God and Proof: Part IV

I will introduce you to what I consider to be the ‘four cardinal rules of logic’; for we cannot show precisely why those who demand proofs quarantine themselves from good rationale until we look at the four different ways that we construct logic. Once we have looked at the four cardinal rules of logic I can then show why the demands for proof are not only ill-conceived but solecisms against robust enquiry.

Godel’s theorem warns us that the axiomatic method of making logical deductions from given assumptions cannot in general provide a system which is both provably complete and consistent. There will always be truth that lies beyond human scope; truth that cannot be reached from a finite collection of axioms. This also means that no door in the labyrinthe palace of empiricism opens directly onto the ‘Absolute’ - there are hints of the infinite in mathematics (Cantor’s Absolute), but any complete unity must include itself, thus we hit the self-referencing problem of Russell’s paradox. But what we do know from our cognitive set-up is that we are created with a vacancy in our hearts that Christ is waiting to fill. Moreover, that our ‘minds’ can attune themselves into the ‘nature’ of the Absolute gives us the biggest hint that we are truly meant to be here, and that this life is but a shadow of a deeper and more astounding reality.

In the past on Network Norwich and Norfolk we have had two periodic contributors, both called Mike (Mike H and Mike 2), both of which claim to be unbelievers, and both of which set up their framework for objection by continually insisting that there is no proof for God, and until there is, they will remain unfalteringly sceptical. It is here that we must cover something very important – the world isn’t quite like that, and the two Mikes might end up in a perpetual cycle of disappointment because they made demands that were not strictly realistic. The truth of the matter is this; there will always be statements which are true but that one cannot prove are true.

Take the following statement (call it ‘S’)..

S - “Mike cannot prove this statement to be true”

Suppose Mike were to arrive at the conclusion that S is true - this means that the contents of S will have been falsified, because Mike will have just done so. But if S is falsified, S cannot be true. Thus if Mike answers ‘true’ to S, he will have arrived at a false conclusion, contradicting its infallibility. Hence Mike cannot answer ‘true’. That means that S is true; but in arriving at that conclusion we have demonstrated that Mike cannot arrive at that conclusion. This means we know something to be true that cannot be demonstrated to be true.

Now consider something a little different. Let us say that we meet a man for five minutes that we have never met before and will never meet again. Our job is to find out if he can speak English. If he remains silent throughout the five minutes and he disappears never to be seen again, we cannot prove that he cannot speak English but we have no evidence that he can. If, however, he were to say the words ‘My name is Robert and I can speak English’ we would, of course, have the deductive proof that he can speak English, as the English words themselves would be contained within the statement.

This is different from the first example, for the first example is about the axiomatic method of logical proof itself and is not a property of the statements one is trying to prove or disprove. One can always make the truth of a statement that is unprovable in a given axiom system ITSELF an axiom of some extended system. But then there will always be other statements in the self same system that are unprovable.

Now we come to something else that is key - in the first example there is no new predicate that can be added to S (without changes to its intrinsic structure) that can alter the fact that S cannot be shown to be true. Now very obviously that is not the case with the second example - if we were told that Robert was an English lecturer and that there was footage of one of his lectures, we could show that ‘Robert can speak English’ is a fact without having to prove it in those five minutes. Moreover, unless we start flirting with nonsense there are a number of things we could find out about Robert that improve the probability that he could speak English.

S1 - Robert was born and raised in Ghana
S2 - Robert was born and raised in Mozambique

It is very clear which out of S1 ad S2 is more likely to be suffixed with the statement ‘Robert speaks English’ - S1 because Ghana is a former British colony whereas Mozambique is a former Portuguese colony. Of course S1 and S2 might only improve the probability very slightly, but this is what we do in all walks of life. Knowing, as most mathematicians do, that there are some statements of logic that cannot be proved to be true (one can also read about the distinctions between realism and antirealism) we use our perceptive and investigative toolkit to reason our way through these things. If for example Robert lives and works in this country it is much more likely that he speaks English than if he lives and works in Ecuador.

One must also bear in mind that there are many axioms or regularities that only become that way by our adding something to facts. Look at this set of six numbers (all single integers used are under the value of six)

234232 - 344232 - 121232 - 523334 - 552555 - 122311

A Turing machine can show which number sets are computable given a set of rules. If the rule is, say, take the first number of the first set and add 1 (giving us 3), do the same to the second number in the second set (giving us 5), the third in the third (giving us 2) , and so on, we find that with that rule in place we have the number 352462. Unlike the “Mike cannot prove this statement to be true” example, this time we have created a rule or procedure and shown that logical deductions can be reached without messing around with the axioms in logic. For example, given this rule, I know that if I have the answer 352462 then none of the sets will contain the exact sequence 352462.

We are beginning to see why demands for proof of God’s existence are knottier than the sceptics realise, and that greater mental prudence is needed before such demands are made. We certainly do not completely abandon a mechanical procedure for investigating mathematics because of Godel’s theorem and Turing’s halting system. Those unprovables are rare elements of mathematics and can be sifted out allowing us to continue on a logical trajectory, and that is precisely what we do with our enquiries about God; we do not churlishly shout for evidence or make unreasonable empirical demands, we must take the sagacious approach and realise that sense-making is about joining the dots, not demanding the whole picture in front of our eyes. How silly it is to stridently decree ‘Unless there is proof of God’s existence, I’m going to carrying on believing that He doesn’t exist’.

Now we reach the last of the cardinal rules – demonstrated in Chaitin’s theorem. Having shown you with Turing that there are mathematical problems that cannot be proved by any fixed heuristic procedures, we now move on to how we know if what we know (or contend) is right or whether further compressibility is required.

It also ought to be remembered that one can compress something too much into logical nonentity - the biggest example being with self-referencing paradoxes such as ‘This statement is false’ - here we have something that is too compressed to be logical, because if it’s true then it’s false and if it’s false then it’s true. It is nonsensical because there is no subject or predicate pointer extended to ‘false’. The statement “3 + 5 = 9 is false” is true because ‘false’ has mathematical integer subjects extended to it - it has the ideal compressibility for deductive analysis. Now in Chaitin’s theorem, a computer is given this command - “Search for a string of digits that can only be generated by a program longer than this one”. Now obviously if the search succeeds the search program itself will have generated the digit string. But then the digit string cannot be “one that can only be generated by a program longer than this”. This obviously leads to the fact that the search must fail, even if it is an infinite search. The search was intended to find a digit string that needed a generating program at least as big as the search program, which is to say that any shorter program has to be ruled out. But as the search fails, we cannot be sure there is no shorter program, as we do not know whether a given digit string can be encoded in a program shorter than the one we happen to have discovered.

Now here’s the rub - a random sequence is one that cannot be algorithmically compressed - but as I have just shown, you cannot know whether or not a shorter program exists for generating that sequence. The cardinal point in these algorithmic programs is that you never know if you’ve unturned every stone in trying to shorten the description. Therefore you cannot prove that a sequence is random, although you could disprove it by actually finding a compression. If you are paying close attention you will see that this is congruous with the Robert speaking English model - here you have much greater access to empirical evidence (certainly less complex than algorithmic mathematics) but you can find the shortest compression (so to speak) by hearing Robert speaking English.

