Can a godless universe explain logic?

Because of its denial of the existence of a personal, intelligent creator of the universe, atheism necessarily relies on a philosophy known as naturalism (more accurately: philosophical or metaphysical naturalism), which attempts to explain everything in terms of the materialistic laws of physics. This philosophy requires that every aspect of reality be understood as a product of natural forces. No part of reality can be exempt from this approach, otherwise atheism becomes nothing more than a meaningless word (or is limited to a partial meaning, an example being the case of early Christians accused of being ‘atheists’, due to their refusal to worship the Roman pantheon of gods).

Logic, reason and rationality are part of reality. Therefore, if atheism is true, then this fundamental component of human intelligence needs to be explained as a product of nature. Let us see where this explanation leads us…

An illusion fashioned by impersonal forces
Nature is impersonal, unconscious and mindless. According to atheism, the forces of nature are not controlled and applied by a higher personal and intelligent reality to achieve some desired effect, but rather they act on their own without any external guidance. Thus whatever such forces produce lacks any overall purpose. Such a product of nature is nothing more than an effect of impersonal causes, and any design it possesses is merely an illusion, rather like the chance configuration of clouds that just happens to form the image of a face.

Although this product of nature is not designed, it nevertheless must possess one fundamental property: it must reflect something of the nature of the forces which created it. Given that the forces of nature are impersonal, then they are necessarily deterministic. Within a deterministic system the properties of an effect must directly reflect the properties of its cause. Such an effect cannot truly possess free will, which would enable it to ‘rebel’ and distort its own properties such that they no longer reveal the nature of its cause. The properties of the human mind must therefore reflect nature, which (according to atheism) caused it. Free will is, of course, an illusion, within an entirely deterministic universe.

Merely a tool to aid survival?
Now if atheism is true, then reason is merely a property of human intelligence, which is itself an emergent property of the evolved (and presumably still evolving) human brain. This process of evolution – natural selection – is the means by which nature is believed to select properties which confer fitness on the organism, to enable it to survive and thrive. Reason, being thus considered an emergent property of the brain, would therefore have emerged as a tool to aid survival. Therefore it exists for entirely utilitarian reasons. How therefore can a mere tool tell us anything about reality as a whole? How can logic, being nothing more than a device of a finite brain, possess objective validity and absolute authority such that mathematicians can use it to solve problems that cannot be tested empirically (Fermat’s Last Theorem, for example), because of the impossibility of computing every example within an infinite series?

Now the answer to this question may run something like this: logic is merely human, but it is a human discovery of something that is part of nature; because nature is rational, so the evolved human brain has detected this rationality through the methods of science.

This answer appears at first sight to be sound, but it is actually deeply flawed, as I will explain…

Nature’s uncertain message
Firstly, nature (if it is the cause of human reason) has not only produced rationality within the human brain, but also irrationality. If the phenomenon of rationality within the human brain speaks of a fundamental rationality governing nature, then it follows that there must also be a fundamental irrationality governing nature, given the undeniable phenomenon of human irrationality. Naturalists cannot have it both ways. If we credit nature for our rationality, then we must also blame nature for our irrationality. As the saying goes… “a tree is known by its fruit”. If nature is the only ‘tree’ (cause) of the ‘fruit’ (effects, such as rationality and irrationality), then how can we trust any fruit from this tree, if we know that at least some of the fruit is bad? If we know that the tree produces ‘irrational’ fruit, then how do we know whether the so called ‘rational’ fruit is not also irrational?

Now the retort to this argument may be that we can sift the “good fruit” (what is rational) from the “bad fruit” (the irrational) by the methods of science. And this brings me to my second point…

Science operates by means of the empirical method of observation and experimentation. This method can only work on the basis of certain ‘givens’ or presuppositions, which are themselves beyond empirical testing. When an experiment is conducted in one particular place, we assume that the same result will obtain when the same experiment is conducted in a different place subject to the same or similar physical conditions. Thus a chemical reaction that works in Paris will also work in London, New York or Tokyo. In other words, a successful experiment in Paris allows us to infer that we would achieve the same result in these other places, unless there were known physical properties about those other places that would have a direct bearing on the experiment to produce a different result. Science therefore assumes that the laws of physics hold true throughout the universe; that they are universal and consistent. If we cannot make this assumption, then science is impossible, because no inference could be made from any observation or experiment. Of course, it goes without saying that we cannot empirically test the universality of the laws of nature, because we first have to assume that they are universal and consistent in order for the empirical test to have validity. It would be rather like someone trying to conduct an experiment to prove to himself that he existed, when his existence is a precondition for possessing the ability to conduct any experiment at all!

