Can a godless universe explain logic?

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December 14, 2015 by allistairg

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.

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