The practical conclusion here is twofold. In the first place, one can prove mathematically that almost all digit strings are random, but one cannot know precisely which. But more essentially for everyday purposes, taking the cosmos as an algorithmic whole, events or activities that appear random may not be random at all - even things like the indeterminism of quantum mechanics. The cardinal point here is not that something like, say, Heisenberg’s Uncertainty Principle probably belongs to uniform laws of which we as yet know nothing. The cardinal point is that we might never be able to know - in fact, Chaitin’s theorem ensures that we can never ‘prove’ that quantum mechanical measurement outcomes are random.

Falsification and verification:
Some philosophers, most notably Karl Popper, contended that because science aims at making universally quantified statements (for example, all Xs are Y) the principal issue was not whether such statements are verifiable but whether they are falsifiable. In other words, according to Popper falsifiability has greater meaningfulness than verifiability.

However, as a theist one must remember that the boundaries must be reconstituted to make way for infinite complexity within a God-created reality, and that given our present (finite) limitations, we must also remind ourselves of what we covered in the foregoing sections – that within this theory there will be some things that are axiomatically true yet non-falsifiable (non-contextually - in the Absolute sense) and that the efficacy of a contention is not predicated on its falsifiability. What Popper meant by falsifiability should not be misunderstood as an accusation levelled at reason itself, merely to construct parameters and reconstitute boundaries within the edifice of reasoning and rationale. Furthermore it is difficult, often impossible, to apply falsifiability to psychological, historical, sociological, and emotional aspects of life, as they are rarely amenable to falsifiability and are individual and unique events or facts. Our perceptive qualities and, more importantly, our ability to assess the validity of a theory based upon its appearance in front of our perceptive tools is what we can use.

The greater a theory’s potential for falsification the better and more enduring it can be. We see so often that a theory that could easily be falsified but never is, often endures in a most robust way. For example, the theory 'all plants have DNA' is not as good as the theory 'all life has DNA' because the set of objects 'plants' is a subset of 'life' and hence the 'life' theory has more scope for falsification - it is a more general and robust theory. The Popperian demarcation of ‘probability’ and ‘degree of corroboration’ is reasonable providing the burden of verifiability isn’t too great. The statement ‘It is going to rain somewhere in the world in the next hundred years’ has a much less burden of verifiability than the statement ‘It is going to rain on Buckingham Palace at 1:23pm on Thursday 23 April 2010’. In the sense of our assumptions about the Divinely created order, logical improbability, of course, does not take its place in the predicative inner-context of the sentence alone (as is the case with the second prediction about the rain on Buckingham Palace), for it will have to be admitted that any thoughts of falsification and non-verification add no weight to an argument so grand in scope; it envelops principles higher than those in the purview of ‘logical probability’ and ‘logical improbability’, although with the concept of Aseity one can make a good assessment based on a structural underwritten logical framework, particularly if it exposes the infinite regress problem.

The falsification principle falls down with the realisation that no individual theory is anything other than a constituent part of a ‘chain of validity’ – a chain that we apprehend bit by bit, by the aforementioned method of joining the ontological dots, and thus can even be positively affirmed in a partially-isolated context yet at the same time amount to a discordant cell on one link of the ‘chain of validity’. In other words falsifying something (singularly) might not upset the link in the chain. This a slight reworking of the ‘verisimilitude’ of a theory - that is, its appearance of truth; this is the extent to which a theory corresponds to the totality of reality, rather than just those in the immediate proximity (I would say that any providential being with a priori complexity would need to furnish us with the perceptive qualities necessary for such an understanding, if we are to have a relationship with Him).

Having already shown that there are many tenets to existence that are not amenable to the test/refute procedural analysis and are therefore not disposable in the sense that atheists wish for, I think the Popperian caricature is relevant in their thinking; for the general rule of sense-making must readily include the theistic ventures which Christians say are an essential part of our epistemic framework. This is compounded by the fact that the vast non-testable domains covered by our best efforts for analysis, along with the limitations of human perceptual resources, only allow a very sparse interrelational sampling of life. Formalisation of our best theoretics are in the strictest sense simulations unless they and conflated with experience to provide us with ideas of validity, otherwise the trail would stop dead. In the truest Popperian sense, and given the stakes, I would say that many atheists treat the question of God’s existence far too frivolously and unconscientiously as they attempt to decide which out of theism and atheism makes the more easily refutable claims. All they end up doing is forming an allegiance with the side that makes the best impression on their emotions, but as any who have witnessed the cults ensnaring people at their most vulnerable will tell you, this is a potentially dangerous allegiance.

God and Proof: Part III

Do Christians deal with Proofs?
I have already said that as Christians we do not deal with proofs – certainly not in the traditional sense – we do not prove God like we prove a mathematical theorem. However, I once wrote a couple of articles (here and here) which speak of a proof by experience; that is, an a priori certainty that one can distil from his or her own relationship with God. Although they are vitally important as one seeks to affirm the really of God through one’s one experience they are tangential to the tenet of ‘proofs’ that we are discussing here.

As a reminder about what we are dealing with here let me make an allusion to what I said last week; one must realise that God is an infinitely complex personality, so the best we can do is sample Him. The Father has revealed Himself to us in Christ Jesus, and although the Bible is the word of God – one can learn lots more about God both from creation around us, and from having a relationship with Him.

The sceptics who say there is absolutely no evidence for God are not living in the same world in which I am living – to me the world doesn’t just hint of God’s existence, it shouts it at the top of its voice. The question is this: given that in the eyes of the sceptic, awareness even of the most elementary facts of God into which all other blessings should percolate is accessible only by a form of contemplative reasoning towards which they have little desire to gravitate, and for which they often lack the inclination, capacity for discernment and quite often the emotional resources, how might they be expected to realise their need for a change of thinking?.

There is a great story often recounted about Elizabeth Anscombe saying to the brilliant Wittgenstein, that she can understand why people thought that the sun revolves around the earth. Wittgenstein asks, “Why?” - Anscombe says, “Well, it looks that way.” - To which Wittgenstein responds, “And how would it look if the earth revolved around the sun?” In other words, the way something looks from a certain standpoint is, from the individual’s perspective, a direct proprietary fact about the person's perception of that 'something'. ‘How it appears from a certain place’ is, nonetheless, also of interest in its own right and belongs to what is sometimes called ‘the reality of the appearance’. In Biblical times the ancient Hebrews referred to it as 'language by appearance' – so, for example, if something 'filled the earth' it did not necessarily, in the literal sense, fill it entirely.

The Christian view of proof
We are now ready to ask the question: Do Christians deal with proofs? In the strictest sense, no we do not. Those that ask for empirical proof seem to overlook the fact that, in one sense, Christians do not believe what they believe because of empirical proof, although empiricism does play a part in the totality of a Christian’s psychological make-up. The Bible talks of certainty, that we can be certain of Christ in us, therefore even a posteriori empirical evidence of some kind would not be as powerful as the relationship with God from within a priori selfhood. What I mean is this; a man can have a much better idea of God by how He works inside him than he can by what he sees in the external world – God’s method of communication is at its strongest when Jesus Christ works inside our minds in ways that show it is Him and not us. The Bible, in fact, confirms that the man that knows God but hasn’t seen empirical evidence has much greater certainty (impregnable certainty) than the man that has been shown a miracle but has no relationship (see Matthew 11:21-24). Absolute Certainty, as the book of Galatians implies, can only occur a priori.