The method of making general inferences from observations and experiments is known as “inductive logic”. Inductive logic is the logic of probability, not absolute certainty. It is the method by which a general law or principle is inferred from observed particular instances. So the finite human mind observes phenomena in nature and then makes inferences about the fundamental nature of reality based on certain presuppositions. Hypotheses are constructed and then tested empirically and a general feeling of certainty and confidence is generated by the repetition of the same results. This confidence is by no means a proof, but considered a solid working theory, that may even be promoted to the status of “scientific fact”. Most scientific results, which impact on our daily lives, are so well established and tested, that only someone afflicted with hyper-Cartesian doubt would question them.

So the science of daily life is useful to sift the rational from the irrational, because of the power of human experience. I have no doubt at all that the computer, on which I am writing this article, actually exists. The reality of this computer bears down directly and powerfully on my own personal experience and I find a certain manipulation of the keyboard produces the desired result. Therefore an overwhelming confidence in the existence of my computer is continually confirmed to me by my behaviour, which is a form of empirical testing. If someone were to argue with me that my computer does not exist, then I would conclude that his view was irrational and that my belief in my computer’s existence was rational.

Now, because we find that the phenomena of daily life bear down on us and assure us of their existence and function, we assume that empirical testing can be applied to the whole of reality. Thus we are led to believe that the empirical method is the means by which we can discern the rational from the irrational, and that therefore science is the arbiter for all questions relating to any aspect of reality. This is a myth. The scientific method is itself entirely dependent on certain empirically untestable ‘givens’ and they themselves also rely on the objective validity of logic.

Instincts, reflexes and projection
The problem with naturalism (materialism) is that the empirical method is all we have, if that philosophy is true. If human rationality is nothing more than an emergent property of the evolved human brain (as indeed it must be if naturalism is true), then all we have is a finite perception of material phenomena. All we have is, as it were, what is in front of our eyes. We then perceive certain patterns and manipulate the world around us to aid our own survival. We learn through trial and error to make tools, and through the repetition of this process over millennia the instinct of thinking in terms of “cause and effect” is inculcated in us. And then we project that idea onto reality as a whole. But, of course, this is not a rational conclusion, but merely an assumption based on guesswork and conditioning.

Or over huge spans of time we perceive that certain objects are similar to each other, and so we may gather them together (say, rocks to build a wall or house), and the idea of categories and sets is induced in us. And we learn to compute by adding together similar objects. Or we emit certain noises, which we find we can use to communicate to other people, and associate certain sounds with certain objects and find the association useful. And so language is born, which generates a feeling of order within groups of humans, from which rationality is generated, which is then projected onto reality as a whole. But this ‘rationality’ is merely a collection of instincts and reflexes that seem to ‘work’ in order to achieve certain goals in human experience, the chief one being survival. This ‘rationality’ cannot tell us anything about the fundamental nature of reality.

Through this process of perception, the ideas of logic are developed, but only as a sophisticated method of survival. Such logic, being the product of finite human minds cannot tell us – with authority – what is absolutely true. Logic cannot be discovered, since a finite mind, by definition, cannot discover something which is infinite and absolute.

But then someone may argue that logic does not need to be absolute; it can serve as a useful tool, but its importance should not be overstated.

Well, this is simply false, as I will show.

The absolute authority of logic
As I have explained, the empirical scientific method employs the method of induction. Inductive logic is to be distinguished from deductive logic.

In deductive logic it is impossible to deny the conclusion of sound premises without contradicting oneself. It moves from premises to conclusion in a way that does not allow any room for probability or ambiguity. For example:

Premise A: All planets in our solar system orbit the sun.
Premise B: Mars is a planet in our solar system.
Conclusion C: Therefore Mars orbits the sun.

