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Is God Irish?

Roger McCann maps the limits of theology.

“Logic, like whiskey, loses its beneficial effect when taken in too large quantities.” Lord Dunsany (Edward Plunkett)

Philosophers, clerics, atheists, and assorted others have attempted to prove the existence or non-existence of God for thousands of years. This articles considers the use of logic for this purpose, centering on two questions ‘Can ‘God’ be defined in a logically coherent way?’ and ‘Is it possible to decide logically whether God exists?’ I do not attempt to answer these questions; rather, I will describe some logical difficulties inherent in attempting to answer them.

Unfortunately, many arguments concerning the existence of God are made with the intent of justifying an already-held opinion. I hope the reader will assess my thoughts without the certainty of a closed mind, and in doing so become (or remain) an exception to Mark Twain’s sarcasm: “In religion and politics people’s beliefs and convictions are in almost every case gotten at second-hand, and without examination, from authorities who have not themselves examined the questions at issue but have taken them at second-hand from other non-examiners, whose opinions about them were not worth a brass farthing.” (Autobiography of Mark Twain).

The Roots of Reason

The application of logic to God has roots in rationalism, a philosophy that sees reason (here a synonym for logic) as a superior source of knowledge to experience. Rationalism was embedded in Western philosophy through the works of Plato (424-348 B.C.E.), René Descartes (1596-1650), Baruch Spinoza (1632-1677), Gottfried Leibniz (1646-1716), and Immanuel Kant (1724-1804), among others. Some proponents of rationalism, such as Spinoza and Leibniz, argued that one can deduce all possible knowledge from a suitable set of axioms, analogous to the axioms of geometry. Others, such as Descartes and Kant, argued that both reason and experience are necessary for knowledge.

One prominent rationalist argument for the existence of God, the ontological argument, was first proposed around 1078, and modified by the Italian Benedictine monk, Anselm of Bec (1033-1109). Later the argument was ‘borrowed’ by Descartes. (For more info, see The Proof of God: The Debate That Shaped Modern Belief, Larry Witham, 2008.) While Anselm’s argument has been accepted by some philosophers, it has been rejected by others, including William of Ockham (1287-1347), of ‘Ockham’s razor’ fame, and Kant and Schopenhauer (1788-1860). One common criticism from its detractors was that reason is not applicable to questions about God, or, as we might now say, questions of God’s existence are logically undecidable.

In spite of the wide applicability of reason to everyday problems, rationalism is not the only approach to knowledge, especially in Eastern religions. For example, in Zen Buddhism, the primary purpose of meditating on a koan (a paradoxical question, such as ‘What is the sound of one hand clapping?’) is to exhaust the rational intellect, thereby leaving the mind open to more intuitive responses. Similarly, for some the question ‘Is God Irish?’ is so absurd that, like a Zen koan, it cannot be answered with rational thinking. Others have no difficulty in answering ‘Is God Irish?’: for those who are overly proud of their Irish heritage, the answer is a definite ‘Yes’ because ‘God is Irish’ is a tautology; for others, the answer is a definite ‘No’. How can God be Irish when He (or She or It) is obviously Jewish, Italian, American, or whatever is the heritage of the responder? The answer is also ‘No’ for those who believe there is no God. For agnostics, who believe it is impossible to know whether there is a God, the question is nonsense. Still others may find the question blasphemous. Whatever your response to this question, I challenge you to prove it logically. No matter how good your proof, there are two major reasons many will not accept its validity: there is ambiguity in the meaning of ‘proof’, and there is no agreed-upon definition of God. For one example of the former problem, some view the rising of the sun as proof that God exists, while others do not. In this article, ‘proof’ will refer to a valid logical (or rationalist) argument, such as those found in mathematical proofs.

Who Is This God Person Anyway?

Arguments both for and against the existence of God have a common inherent defect: there is an implicit assumption of an agreed-upon definition of God, although personal experience indicates that this is far from the case.