Let us say that a man observes an event which by ordinary definitions of empirical investigation could be construed consensually as a miracle. Let’s say that it happens to some of the biggest sceptics in the public domain - would that be the certainty they are looking for? Perhaps in the sense of satisfying evidential demands, but even the event or, more accurately, their observing the event has connotations which cannot help but diminish slightly the content of certainty. Their observation of this miracle would be a proprietary event occurring personally in first-person selfhood, and as long as they continue to analyse the evidence or certainty, and as long as they attempt to convey it linguistically, they will be in the strictest sense letting go of the a priori certainty, for in the strictest sense a priori certainties involve no adulteration whatsoever - an absence of cognitive or descriptive embellishment. All external realities must be perceived by the self before one can have assessment and knowledge of them, therefore the business of looking for proof or certainty via perception of events in the external world is never as compelling as the knowledge of God that one can acquire from His working inside us. This, I think, is why Jesus placed so much emphasis on our asking God for revelation in ways that can occur inside one’s own personhood directly from God – for He knew that what we perceived externally would never be as compelling evidence as what we receive internally.

So when we talk of certainty, that is, being certain that God exists and that we can have a relationship with Him, the certainty that one searches for is the certainty that need not involve any a posteriori facts. Of course, the fantastic evidence for Christianity being true is overwhelming and a likely catalyst in one’s searching for a relationship with Him, but when folk talk foolishly of ‘no evidence for God’ or they overlook this greater reality of the situation, they are guilty of emphatic errors of thinking. I understand that it is hard to reconcile for those who are sceptical, but the Socratic paradox about a man lacking the courage to venture out upon so perilous a voyage of discovery without God behind him is not far from the truth. That is to say, if the event of man knowing God has to come from God first he must trust that the casting of his net will be fruitful because it is not just his arm doing the casting, but God’s too.

There is another thing to consider regarding proof, and in particular, hasty demands for proof - one might be quite startled to learn that there are mathematical conditions under which the opposite situation is true - there are statements that are true if and only if they are unprovable. Most people have heard of Godel’s incompleteness theorem; well further on there is a sort of meta-theorem in that its truth depends crucially on an object-meta-level distinction, which I will explain briefly. Godel considered a simple formal system containing the basic axioms of the arithmetic of whole numbers (stress, whole numbers). He assigned each object-level statement a unique code number, and then he assigned a code number to each proof of an object-level statement. What this shows is that by means of this encoding, object-level statements about numbers can also be understood as expressing meta-level statements about the system, or about individual object-level statements.

Given the foregoing, a question might well be asked: Doesn’t this mean that an extension of this system can be used to show that if in most cases there are formal systems incapable of proving some truths there must be a self-same system which insists that no formal system can prove all truths? Yes, in principle that is true, but it is a bankrupt enterprise trying to impute this onto the non-mathematical subjects in place, in the ‘God or no God’ debate. I said that in mathematical terms this object-level statement about whole numbers says of itself, via the numerical coding, that it is not provable. If the axioms are all true and the system is consistent, it is possible to conclude that such statements (that are true if and only if they are unprovable) are neither provable nor disprovable from the axioms - that it is independent of them. Therefore I would be cautious about using the word ‘proof’ when using inductive techniques to consider whether or not God exists, particularly bearing in mind that the warrant for the use of the inductive principle of inference is the inductive principle itself.

Of course, as atheism shows, understanding the self does not come without distractions and, again as atheism has shown, some of the distractions are strong enough to turn a man into trouble - nature’s digressions and distractions lead folk away from the truth. There is a better chance of a man realising this if he remembers that Christ does not just claim to have access to the truth, or that He is able to lead a man to the truth, in fact, He claims to BE the truth. That is why, if Christ is the truth, it is impossible to hold on to satisfaction, fulfilment, blessedness, and wisdom without Him – He is the vine, we are the branches connected to Him. By definition every act that recedes from the Truth must be arbitrary or pernicious, for you can be sure that all the very best things on earth will be from Him. Even the caprice that lurks in the hearts of those that follow false religions is entirely knowable the moment one steps outside looking for the truth. The only other gods that really exist are the false gods that have been created by the self, usually as a result of some arbitrary thinking process or pattern; that is, the falsity attaches itself to human reasoning like a leech to skin and confounds the reasoning process so that even clear thinking can be transposed into some muddled perceptivity, all the time not affecting the proprietary convictions and supposed certainty felt from within.

The sensible man knows how important the truth is, but equally he knows how dangerous falsehood is, and that if Christ is the Truth, falsehood must underpin every instance of badness that we see in the world. If one searches for the Truth then things like moral goodness, wisdom, good judgement, character development, greater vision, tangible life goals and awareness of reality in a wider and more glorious framework will follow.

I have said from day one, and I will continue to say it - we do not deal with proofs on here, not in the way that atheists are demanding. Of course some Christians maintain that no proof is a good thing because it helps define for them what ‘faith’ really is all about, but I do not think this view is always helpful, particularly for the atheists who frequently misunderstand what faith really is. ‘Proof’ of complex activity such as, say, macroevolution just isn’t humanly possible (although that is no reason to disbelieve it - we have overwhelming ‘evidence’ that macro-evolutionary theory is true) - all we ever do is perceive samples emanating from the subject in question, samples that provide us with palpable indication of the efficacy of that which is being sampled. ‘Proof’ is an impossible demand to fulfill - either for evolution or for God (but there is great ‘evidence’ for both). Given that no set of finite samples is as big as the source object; the best we can get is ‘evidence’, and from evidence we can use our rationale to make logical inferences. It is by doing this that we shall get closer to the truth about the awesome majesty of God and we will see Him in places that we could not have previously anticipated. And here is the most important point:

No-one has ever seen God, but God the One and Only, who is at the Father's side, has made Him known. John 1:18

God has made Himself known, but not by some emphatic exhibition for all to see, but through the person of Jesus Christ - that is how He chose to make Himself known. Any that have seen and understood who He really is would be able to recognise the Father in Him (John 14:7). God is not a static object like a huge table or chair or planet, He is a tri-aspectual personality (Father, Son and Holy Spirit) and can only ever be sampled bit by bit. We sample Him by getting to know His personality through the express revelation of Christ and the Holy Spirit that lives in us. It ought to be quite clear really, after all, in human terms we only ever sample personalities bit by bit; the quintessence of relationships is that they are cumulative, expressive, gradual, productive, and their true qualities all come about by development and growth. When sceptics ask to see God as some evidential ‘whole’ their demand is as silly as a man saying to another man’s wife – ‘show me everything she is, the whole person in totality’ or saying to his friend ‘you say there is a society out there, go and get it and bring it to me so I can see it’.