Assuming that premises A and B are true, then conclusion C is true without any doubt at all.

Now clearly if deductive logic did not possess absolute authority – in other words, there could be situations where it did not apply – then we could have the following syllogism:

Premise A: All planets in our solar system orbit the sun.
Premise B: Mars is a planet in our solar system.
“Conclusion” C: Therefore Mars
may possibly orbit the sun (but we can’t be sure!).

Well clearly this is absurd. If one such conclusion is to be doubted, then all conclusions in all syllogisms could be doubted. Thus certainty becomes impossible. If logic is not infinite and absolute, then it is nothing at all.

Mathematics (on which physics relies) requires logic to be absolute, as also does science. As I explained, the inductive logic of the empirical method relies on deducing from certain presuppositions (such as the universality and consistency of the laws of nature). Inferences are made on the basis of these presuppositions. Thus we have the following implied syllogism at the heart of science:

Premise A: The laws of physics are universal and consistent throughout the universe.
Premise B: (We observe that…) Matter – subject to the laws of physics – behaves in a certain way in the Milky Way galaxy.
Conclusion C: Therefore we infer that matter will behave in the same way elsewhere in the universe, where there are similar observed conditions.

If this kind of conclusion cannot be deduced with absolute confidence, then science is dead.

Now clearly logic can only possess absolute authority if it is, in some sense, ‘above’ nature. Indeed logic must even transcend infinity (as I will explain). How therefore can logic be merely the product of a finite human brain? Or how could a finite human brain discover something above nature, when, by definition, a finite being is merely a product of nature? Clearly it cannot.

Logic and infinity
The human mind is finite. Logic is infinite. Therefore logic cannot be a product of the human mind.

In what sense is logic infinite?

The answer to this lies in pure mathematics.

Fermat’s Last Theorem was solved in 1994 by Prof. Andrew Wiles, and it states the following:

x^n + y^n = z^n has no non-zero integer solutions for x, y and z when n > 2.

Now clearly Andrew Wiles did not attempt to solve the problem by ‘empirical’ sheer brute force calculation, because obviously n can be any value above 2. This is an infinite series. Likewise, for every value of n, there are infinite values of x and y to investigate in order to see whether they equal z to the power of n. On the contrary, Professor Wiles would have had to resort to deductive logic. His proof has been accepted by the mathematics community, and yet it is an argument that holds true for an infinite series. This indicates a belief that the logic employed in the proof has authority over the entire infinite series implicit within the theorem.

Of course, this is true of many theorems and hypotheses. The famous unsolved Riemann Hypothesis has been inductively shown to be (most probably) true, given that it has been subject to brute force testing by over trillions of calculations (of the non-trivial zeros all found on the critical line of the complex plane of the zeta function), but this inductive ‘proof’ simply does not count as a proper mathematical proof. It would certainly suffice within the natural sciences. Only a deductive argument, by which something could be said definitively about the entire (presumed) infinite series of zeros, would be recognised as a legitimate proof. Thus it is implicit within mathematics that the empirical method (brute computer calculation) cannot deliver a satisfactory proof, but that the tool of deductive logic can and must speak authoritatively about an infinite series of numbers. If a mathematician were to doubt the absolute authority of logic, then he would have to resort to inductive logic, and thus a further proof of the Riemann Hypothesis would be redundant, given that it has already been ‘proven’ on the basis of a high level of probability. In this case deductive logic would simply collapse into inductive logic.

Therefore the application of logic has to be infinite, otherwise mathematics is dead (along with physics, and, by extension, all the natural sciences).

Cause and effect
It is a given within science that an effect cannot be greater than its cause (‘cause’ taken here to mean either a single cause or a composite of causes producing a single effect). I have shown that logic has to have absolute authority and must be infinite in nature. It therefore cannot be the product of the finite human brain. If someone were to argue that the human brain did not produce logic, but merely discovered it, then the same argument holds true. A finite brain cannot discover something infinite, because such a brain would need the capacity to recognise the infinite. By definition a finite brain has a finite perception, and therefore has no such capacity.