Defining God is a secular endeavor. Religions tend not to bother with such formalities. Defining God replaces mystery and holiness with limitations and restrictions. This has been recognized in many civilizations since antiquity. Amun, ‘the hidden one’, became one of the primary gods of ancient Egypt, and the mysterious nature of God in Judaism is evidenced by the Jewish prohibition on pronouncing God’s name, and by God’s enigmatic response to Moses about who He is: “I Am that I Am” (Exodus 3:14). Islamic tradition has 99 names of Allah, each describing an attribute of Allah. One of these names is ‘The Hidden’ (Al-Batin). The hidden aspect of God in these traditions acknowledges the impossibility of defining God. Not defining God is a widespread tradition that maintains mystery and holiness with the possibly unintended auxiliary benefit of avoiding logical inconsistencies and paradoxes. (The recognition that certain basic religious concepts are indefinable is not restricted to Western religions. For example, the Dao De Ching explicitly states that the Dao (Tao) is both indefinable and unknowable.)

Where there are definitions of God, these often use words attributing qualities that are without limits or are all-encompassing . For example, one definition of God is “A being conceived as the perfect, omnipotent, omniscient originator and ruler of the universe, the principal object of faith and worship in monotheistic religions.” (education.yahoo.com/reference/dictionary/entry/god) For many people ‘perfect’, ‘omnipotent’, ‘omniscient’, or similar all-inclusive words are part of their concept of God; but this is a source of problems when tackling God logically. Consider Bertrand Russell’s often-heard paradoxical question, ‘Can God make a rock so large that He cannot lift it?’ An answer of either ‘Yes’ or ‘No’ contradicts the idea of God’s omnipotence.

This paradox does not relate to the existence of God per se, but only to this particular definition of God. However, I suspect the inclusion of any absolute term, such as omnipotent or omniscient, in the definition of God, inevitably leads to similar paradoxes. If this is true, it is likely that this does not allow a logically-consistent (ie meaningful) definition of God in these terms. It would certainly place this God beyond logical consideration, as Kant and others claimed.

In any system of thought there are concepts, sometimes called ‘primitive notions’, which, like axioms, are formulated perhaps by appealing to intuition or to direct experience. If ‘God’ is a primitive notion, then the concept of God exists by assumption rather than by logical deduction. (The distinction between the concept of God and God per se is important. Accepting the concept of God does not imply the existence of God anymore than acknowledging the concept of Tolkien’s Ents implies the existence of anthropomorphic trees. Unfortunately the distinction is sometimes blurred, as in Anselm’s ontological argument, which in essence says, ‘Since I can conceive of a perfect God, a perfect God exists.’)

For the sake of argument let’s suppose that ‘God’ is a primitive notion. Such an entity is often partially described (but not fully defined) by listing some of its attributes, such as Islam’s 99 names of Allah. Religion is not alone in (partially) defining concepts by listing attributes. Ether and black holes are two such examples in science. The ether is a concept used in nineteenth-century physics that is defined by the attribute of being a medium that allows the propagation of light in space. A black hole is a region of space with the property that nothing, not even light, can escape from it. The non-existence of ether and the existence of black holes are now generally accepted, due to observations and arguments based on the Theory of Relativity. In fact, though there are at least four types of regions with the property that nothing can escape from it. This shows that a list of attributes might allow us to conclude that something does not exist, if there is nothing that has those attributes, but it cannot allow us to conclude that something exists: the best we can conclude is that something satisfies the listed attributes. The thing itself might have to be defined in more detail. Moreover, there may be more than one entity with the same attributes. Having more than one entity satisfy a list of attributes of God would be anathema for many people. This raises the question as to whether there is a list of attributes that implies a unique God, without using a tautology.

Logic & Limitations

However, the inability to define something precisely does not necessarily preclude deciding whether it exists, or even whether it is likely to exist. Consequently, it is reasonable to consider the statement ‘God exists’. This seems to be a straightforward proposition. Isn’t a simple statement, such as ‘God exists’, either true or false? Possibly most people think this is the case. Unfortunately, things are not so simple.