God and Proof: Part II

Who has the burden of proof, the theists or the atheists?
The first thing I ought to say on this matter is that the term ‘burden of proof’ should really be supplanted for ‘burden of evidence’, for as Bertrand Russell showed with his celestial teapot illustration, it is impossible to prove a negative existential claim (that is, a claim that a thing does not exist), and it is impossible on these terms to prove the positive to that negative. As Christians we do not offer proof that God exists or that Christ was God incarnate – we supply evidence and testimony which assist people in building their epistemological framework. Unless the theist and atheist admit this from the outset there will probably be a stalemate. Before we get on to the theistic situation, let me recount a famous story from the Hellenistic period:

There was a Sophist philosopher Protagoras who agreed to instruct Euathlus in rhetoric so the latter could practice law. Euathlus in turn agreed to pay Protagoras his fee only after winning his first case. However, Euathlus chose not to practice law upon completing his training, and so Protagoras sued him for his fee. Protagoras maintained that he should be paid no matter what; he argued that if he won the case he should be paid by order of the court; while if he lost he should be paid by the terms of his agreement with Euathlus. Euathlus, who had learned something from his study with Protagoras, maintained that he should not pay no matter what; he argued that if he won the case he should not pay by order of the court; while if he lost he should not pay by the terms of his agreement with Protagoras

This describes a stalemate much like the stalemate often reached when theists and atheists argue about the burden of proof and with whom it should lay. Just like the case above, burdens of proof are often dilemmas that invariably lead to counter-dilemmas – one must define exactly what the belief is before any talk of burden of proof – after all, most of the atheists I have met do not disbelieve in the actual God of the Bible, they disbelieve in a God that they have created or imagined in their own heads. Let’s have a look at how the situation with Protagoras and Euathlus created a stalemate and how it is synonymous with position of the theist and atheist. Protagoras had a rather disingenuous scheme in bringing the suit in the first place, but the situation really boils down to Euathlus wanting to show off his mental dexterity. Had Euathlus hired another lawyer he could have escaped the paradoxical situation in which he found himself; if he won with a lawyer, his victory would be non-paradoxical, and if he lost with a lawyer, he would have not yet won his first case. But even if he appeared in a stalemate, one might suggest that equity favours Protagoras, and that if he’d have sued in a second case he would have won.

Yet equally a judge could put paid to this by ordering a reconstitution of the contractual boundaries, or he could decree that this case will not count as Euathlus's first case. Without bringing in policies or principles of this kind, in fact, it is difficult to see how the case could be decided, since the only positive argument favouring both Protagoras and Euathlus relies on a contradiction in the alternative position. Here we see that if the two arguments are truly equal in weight, the one with the burden of proof must find himself in the more precarious position out of the two (in this case this works against the plaintiff Protagoras). The only way this can be resolved outside of the demarcation lines is if one of the two men relents and offers the hand of grace to the other, or if the contract is positively reformed in equity by an external agent.

It is often thought that because the theists are claiming a positive (that there is a God) to the atheists’ negative (that there is no God) this means that the burden lies with the theists, but I have never been happy with this conclusion, and it is for this reason. However far back we search philosophically in trying to ascertain why we exist at all we will not find a good epistemological trail by simply going back further and further expecting the answer to lie in something elementally simple. In naturalistic terms, whatever we ascribe to the meaning of existence we will have to omit the thing itself – nature cannot contain her own explanation unless she is self-evident, and that is impossible. In other words, how the universe came about cannot be explained by the laws of nature – however far back you go looking for an explanation, the last initial explanation still needs explaining if one is a naturalist. However far back you go, you still need an initial explanation of causation – otherwise you are faced with an infinite regress and thus the burden is too great to reconcile with the truth.

As I said, if we keep going back further we eventually reach a point where we have to admit that existence cannot contain its own explanation - there must be something that is self-evident, and such a Being would be infinitely complex. The Christian has a positive answer to this dilemma; he contends that the source of all human activity, that is, the power behind human decision making, is from a Being that exists outside of nature itself. The Christian cannot reconcile the whole complex nexus of choice, free will, moral conscience, emotions and, most importantly, existence itself with an impersonal and uncaring nature – much less settle for an infinite regress as his best explanation; for he knows that in order to avoid the infinite regress problem he must contend that there is something of a priori infinite complexity that bootstraps existence - a fact that is self-evident, a fact that has no cause - a fact that contains its own explanation. The Christian has found the explanation that contradicts the logical hiatus that sullies the infinite regress problem.

Given the foregoing analysis – a logical truth that I cannot get beyond – the burden lies with the atheist not the theist, for the atheist has the infinite regress problem to surmount before he can discharge any burden.

What I have described thus far is the cardinal difficulty for the atheist – a difficulty which removes the manacles from the theist. But in truth this is an area of analysis that is scarcely reached, after all, most sceptics really want to bemoan a lack of evidence for any supernatural God, so now the discussion between the theist and atheist becomes a bit like a case in a court of law (as per above). In an ordinary court of law case, the burden of proof (as much as proof can ever be obtained) is on the prosecution counsel; the prosecuting lawyer must convince the jury that the defendant is guilty – hence the term ‘innocent until proven guilty’. If the prosecution counsel fails to present enough convincing evidence, the jury will ordinarily acquit the defendant.

With Christian apologetics and other forms of justification for the existence of God, we are like the defendant being cross-examined by a prosecuting atheism – unless we can be shown to be guilty of fallacy we should be acquitted. There will, however, be times when this scenario is not played out – the atheist will probably not think it worth his while trying to prosecute and he will probably insist that as he has been given no reason to believe, he can be justified with his atheism. In effect, what he’s saying is "I don't believe in God because no one has provided me with any credible evidence that God exists". And this, of course, is a duty we must take up in convincing the atheist that God is ready to reveal Himself to all who ask.

Here in admitting this we have uncovered something very important when it comes to burdens of evidence. The atheist when he adopts a rather arbitrary form of atheism actually impels the theist to shoulder the burden. In other words, the one who says there is probably no God impels the theist to say why he thinks there is a God, but the one who says there is almost certainly no God stigmatises himself with the burden of demonstrating why he is so convinced. So we see that burdens of evidence depend on the claim being made, but they are also conditioned by the strength of the convictions of those debating the issue in the first place.

I have shown why the burden of proof or burden of evidence is epistemologically intractable, but I have also shown why, if it lays anywhere first off, it lays with the atheist – he must explain what if not God can contain its own explanation. But as we know, when it comes to this problem the atheists choose to disregard the problem and choose to live in denial; roughly, “If I don’t think about it, it no longer remains a problem”. Instead they hope to justify their position by claiming that if such an awesome God exists He would ‘prove His existence’, or that there would at least be better evidence of His existence, and this is what I will tackle in next week’s article.

God and Proof: Part I

Why isn’t God more obvious? The easy answer is ‘He is obvious’. The vast amounts of people who can testify to miraculous salvation (as well as the many other miracles experienced) and the vast historical and archaeological evidence that the Bible is the word of God belie the claim that evidence is scarce. All atheists really mean when they say there has been no evidence for the existence of God is that they do not really wish to look for any. They say ‘Show me the evidence now!’ knowing full well that their demand is impossible, and they walk away smugly, feeling vindicated – but the truth, as we shall see, is that they are behaving injudiciously and setting themselves up for an ill-conceived position.

Obviously an experience of God can only ever be a sample, just as my experience of centripetal acceleration or, much better, gravity, is only a sample of a far greater complex reality, most of which is background activity behind the scenes of this earthly drama. Therefore it is foolish to expect that such a complex entity as God can be experienced by anyone demanding evidence; for even Christians who have a relationship with Him are only experiencing parts of His fullness – a relationship through which He reveals more and more of Himself as we progress on our journey. Thus one must realise that God is an infinitely complex personality and is not necessarily going to deign Himself to everyday human test/refute sampling; nor will proof of His existence necessarily arrive on the doorstep with bells hanging and trumpets playing. What one must remember is that no set of finite moments in which we capture and comprehend a little part of Him are as big as the source object in the Divine realm, and therefore it is unreasonable to demand ‘proof’ in this way; the best we can get is ‘evidence’ of God working in nature and in people’s lives, and from that evidence we can use our rationale to make logical inferences, which will hopefully lead to our receiving revelation and beginning a relationship with Christ.