However, as I have argued, we need to be committed to a belief that logic is both absolute and infinite, in order for both mathematics and science to work. In fact, no knowledge is possible unless this condition is fulfilled.

Philosophical naturalism (reductionist materialism) posits that the human mind is merely a product of the human brain, which evolved by the operation of mindless laws, and which developed for the purpose of survival. Within this theory, the human brain is merely a tool. Nothing more.

But human rationality requires the operation of an infinite mind, which cannot be merely the product of natural forces. This conclusion undermines the claims of atheism. The operation of logic itself clearly shows that there exists an infinite rationality and intelligence behind and above nature, which interacts with the human mind to enable us to make sense of our intelligible universe.

Only the reality of an infinite mind operating on the human mind can explain human intelligence and rationality. Otherwise all human rationality is an illusion.


Why atheism cannot be true (part 2)

In part one of “Why atheism cannot be true” I looked at the subject of the ultimate origin of the universe, and concluded that none of the options available to the rational human mind supports the view that an intelligent personal creator does not exist. In summary: the ideas of the universe from nothing, infinite regress and a beginning of the universe from a pre-existing impersonal state are all incoherent. On the other hand, the idea that the universe had a definite beginning which resulted from the actions of an intelligent, conscious, personal being with free will overcomes the difficulties inherent in the atheistic hypotheses.

But cosmology is not the only area in which it can be shown that the atheistic view of reality can be refuted. The most fundamental subject within human learning – an area of study that undergirds both science and mathematics – reveals the inadequacy of the view that reality can only be explained in purely naturalistic terms. This discipline is epistemology: the study of knowledge itself.

Every claim about reality stands or falls on its epistemological credentials. If epistemology judges a truth claim to be incoherent and self-refuting, then such a claim cannot conceivably be true. There is no proof more compelling than an epistemological one. Mathematics is often perceived to be the most ‘elemental’ of all subjects, but this is not the case. All mathematical proofs presuppose the objective validity of reason. If a claim about reality fails to uphold and explain reason itself, then nothing else can be proven to be true within that worldview.

Atheism and the idea of ‘evidence’
The following are frequent claims by atheists, and such assertions populate the internet as well as publications promoting the view that no God exists:

“There is no evidence for God’s existence and therefore all gods must be assumed not to exist” – anonymous atheist on the internet.

“Despite such well-financed efforts [by the ‘infamous’ Templeton Foundation], no evidence for God’s existence has yet appeared.” – Richard Dawkins

“That which can be asserted without evidence, can be dismissed without evidence.” – Christopher Hitchens (with reference to claims about God).

“Extraordinary claims require extraordinary evidence.” – Carl Sagan (as with the Hitchens’ quote, this is also with reference to claims about God)

All these comments have one thing in common: they tacitly claim some level of competence in the field of epistemology. All these authors assume that their naturalistic (therefore atheistic) view of reality is epistemologically sound and rationally valid, and therefore any other view of reality is to be rejected.

I will now investigate this implied claim, to discover whether it really is sound and coherent.

The anonymous internet atheist and the three well-known atheists quoted above all make comments which presuppose a certain definition of the concept of ‘evidence’. All four comments state, in different ways, that “there is no evidence for the existence of God” – or there is “no ordinary evidence” (therefore the only evidence that could be adduced for God has to be ‘extraordinary’, whatever that means!).

Because the claim that “there is no evidence for God” is often not explained, we are left to guess what kind of evidence the atheist would accept. If we define ‘God’ as “the intelligent, personal – and therefore conscious – all-powerful creator and sustainer of the universe”, then it is not unreasonable to infer His existence from at least certain aspects of reality (for example, high levels of order and complexity within nature, the validity of reason, free will, the moral sense, consciousness). Even if some people do not accept that we could ‘prove’ that God exists on the basis of these inferences, they cannot logically dismiss the validity of such an approach. It is not irrational to infer intelligent causation of intelligent and intelligible effects. If that were the case, then we would require proof that only a non-intelligent cause can produce an intelligent and / or intelligible effect, which is clearly absurd.

