other words Darwin finally made it possible to give a plausible explanation for the origins of complex life in such a way that intellectuals could thereby exclude the idea of God without compromising their intellectual credibility- which before then was not possible. As far as atheists are concerned "evolution is the only game in town". Here perhaps lies the clue to the religious nature and reason for the dogmatic tenacity of the theory of unguided evolution against growing evidence to the contrary.
Far from being scientifically neutral- evolution has deep religious and philosophical connotations.
Plantinga again- "among the secularists, evolution functions as a myth, in a technical sense of that term: a shared way of understanding ourselves at the deep level of religion, a deep interpretation of ourselves to ourselves, a way of telling us why we are here, where we come from, and where we are going."
From this it is clear that science has radically abandoned its territory of answering the "how" questions and blustered drunkenly into the realm of philosophers and theologians to ask the "why" questions.

In his book " The Biblical Philosophy of History" R.J. Rushdoony re-iterated the principle that   getting an "ought from an is" poses an insurmountable problem for naturalism:  There is no attempt to give the obvious answer,..., that meaning always escapes man when he seeks it in the realm of creation rather than in God. Because all things are made by God, nothing is understandable in terms of itself, but only in terms of God the Creator. Neither fact nor man can be understood in reference to himself alone, or to any created combination, but only in terms of God. Remove God, and, eventually, you remove meaning. John C. Greene has pointed out that the idea of evolution is philosophical and means progress, which is a value judgement. Attempts to "arrive at an objective, value-free definition of progress" soon fall. We can add that every attempt to do without God leads to an elimination not only of values, but also of meaning, as well. The issue is clear: no God, no meaning.

Finally what was there to decide that survival of the fittest was a goal (which evolution apparently accomplishes, or at least supposedly makes progress toward) worthy or better than anhilation? Mindless nature? One cannot even speak of something (survival of the fittest) being better or worse than another possibility (anhilation) without involking morality which again is a property of moral agents and rational minds (a question the philosophers and theologians should be better equipped to answer). The idea and language of evolution as progress toward a goal is replete with meanings that are inseparable abstractions of a mind or minds.

In all of this I have not once concluded that evolution isn't true but that in the current state of the continuing saga it seems to me to be much more reasonable given the sort of language employed by the evolutionists themselves that to posit a mind at back of their theory is much more cogent than to deny any semblance of mind altogether. And the reason for the denial is patently obvious- to posit a mind at the back of evolution is to run the risk of being thought a creationist! Something that most are irrevocably committed against.
According to the popular theory there is no mind working throughout the process, but the terms commonly in use are incongruous outside of a reasoning mind. It pretty soon becomes clear that when it is found impossible to describe the so-called reality of the origin of species without using language that is exclusive to rational minds then by default we ought to give up the charade and admit that nature is actually rational and has a mind. Maybe then they ought to revise their definition of nature.


It is a contradiction in terms to deem everything as the result of time plus matter plus chance while all the while using terms normatively reserved for a rational, logical, reasoning mind.

If nature has a mind and nature is non-material then how do you account for non-matter having rational being?
Perhaps evolutionists should give up the pretense of a mindless "Nature" that favours, designs, rewards et al and give the name countless others have: God.


One of the phrases employed in the piece refers to cornerstones.

"Natural selection is one of the cornerstones of modern biology…"

It is my understanding that this metaphor is speaking of an essential and foundational truth upon which a whole gamut of understanding is based. If the cornerstone is faulty then the whole building is likely to collapse.
Interestingly the source of this metaphor is most likely biblical.

(1 Peter 2:6,7,8) Wherefore also it is contained in the scripture, Behold, I lay in Sion a chief corner stone, elect, precious: and he that believeth on him shall not be ashamed. Unto you therefore which believe he is precious: but unto them which be disobedient, the stone which the builders disallowed, the same is made the head of the corner, (cornerstone) And a stone of stumbling, and a rock of offence, even to them which stumble at the word, being disobedient: whereunto also they were appointed.

Of course there is a ready answer but one which to many is too unpalatable to contemplate.


(Psalms 19:1) To the chief Musician, A Psalm of David. The heavens declare the glory of God; and the firmament sheweth his handywork.