Having established that an intuitive knowledge of God is evidence relevant to the existence and will of God, and that such ‘evidence’ is a mere sample of God’s work in creation not of God Himself, it seems perfectly obvious that God cannot be presented to a person empirically, like a precious stone or an ancient fossil or a newly discovered mountain. Therefore we must look at the matter of receiving evidence for Him in a different way, by focusing on what God requires of an individual, not what the individual thinks they require of God. This adds weight to the silliness of the insistence that God shows us the evidence at the behest of the stridently assertive atheist, for Christians have said from the beginning that that is not how God does His business with creation, therefore how foolish of them to reject Christianity based not on its true realities but on their own faulty perception of the thing they are assessing. If it seems that God’s presence is too unfamiliar or unnoticeable, it may well be true, as Kierkegaard one remarked, that it His way of giving us the freedom to be ourselves:

Omnipotence which can lay its hand so heavily upon the world can also make its touch so light that the creature receives independence.

When assessing the nature of a personal, interested, willing and loving God, and His apparent absence or intractability, one must bear in mind that God has given us an opportunity for salvation; in fact, it is easier than that which the atheist has demanded – God doesn’t need to show Himself with trumpets playing and bells ringing, appearing in front of us like a genie popping out of a lamp, He will do much more than that – if we ask He will transform our whole personhood; that is the primary evidence beyond all other kinds of evidence, for then He really will be unmistakable, as millions of Christians all over the world will testify.

The Christian says God’s call to ‘seek and you will find’ is a promise fully kept by Christ, yet the atheists deny this, claiming it to be false. So what we have here is a chasm - roughly as follows:

A) The Christian claims that God’s call to ‘seek and you will find’ is a promise fully kept by Christ.

B) The atheist says that a personal, interested, willing and loving God would be more obvious.

Believing as I do that A is correct, it seems that the perceived lack of obviousness contained in B involves a misunderstanding, and I think I can show that this is the case by telling you why my own experience of God indicates to me that this is a misunderstanding, a misunderstanding on a par with ‘What is the point of asking God to do things in prayer when He could have done them anyway if He’d wanted to?’

Let me offer you what I consider to be a better way of viewing the situation. Let us say that God is represented by ‘3’, and let us say that man is represented by ‘1’ - we can then call a man that becomes a Christian ‘2’, that is, not God but not a normal man either - what St Paul refers to in Galatians as a ‘new creation’ – a man who has found God. Please note, this is nothing to do with any Christian/non-Christian superiority, I am simply talking about a position in relation to knowing God.

So for the purposes here we have:

3 = God
2 = Christian
1= Non-Christian

Now those that claim A is true might refer to position 2 as an inner revelatory experience, yet this is rightly problematic for those in position 1 because in one sense every conscious experience classifies as the mind’s experience of the self and its surroundings, from sense data, through to perception, intuition, and to the deeper cogitations in life. In actual fact, a broad and deep gamut of experience is actually implicated as the agent of any sensation, revelation or new perceptual position or conviction. The intuitive moment of epiphany from 1 to 2 is vogue in many Christian cultures that place greater emphasis on right-brain intuition over left-brain analyticity (particularly the Pentecostal, Evangelical and Charismatic styles of worship), but that depiction probably denies those in 1 from properly apprehending the everyday trail of experience that makes up sense data, perception, intuition, and to the deeper cogitations in life. Please do not misunderstand me, I do not wish to gainsay this approach or cast aspersions over such experiences, for in fact my own style of worship is underlain by a strong affiliation with a very charismatic style of praise for our Lord, so one must accept that the point at which one receives the Holy Spirit can send one’s trail of experience onto a rather ebullient new pathway – eureka moments and sudden bursts of ‘hallelujah’ do happen.

But here we find something very important - the atheist who ‘expects’ such an epiphany or who second guesses precisely how the moment of knowing God might occur could well be weakening the bridge over which he will at some point wish he could cross; that is, he might wait around for the hallelujah moment and always stay waiting because he fails to realise that experience and daily samplings in life play a key part in realising who God is and how He is speaking to us. To make this point clearer with an illustration, let’s call this “Human Potentiality” (HP) – how might God be speaking to the atheist through his own HP?

Bearing 1, 2 and 3 in mind, we must remember that if we were created by God, we are, of course dependent beings that would be nothing without His input in the first place. In other words, without 3, there would be no 2 and 1. Now if we have a quantum of human potentiality (emotional intelligence) represented by HP then clearly for humans HP > 1. God clearly has the choice of granting us a grace impartation whereby knowledge and awareness of the Divine occurs, but it is very obvious that this depends on our abilities for recognition, our willingness to make the transition from 1 > 2 and our readiness in accepting the changes in HP that accompany the blessing that accompanies the 1 to 2 transition.

Now if the command is for those in 1 to seek (S) in the way that God intends then clearly this has a value S3 in Divine terms and S1 in human terms. Thus it seems pretty clear that 1 has a value too low for Divine satisfaction but S1 has a value too high for many that are stuck in a 1 comfort zone – in other words the process of getting to grips with their own desires for salvation is for some a pathway too dark and hazy to contemplate, keeping them rooted in 1. But once one casts aside his own fears and doubts and hands them over to God, even by an outrageous and (what would be to him) a quite irrational dispensation and indulgence of blind trust, the human mind can construct a positive ingress into S1 - a sort of gravitation towards progression by willingness to do all that is asked of Him - by innovating a series of precursors that can be modified according to his truest and most lucid experiences. What this really amounts to is facing up to the fact that it is rather silly rejecting or dismissing the demands of God based on one’s own terms – much more sensible to embrace the situation on His terms – after all, if Christianity is the truth we are only likely to realise it if we accept what Christ has to say.

This really amounts to a person saying with all honesty - ‘God, if you are up there, I really want to know you’. Thus the instruction to seek will be a rewarding and fruitful instruction if one progresses towards greater and more expansive growth with the desire to make the changes that are necessary. That is why the final step is often the hardest, and why I have known many people that were able to believe that Christianity is the truth, yet still take incommensurably longer going forward from 1.9 to 2. What you have to remember is that upon seeking, when God says ‘you will find’ He means with respect to S1 not with respect to 1. It is no use bemoaning the fact that a supposedly personal, interested, willing and loving God would be more obvious, because we are bound to leave a residue of unfulfilment and dissatisfaction when we approach God on our terms and not His – because we fail to consider what is wrong in our own hearts and what it is that is stopping a genuine search.

And here we have identified the central problem with demanding evidence with bells ringing - it won’t work. Many have asked God to reveal Himself with 1 rather than S1 – they have enquired on the wrong terms – not His but their own. If the truth be known each man that does this is a recusant in supplicatory clothing - in other words, in his heart he might kid himself that he tried his best to make a genuine search, but in his head he knows that he never really offered himself up to God.