So obviously the atheist who claims that “there is no evidence for God” cannot include inference in his definition of the idea of ‘evidence’. If that is the case, then what are we left with? There are a couple of famous atheist analogies that can help us to answer this question…

Carl Sagan’s “Dragon in the Garage” analogy:

Someone claims that “a fire-breathing dragon lives in my garage”. This (apparently female) dragon is also invisible and floats in the air, so cannot leave footprints, if we try to capture images of them by spreading flour on the garage floor. The dragon’s fire also possesses no heat, so cannot be detected by an infrared sensor. The dragon is also incorporeal, so spray painting will not reveal her existence. Every physical test of her existence is countered with a “special explanation” of why it won’t work.

Sagan then asks: “What’s the difference between an invisible, incorporeal, floating dragon who spits heatless fire and no dragon at all?”

The other well-known atheist analogy is John Wisdom’s “Parable of the Invisible Gardener” which was later developed by Anthony Flew:

“Once upon a time two explorers came upon a clearing in the jungle. In the clearing were growing many flowers and many weeds. One explorer says, ‘Some gardener must tend this plot’. The other disagrees, ‘There is no gardener’. So they pitch their tents and set a watch. No gardener is ever seen. ‘But perhaps he is an invisible gardener.’ So they set up a barbed-wire fence. They electrify it. They patrol with bloodhounds. But no shrieks ever suggest that some intruder has received a shock. No movements of the wire ever betray an invisible climber. The bloodhounds never give cry. Yet still the Believer is not convinced. ‘But there is a gardener, invisible, intangible, insensible to electric shocks, a gardener who has no scent and makes no sound, a gardener who comes secretly to look after the garden which he loves.’ At last the Sceptic despairs, ‘But what remains of our original assertion? Just how does what you call an invisible, intangible, eternally elusive gardener differ from an imaginary gardener or even from no gardener at all?’”

Now both these analogies have something in common: they both assume that the evidence for the existence of something – or someone – must involve some element of direct observation or sense perception. Both are examples of “strong empiricism”, which claims that “all knowledge comes via sense perception” – i.e. we can only know what we can observe or perceive with our senses.

Of course, we assume that there is no “invisible dragon” in the garage or “invisible gardener” tending a plot in a clearing in the jungle. But these are not valid analogies of God, because these ideas are trivial, whereas the idea of God is non-trivial. Thus both analogies commit the fallacy of a category error. A trivial idea has no – or little – effect on reality, whereas a non-trivial idea has strong explanatory force. Therefore to lump Russell’s teapot, Sagan’s dragon, Wisdom and Flew’s gardener, the Flying Spaghetti Monster, the Invisible Pink Unicorn, invisible fairies down the bottom of the garden etc etc, in the same category as the intelligent, personal creator of the universe, is rationally inadmissible. The concept of a supreme, intelligent, personal creator implies something about the nature of reality, whereas these other ideas cannot imply anything at all.

If certain effects were observed, which could only reasonably be caused by an invisible dragon in a garage or by an invisible gardener in a jungle clearing, then we would be justified in stating that “there is evidence for the existence of these beings”, even if they were imperceptible to our senses. We would be constructing this theory on the basis of inference.

Science uses inference all the time. In fact, the scientific method is impossible without it. We could not infer the Big Bang, dark matter, most of the process of evolution or even draw conclusions about most of the functioning of the universe without inference. The only way we can draw any conclusion from any scientific experiment is to bridge the gap between that particular experiment and the general functioning of the universe by assuming – thus inferring – that the laws of physics and chemistry hold true throughout the whole of nature. If, for example, we observe matter functioning in a certain way in London, we infer that it would function in the same way in Paris or New York. Do we really need to repeat the experiment in every place, before we could draw a conclusion? We infer that matter is essentially the same in Paris and New York as it is in London.

Thus the atheist view of ‘evidence’ is far too restricted and unworkable even within science. The claim that “there is no evidence for God” has to be translated as “there is no direct observational evidence of the being of God according to the tenets of strong empiricism”. And I would agree. God is not a physical being floating around somewhere in the air. Indeed if He were, He would not be God, who transcends space and time.