Wednesday, May 21, 2008

Yes, this is true:




I have often been intrigued about beauty. We talk about beauty being "in the eye of the beholder" but how true is that statement? The question needs to be asked- Is the object really beautiful (objectively beautiful) or is it merely an object and the beauty is in my head? Is beauty something I have been conditioned to confer on it or attribute to it or is there intrinsic beauty that resonates within me -Does it have actual beauty instilled in its very nature? Or then again- is it both objectively beautiful (in itself) and reflectively beautiful (in my head)?
One of the ways of ascertaining objectivity is repeatability, its universality. While beauty has an element of preference (in certain Pacific Island cultures big is beautiful, while in others the slim look is in vogue) there is also its universality. Whatever the personal preferences involved, beauty is a universal fact of human existence.
If an object of beauty is recognized by many over a long period of time one can be more confident of it being objectively beautiful. So essentially, we may assume that beauty is intrinsic, not just something humanly and arbitrarily in the eye of the beholder. This stands even clearer when the object is not manmade, for instance- a beautiful mountain lake scene.
Please bear with me a little longer. There is a point to all this!
Let's summarize what we have covered.
Beauty is a human thing, or to be more precise it is a mind thing, a capacity of the intellect. One needs to ask the question what do we mean by beautiful? Whatever else you may say about it, one thing is sure- it is personal. By that I don't mean it is a matter of personal taste or preference but I mean that only persons are capable of appreciating beauty. I mean the appreciation of beauty is a capacity of the intellect.
It is also has objectivity, universality- so it is not necessarily dependent on our humanity. A beautiful lake scene does not rely on us to be beautiful, even if we aren't there it remains beautiful.
This poses a difficulty and another question: How can it be intrinsically (in itself) beautiful without us, if we are'nt even there, if we have already decided that beauty is a quality of intellect both to fashion and create or to appreciate and apprehend? Many people have commented on not just the beauty of material things but of immaterial things. Like beauty in mathematics. Einstein once said "The eternal mystery of the world is its comprehensibility"
Beauty, like mathematics (see the piece "Mathematics and God" http://struth-his-or-yours.blogspot.com/2008/11/mathematics-and-god.html ) reflect the work of intellect or mind, and yet maths just like beauty do not depend on the human mind, maths was if you like discovered but not invented, and yet it- like beauty- is a necessary corollary of mind. That is- without mind there is no maths or beauty.
As Arthur Peacocke in his book "Paths From Science Towards God"- "...why should the world possess this embedded rationality amenable to the most comprehensive analysis of which the human mind is capable and to formulation in terms of often the most abstract of human concepts? The simplest explanation, and so the best in this global context, is that at the source of the existence of all being, the Ultimate Reality, must posess something akin to, but far surpassing, human rationality -must be supremely and unsurpassedly rational." (Emphasis in bold mine)
Given the truth of all the above the most reasonable conclusion is that even "natural beauty" has had the benefit of a master craftsmans intellect to fashion it.
Many are constantly admiring the beautiful design in the universe, whoever heard of design without a designer?
In exactly the same way, beauty is both instilled in the object by a supreme intellect and we as recipients of that cosmic designer have had the capacity to fashion and comprehend beauty in order that beauty resonate within us.
The appreciation of beauty is not a requirement of evolution.
The intrigue is in the fact that not only is a thing beautiful but we are able to perceive the beauty. It seemed an intuitive thing to know the wonder in this.
Yes this is true, we recognize a thing of beauty because primarily a Creative, beautiful God first made it beautiful, instilled beauty into it and correspondingly gave us an eye to perceive or recognize that beauty. This is what recognition truly means. God is cognizant of beauty; he knows- is conscious- of it and instils it in something/someone and we re-know it, seeing it after him.
What I hadn’t reckoned on is the narrow view I had taken of this phenomenon.
Not just beauty but all knowable facts are available for us to search out only because God has made the universe intelligible, he has firstly put an interpretation on them, and then gave us certain capacities to know this after him.
From this it follows, that every fact known presupposes the existence of God, because the intelligibility of the universe is a cogent witness to an already interpreted reality.
For example, it is a known fact that H2O is the chemical name for a molecule of water so named because for every two atoms of Hydrogen there is one atom of Oxygen.
Every molecule of water has two atoms of hdrogen and one atom of oxygen. The formula H2O remains true, no mattter what race of people or what gender anlalyzes it. Can one really say, "Its not fair to oxygen that there are two atoms of hydrogen in water; so to be fair, there should be two atoms of oxygen as well? You can give two atoms of oxygen if you want to -but if you drink it, it will bleach your insides, because that would make it hydrogen peroxide and not water. (From Glimpsing the Face of God, Alister McGrath and The Grand Weaver, Ravi Zacharias.)
If it is possible to see that in physics- matter and the naming of the matter are directly connected and not arbitrary at all, because of a prior instilled intelligibility, then is it such a great wonder to acknowledge the universals and absolutes inherent in morality and metaphysics?
The language of love is universal and absolute, good and evil are not merely human constructs conveniently at the disposal of whatever moral code happens to be in vogue.