But the great news is that for those that do search with all their hearts and without artifice, their prayer will be answered. God will only reveal Himself when He knows we’re ready, and when we say that it is only possible when He shows Himself, we mean with respect to HP - that is, it is incremental growth where the increments are consistent with S1 not 1. Thus, failure to meet the standards should be seen in terms of the absence of contour stability given that by itself, if one always holds back, HP = 1. Bearing in mind that even those that have no initial belief in Him whatsoever can still pray for wisdom and clarity, my guess is that most atheists who ask on their own terms instead of on God’s find it difficult to get a determinable purchase on S1 - and in seeing the failure connotations as insuperable they lower their standards so they can be catered for in ‘earthly’ experiences instead of acceding to God’s desire that we look to God for the gift of S1. And with a complex personality like God, presumably the anthropomorphisms are applicable in as far as God has traits that closely parallel our concept of personality (love, grace, justice, intelligence, thought, consciousness, anger, yes - even anger) and can thus be useful in our coming to Him on His terms instead of our own. But the key to receiving His revelation has always been in searching out the terms on which Christ Himself says we will ‘find’ – for only then will those demanding evidence with bells on it be in a strong position to search successfully.

The Neurological Problem

As science has progressed we have come to know more about the nervous system than ever before. There is still a lot more we do not yet understand about the brain (and perhaps never will), but now we can zoom in at a neurological level and observe brain states and how they relate to certain beliefs, behaviours, and our inherent psychological make-up. Religious belief is often assessed by atheists not as something rational but as an unfortunate product of neurological activity over which we have no control. They say that certain people are simply unfortunate enough to be susceptible to it, depending on their brain states and neurogenic disposition.

My first objection would be this: if the atheists are right then every brain must be susceptible to states of this kind, be they religious or some other cognitive state. Why, then, single out faith-based belief as one of the cerebral aberrations? Apart from a bias against faith-based belief (presumably on their terms an inevitable product of neurological activity over which they have no control) there is nothing about brain states that tells them axiomatically whether faith-based beliefs are based on truth or whether they are cerebral anomalies that a person happens to be unfortunate enough to be affected by*. If the functioning brain is a coordinating centre of informational cells functioning entirely because of the universe’s vast stellar, chemical and biological history, the entire process from receiving sensory signals to cognitive configurations is all just nature playing out a realisation of the second law of thermodynamics. But if free will, rational thinking and neurological sense-making precepts entail scepticism about how reliable our minds really are, then the atheists are in the same sort of trouble that they claim the theists are in.

* Given that most people in the world believe in God or gods, and that most others claim a sense of the transcendent, I would say that they are not really ‘anomalous’ states at all.

It should be stated that in the strictest sense those who claim the agent is not wholly responsible for certain beliefs and feelings are not entirely wrong, and in many cases psychiatrists would concur. But when this claim is used against Christianity we see that it is problematic. If a man has a neurological problem and it conditions him to act in a certain way, one could say that good or bad actions are not actions for which their agents are responsible; the agents are passive not active - they are simply victims of a neurosis or inner-conflict. Their activity is determined by what goes on in their unconscious. Some would therefore contend that it is the neuroses that are responsible and not the agents.

There was a very well publicised case of a man who was in a loving relationship with his wife and children – this man was a good husband and a good father. However, after a few years, he started making s*xual moves towards his children, which quickly escalated into something even more serious. For their own safety his wife understandably left him and took the children with her, and her husband was left alone, hating himself for what he had done (he claimed such crimes were ‘abhorrent’). Later it was revealed that he had a tumour in his brain. After removal of this tumour, his p*edophilic instincts disappeared. He even managed to convince his wife to reunite the family and give their relationship another try. Then, after another couple of years of the family being together again his p*edophilic behaviour came back. He went for a brain scan and found that the tumour had reappeared. This story, and stories like it, have caused some controversy across the world as some argue that people don't make choices, their brains do. Whether this man could and should have had the moral wherewithal to resist his temptations has been a big debating point between atheists and Christians ever since (the former very often say ‘no’, the latter mostly ‘yes’), but given that in some cases but the brain can be distorted into making choices which the conscious mind, the person, otherwise finds ‘abhorrent’, the issue of brain states, and how reliable our beliefs are, is certainly a talking point.

So, as Christians who claim to have a relationship with the risen Christ, how can we be sure that ‘knowing God’ is not simply our brains being the catalyst for religious delusion? If personality is mediated by the brain and things like tumors in the brain, stroke damage, carbon monoxide poisoning, neurodegenerative diseases et al show that any conceivable aspect of our personality requires structures in the brain; memory (hippocampus), desire (hypothalamus), decision making (orbitofrontal cortex), emotions (the limbic system), temperament (amygdala), isn’t there is a good prima face case that the same is true of religious belief (usually ascribed to things like temporal lobe epilepsy, left/right hemisphere synthetic activity, or some other neuronal aberration)?

In actual fact, the atheists also contend that further weight can be added to their case by the fact that additional stimulant, treatment, or synthetic neuronal activity can bring about strange phenomenal effects, not least the inducement of religious beliefs and epiphantic instances that can be caused by our interfering with the various parts of the brain. The upshot is the implication behind the atheists’ statement seems to be that religious fervour/conviction/revelation is amenable to neuronal analysis and that chemical activity in both hemispheres of the brain can explain why we ascribe and wrongly elicit supernaturalism in a non-supernatural existence, and thus in their eyes rejection of the supernatural on these grounds is a perfectly reasonable position to take.

The Christian, to the contrary, claims that each first person ontology can be transformed in such a way that selfhood will experience a miracle - a transmutation, without any of the foregoing interference; for we claim that when this happens one can know it is unmistakably God at work in us. Naturally, being a Christian, I agree with this; my own view on neuronal manipulation is that those who have experienced the risen Christ experience something that is not synonymous with everyday neurological caricatures of science - a ‘thief on the cross’ type shift in awareness - the point at which Christ becomes a transforming part of the cognisance. Activities like the ones mentioned above (interfering with people brains) constitute a theoretical attempt at making sense of perception through a very unnatural process. They are therefore part of a more general empiricism but in a much more circumscribed framework than metaphysics (although, in my view, science and metaphysics blend together).
Compound

Although human behaviour has a ‘mind-collective’ interpretative component (a commonality of ‘mind’ where we all know what it is like to be a mind), our perception of God is inextricably linked to our perception of the world and as such is more loosely tied to uncompounded protocols than comparatively tractable neurogenic observations. Therefore, these examples of miraculous salvation exhibit a much greater ability to discharge apparent contra evidence because they are not readily amenable to simple test/refute procedural analysis - they are far more internalized - a central part of what defines mind in the first place. The vastly complex reality of a God created world and our perceptual overload in trying to apprehend it makes it less amenable to assessing such a reality with elementary observational and experimental protocols. This is probably why, when it comes to salvation, Jesus focuses less on the external realities of God’s work and more on our own cognitive dispositions – after all, His assured method for our coming to know Him (‘knock and the door will be opened to you’) involves simply the mind in which such a search is occurring, and God Himself, who chooses the right time for revelation based on numerous interconnecting factors, and on how such revelation will interrelate with the rest of His grand plan for creation. Once the mind of the supplicating man has received Christ as his Lord and Saviour his identify will be defined by his relationship with the living God, and he will see that his initial faith will be reward with the ‘certainty’ that the writer of Hebrews spoke about – that a certainty that only his fellow Christians could apprehend.