The impossibility of the atheist theory of knowledge
It is not simply the case that atheists have a defective and limited understanding of the concept of ‘evidence’, but that their theory of knowledge on which their view of evidence is based, is logically impossible.

The quotes and analogies cited above all presuppose the epistemological theory of “strong empiricism”, which I will henceforth simply refer to as ‘empiricism’ (I say ‘strong’ empiricism to distinguish it from the ‘weak’ empiricism which is mixed with rationalism. Of course, some knowledge comes via sense perception – no sane person doubts that! But “weak empiricism” is really little different from “weak rationalism”, and is irrelevant to this debate.). Some atheists may dispute this point, and state that “of course, there are innate ideas which do not come to us via sense perception”. Fine. But then they have no grounds for asserting the philosophy of naturalism (aka materialism, physicalism), which requires a belief in strong empiricism, given that our only epistemic relationship with nature is through the senses. If they then argue that innate ideas have their origin in nature, they would be guilty of special pleading or question begging – assuming naturalism to be true as the means of concluding that it is true. That is, of course, dishonest.

The theory of empiricism is an idea, and is not derived from sense perception. There is no observation or scientific experiment that tells us that “all knowledge comes to us by means of sense perception”. The concept is not some physical thing floating around in the universe or discernible at the subatomic level. It is an a priori idea, and therefore it precedes sense perception. Therefore the idea of empiricism itself breaks its own fundamental rule: we cannot know empiricism to be true if we believe it is true. In fact, if we believe it is true, then we are breaking its own method of verification. It is the ultimate leap of faith.

Atheists often accuse theists of “taking a leap of faith” into the dark, or into irrationality. They often claim that faith involves ignoring evidence or is even exercised in spite of the evidence. Whether some believers do this or not, it is certainly true that an atheist, who subscribes to the philosophy of naturalism, makes just such a leap of faith. He insists on subscribing to a view of knowledge which is self-refuting, and therefore logically impossible. It defies all logic to hold to a view that “evidence can only be defined and verified empirically” when that very idea cannot be verified empirically.

But it gets worse…
But in the light of this, the atheist could still say, “well, OK, there are innate ideas, and we accept that not all knowledge comes to us by means of sense perception, but we still think that the philosophy of naturalism is most probably true, even if we cannot absolutely prove it, whereas the God theory is implausible.”

This is the position of “atheistically inclined agnosticism”. Firstly, such a position logically disqualifies any atheist from declaring a believer in God to be irrational, which should put an end to the vitriol of much debate on the subject of the existence of God. Secondly, the atheist is saying that a theory, which is logically dependent on a self-refuting theory of knowledge, may be true. Well, “may be true” implies the assertion “it is logically possible that this theory is true”. How can this be the case, when we have already established that the basis of the theory is logically impossible! Modal logic thus disqualifies atheistically inclined agnosticism.

The fundamental problem with atheism, is that this worldview cannot explain reason itself. We are being asked to believe that ‘reason’ derived entirely from the human ‘mind’, which itself derived from the physical human brain, and this evolved without any purpose other than mere survival. Thus, according to this view, reason emerged merely as a survival mechanism. If this is the case, then all ideas (beyond the most immediate perception – and perhaps even these) are equally valid. The “idea of God” is no more invalid than the “idea of naturalism”. According to the philosophy of naturalism both ideas emerged merely as aids to survival. Thus we are told that religious people believe in God, because it helps them cope with reality, but according to this logic atheists do not believe in God for precisely the same reason! Objective truth has nothing to do with it.

Clearly we can see that the philosophy of naturalism is entirely self-refuting. If all ideas (especially metaphysical ideas) are merely aids to survival, then we could never know whether the philosophy of naturalism itself were true (this philosophy being, of course, a metaphysical idea, given that it makes a claim about reality as a whole).

So the philosophy of naturalism is impossible. Of course, there are some atheists who claim to hold to some form of supernaturalism (which is the only alternative to naturalism). This kind of impersonal supernaturalism may really only be an extension of naturalism, but even if it is not, such atheists have no rational grounds for criticising anyone with a religious belief.