This is the certainty that Jesus Christ offers to all those that claim a relationship with Him is simply an unfortunate neurological state from which people need to be cured, but naturally the only method that can remove such doubt is if the doubter asks for revelation himself. That is the covenant God hasmade with man, and, for the sceptics, knowledge of God oneself is the only way that one can remove these doubts. Moreover, the fact that the many miracles experienced are congruent with a particular point in time at which God was asked to them perform (the same is true of healings) shows that the miraculous is not an arbitrary set of occurrences, but very much consonant with the temporal perceptions of those believing in God and the miraculous (an example of which is when I saw a man pray that the Holy Spirit would heal a blind lady, and straight away she was given her sight).

Although I said a few moments ago that examples of miraculous salvation are not readily amenable to simple test/refute procedural analysis and that they exhibit a greater ability to discharge apparent contra evidence, I do not mean that Divine impartations are unempirical - rather that their a priori complexity constitutes an ontology which makes them less amenable to examination, as elemental experimental protocols are bound up with a vastly complex psychological nexus, which have a bearing in the formation of our own perception. As I said a moment ago, I certainly think with science and metaphysics one blends into the other, but at the level of analysis that we are describing it is very probably impalpable. Moreover, when observing any man that seems to alter his perception of supernaturalism when his brain is manipulated by external interference (such as in surgery or neuroscientific testing), you would have to consider a great many factors inextricably linked to his state of mind - personality, education, religious background, personal traits, insecurities, allegiances, human propensity to identify with social groups, etc - all of which feed into the evidence in a more general process than institutionalised science often countenances.

Please do not misunderstand me, I am all for scientific endeavour and improved neurological understanding through advanced science, but I think with the cases mentioned and other similar cases, scientists attempting to assemble observational protocols in test/refute circumstances must be aware that Divine activity would not necessarily be a quantity that would encapsulate the notion of the organised complexity we find in organisms.

Let’s assume for a second that there is Divine activity and ordinary human physiology - certainly their dialectic will be a conflated dialectic. I do agree that the engines of neuronal activity create useful work throughout the various scientific gradients, but I see no conflict or contradiction between any of the foregoing and Christianity. If you had a Ford Escort in your driveway and woke up to find a Rolls Royce you would naturally assume someone has switched cars in the night. But if you were standing in front of your Ford Escort and it suddenly morphed into a Rolls Royce you would think it was a miracle.

When one grapples with the subject of Divine activity, you will find that the conceptual complexity cannot be trivialised by comparison with even a well thought out atheism, much less an arbitrary agnostic comfort zone. God is a complex personality forever interacting with those that know Him; He has a psychological, sociological and historical lineage which gives rise to continual cognitive sustenance and revelation. I think atheists are all too aware of the weaknesses that penetrate when their shaky convictions are exposed to a little fire. And if they brush aside any residual doubt as inconsequential, then they are claiming de facto certainty; that is, they are axiomatically conferring upon the self a degree of certainty which is anathema to the self’s own inherent make-up. . And therein lies the problem for atheists - the temptation to attack the theist with their own weapon of certainty should, if they are not quarantined from cognitive reality, leave greater residues of doubt in the mind of the attacker. In my experiences, their confidence and stridency ends up being a lipstick on the ugly face of self-doubt, and to the discerning eye, gives the impression that they are merely covering up for incompetence.

Logic and Christianity

A recent thread on Network Norwich & Norfolk has been created here in which some of the contributors have been wrestling with the science and Christianity problem (a problem only in the sense that they make it one, I hasten to add). I am going to submit a few weekly articles on Christianity and science soon (mostly biological science and evolutionary theory) so I won’t comment on that particular issue here – but the welcome return of non-believers Mike H and Mike 2 has seen the re-emergence of the evidence/proof of God’s existence debate.As I have said from day one, we do not deal with proofs on here. One must realise that God is an infinitely complex personality, so the best we can do is sample Him. The Father has revealed Himself to us in Christ Jesus, and although the Bible is the word of God – one can learn lots more about God both from creation around us, and from having a relationship with Him. I think what the two Mikes (and any sceptics for that matter) should ask themselves is whether the world they see around them does in fact scream out that God exists, and how they might be expected to realise this.There’s a great story often recounted about Elizabeth Anscombe saying to the brilliant Wittgenstein, that she can “understand why people thought that the sun revolves around the earth.” Wittgenstein asks, “why?” - Anscombe says, “Well, it looks that way.” - to which Wittgenstein responds, “and how would it look if the earth revolved around the sun?”In other words, the way something looks from a certain standpoint is, from the individual’s perspective, a direct proprietary fact about the person's perception of that 'something'. ‘How it appears from a certain place’ is, nonetheless, also of interest in its own right and belongs to what is sometimes called ‘the reality of the appearance’. In Biblical times the ancient Hebrews referred to it as 'language by appearance' – so, for example, if something 'filled the earth' it did not necessarily, in the literal sense, fill it entirely.Using my ‘four principle rules of logic’ I can show why the proof arguments are wrong. Godel’s theorem warns us that the axiomatic method of making logical deductions from given assumptions cannot in general provide a system which is both provably complete and consistent. There will always be truth that lies beyond, that cannot be reached from a finite collection of axioms. This also means that no door in the labyrinthe palace of empiricism opens directly onto the ‘Absolute’ - there are hints of the infinite in mathematics (Cantor’s Absolute), but any complete unity must include itself, thus we hit the self-referencing problem of Russell’s paradox. But the way ‘minds’ can attune themselves into the nature of the Absolute gives us the biggest hint that we are truly meant to be here, and that this life is but a shadow of a deeper and more astounding reality.Moreover, there will always be statements which are true but that one cannot prove are true. Take the following statement (call it ‘S’)..S - “Mike cannot prove this statement to be true”Suppose Mike were to arrive at the conclusion that S is true - this means that the contents of S will have been falsified, because Mike will have just done it. But if S is falsified, S cannot be true. Thus if Mike answers ‘true’ to S, he will have arrived at a false conclusion, contradicting its infallibility. Hence Mike cannot answer ‘true’. That means that S is true; but in arriving at that conclusion we have demonstrated that Mike cannot arrive at that conclusion. This means we know something to be true that can’t be demonstrated to be true. Now consider something a little different. Let us say that we meet a man for five minutes that we have never met before and will never meet again. Our job is to find out if he can speak English. If he remains silent throughout the five minutes and he disappears never to be seen again, we cannot prove that he cannot speak English but we have no evidence that he can. If, however, he were to say the words ‘My name is Robert and I can speak English’ we would, of course, have the deductive proof that he can speak English, as the English words themselves would be contained within the statement. This is different from the first example, for the first example is about the axiomatic method of logical proof itself and is not a property of the statements one is trying to prove or disprove. One can always make the truth of a statement that is unprovable in a given axiom system ITSELF an axiom of some extended system. But then there will always be others statements in the self same system that are unprovable. Now we come to something else that is key - in the first example there is no new predicate that can be added to S (without changes to its intrinsic structure) that can alter the fact that S cannot be shown to be true. Now very obviously with the second example that is not the case - if we were told that Robert was an English lecturer and that there was footage of one of his lectures, we could show that ‘Robert can speak English’ is a fact without having to prove it in those five minutes. Moreover, unless we start flirting with nonsense there are a number of things we could find out about Robert that improve the probability that he could speak English.S1 - Robert was born and raised in GhanaS2 - Robert was born and raised in MozambiqueIt is very clear which out of S1 ad S2 is more likely to be suffixed with the statement ‘Robert speaks English’ - S1 because Ghana is a former British colony whereas Mozambique is a former Portuguese colony. Of course S1 and S2 might only improve the probability very slightly, but this is what we do in all walks of life. Knowing, as most mathematicians do, that there are some statements of logic that cannot be proved to be true (also read about the distinctions between realism and antirealism) we use our perceptive and investigative toolkit to reason our way through these things. If Robert lives and works in this country it is much more likely that he speaks English than if he lives and works in Ecuador. Do we completely abandon a mechanical procedure for investigating mathematics because of Godel’s theorem and Turing’s halting system? Of course not!! Those unprovables are rare elements of mathematics and can be sifted out allowing us to continue on a logical trajectory. That’s just one example of how silly it is to stridently decree ‘Unless there is proof of God’s existence, I’m going to carrying on believing that He doesn’t exist’.

One must also bear in mind that there are many axioms or regularities that only become that way by our adding something to facts. Look at this set of six numbers (all single integers used are under the value of six) 234232 - 344232 - 121232 - 523334 - 552555 - 122311. A Turing machine can show which number sets are computable given a set of rules. If the rule is, say, take the first number of the first set and add 1 (giving us 3), do the same to the second number in the second set (giving us 5), the third in the third (giving us 2) , and so on, we find that with that rule in place we have the number 352462. Unlike the “Mike cannot prove this statement to be true” example, this time we have created a rule or procedure and shown that logical deductions can be reached without messing around with the axioms in logic. For example, given this rule, I know that if I have the answer 352462 then none of the sets will contain the exact sequence 352462. Last one….Chaitin’s theorem. Having shown you with Turing that there are mathematical problems that cannot be proved by any fixed heuristic procedures, we now move on to how we know if what we know (or contend) is right or whether further compressibility is required. You also ought to remember that one can compress something too much into logical nonentity - the biggest example being with self-referencing paradoxes such as ‘This statement false’ - here we have something that is too compressed to be logical, because if it’s true then it’s false and if it’s false then it’s true. It is nonsensical because there is no subject or predicate pointer extended to ‘false’. The statement “3 + 5 = 9 is false” is true because ‘false’ has mathematical integer subjects extended to it - it has the ideal compressibility for deductive analysis. Now in Chaitin’s theorem, a computer is given this command - “Search for a string of digits that can only be generated by a program longer than this one”. Now obviously if the search succeeds the search program itself will have generated the digit string. But then the digit string cannot be “one that can only be generated by a program longer than this”. This obviously leads to the fact that the search must fail, even if it is an infinite search. The search was intended to find a digit string that needed a generating program at least as big as the search program, which is to say that any shorter program has to be ruled out. But as the search fails, we cannot be sure there is no shorter program, as we do not know whether a given digit string can be encoded in a program shorter than the one we happen to have discovered. Now here’s the rub - a random sequence is one that cannot be algorithmically compressed - but as I have just shown, you cannot know whether or not a shorter program exists for generating that sequence. The cardinal point in these algorithmic programs is that you never know if you’ve unturned every stone in trying to shorten the description. Therefore you cannot prove that a sequence is random, although you could disprove it by actually finding a compression. If you are paying close attention you will see that this is isomorphic with the Robert speaking English model - here you have much greater access to empirical evidence (certainly less complex than algorithmic mathematics) but you can find the shortest compression (so to speak) by hearing him speaking English. The practical conclusion here is twofold. In the first place, one can prove mathematically that almost all digit strings are random, but one cannot know precisely which. But more essentially for everyday purposes, taking the cosmos as an algorithmic whole, events or activities that appear random may not be random at all - even things like the indeterminism of quantum mechanics. The cardinal point here is not that something like, say, Heisenberg’s Uncertainty Principle might belong to uniform laws of which we as yet know nothing, because I am sure that that is the case. The cardinal point is that we might never be able to know - in fact, Chaitin’s theorem ensures that we can never PROVE that quantum mechanical measurement outcomes are random.

But how does that work for the theist - after all, how does God load the quantum dice to have a random yet uniform world as well as having the difficulty of human minds that can affect things in the cosmos with God kindled free will? A stochastic system can produce the ‘random yet uniform’ cosmos, but what about free-thinking minds? Think about it like this; regarding an electron in quantum mechanics a position measurement is indeterministic because it is free to choose among a limited range of possibilities. On the other hand the measuring itself is contingent on whether one is measuring ‘position’ or ‘momentum’ - that is to say, the nature of the alternatives is fixed by an external agent - the one doing the measuring. To make this clearer, imagine a game in which you have to guess which whole number I am thinking of between 1 and 250 - you only have 20 questions or guesses and I can only answer ‘yes’ or ‘no’. imagine your questions begin as follows - Q1 - Is it bigger than 125? A - Yes; Q2 - Is it even?A YesQ3 - Is it divisible by 7?A -Yes Q4 - Is it 232?A - Yes. Now here’s the trick; let us say that I hadn’t chosen any number in advance - I had agreed to answer purely at random subject to consistency only with the previous questions. The answer was not determined in advance, but it was not arbitrary either - its nature was decided particularly by the questions asked but partly by chance (depending on what was being asked, and when the final guess was offered and the final answer given). After question 1, my answer was limited to 126-250, after the second question my answer was limited to all even numbers between 126 and 250, after the third question the range was lessened to those divisible by seven, thus preventing me from answering, say, 233 but giving me several other options. If the fifth question to which I randomly answered ‘yes’ was ‘Is it greater than 230?’ - then the only remaining number that would fit the five ‘yes’ criteria would be 238. In the same way, the reality of quantum mechanics is decided in part by the question - whether one is asking about the position of the electron or its momentum and in part by the uncertain nature of the values obtained for these quantities. The Divine analogue here is that God determines certain uniform facts about creation and what other options are available in any given system, but a variety of subsystems in which randomness plays a part too in choosing among several alternatives. The freedom of the individuals’ choices is much the same, it is freedom within a set of ordinances that are statistically part of a uniform plan - an end result that has already been predetermined by God outside of creation. Just because God already knows which way the coin will land before I throw it, it doesn’t alter the fact that for a free-thinking mind like my own the result is an unpredictable 50-50. So, regarding this subject, these are the four basic principles of logical analysis - and one must be mindful of the above when contemplating the big question of whether God exists or not.

The Harmony Between Christianity and Science

The harmony between Christianity and science progresses on the basis that when we discover new information about our world and our universe we embrace it and alter our perception of the cosmic blueprint to accord with fresh knowledge and innovation – a bit like completing a jigsaw piece by piece. It is when the opposite happens that problems begin; that is, when Christians think they already know the blueprint and reject new innovations and fresh knowledge, willfully keeping themselves fixed in the dark ages. Equally many atheists take a very myopic view of what the Christian faith is, and resort to straw man caricatures as they attempt to justify their unbelief. It is much to hope that this false dichotomy will be exposed with greater ubiquity than is presently the case.