In 1931 the Austrian logician Kurt Gödel (1906-1978) proved his Incompleteness Theorem, which says that within any rationally-definable logical system, statements exist that are neither provable nor disprovable using the axioms of that system. The Incompleteness Theorem had immediate and profound implications in mathematics, logic, and philosophy. In particular, the Theorem had fatal implications for the school of rationalism that argued that all possible knowledge could be deduced from a basic set of self-evident principles.

Could ‘God exists.’ be one of Gödel’s logically-unprovable statements? The logical undecidability of ‘God exists’ would be compatible with the philosophies that claim God is beyond rational thought. (Gödel’s logical undecidability does not impinge on whether God exits per se, only on whether God’s existence can be determined using logic.) For many there is a compelling reason to want ‘God exists’ to be logically undecidable. Faith is fundamental in Judaism, Christianity, and Islam. If the existence of God could be logically proved (or disproved), faith would be meaningless.

For the sake of argument, let’s suppose ‘God exists’ is unprovable in a given logical system. Then ‘God exists’ or ‘God does not exist’ could be added to that system as an axiom without affecting any existing conclusions. So if evolution is a logical conclusion in a system in which ‘God exists’ is logically unprovable, then evolution is still a logical conclusion if we add ‘God exists’ as an axiom.

There are widely diverse axioms in commonly encountered systems of thought. Science and agnosticism do not include either ‘God exists’ or ‘God does not exist’ as axioms in their logic systems. Abrahamic religions include ‘God exists’ in their systems; atheists include ‘God does not exist’. It is essential to recognize that these differences arise from different axioms and that it is pointless to debate them on any other level. It is possible that Christians, Jews, Muslims, Buddhists, Hindus, Native Americans, Taoists, Sikhs, Jains, atheists, polytheists, agnostics, and others, all have logically-consistent views of reality based on their concepts of God. In order to determine logically which, if any, of these systems yields reality, we would need a logical system that incorporates all other logical systems so that we could judge the systems against each other. But this is precisely the type of comprehensiveness that leads to the sort of paradox Russell encountered with the definition of God. Consequently, there may be many logical systems containing different axioms related to God, none of which can be shown logically to be ‘more valid’ than the others.

Final Logic

It appears that trying to deal logically with God leads either to a concept that is so absolutist it can be paradoxical or to a statement that is undecidable by logic. This leads to yet another apparent paradox. Assuming God exists, God created humans with logical abilities, but apparently devised logic so that humans could not apply logic to God.

One interpretation of this is that God mocks humans by placing Itself beyond their logical abilities, thereby making ‘satirical’ one of God’s attributes. According to the Hebrew Bible, God created humans in God’s own image (Genesis 1:27). This causes me to wonder what group of humans is most satirical, and therefore most like God. The Irish spring to mind, for they have a long satirical tradition that lies at the core of much of their literature, naturally leading us to answer ‘Yes’ to the titular question, ‘Is God Irish?’

Of course, the logic leading to this conclusion is meant to be facetious. Nonetheless, it is as sound as other logic used to assess the existence of God. But it should be noted that the argument cheats – as do many God-related arguments – by referring to a portion of a religious scripture as though it were a logical axiom or logically-justified conclusion, which it is not, of course.

In summary, it is likely that attempting to establish the existence or non-existence of God rationally/logically is a fruitless endeavor, and that either viewpoint is ultimately a matter of faith, of what you decide to believe. This is in accord with the philosophies of Kant and others.

Originally my thoughts on the logical proofs of the existence of God ended here. Then I realized I could use Gödel’s ‘logical undecidability’ to argue that God, which I take to be a primitive concept with an unknowable aspect, is likely to exist. Admittedly my reasoning is highly personal and will be unconvincing to many. Nonetheless, it may give a reason to think to some, and amusement to others:

1.) For over a thousand years attempts have been made to establish the existence or non-existence of God logically. None have been successful. I conclude that ‘God exists’ is more likely to be logically undecidable than logically decidable.

2.) If God does not exist, I know of no reason why ‘God exists’ is more likely to be logically undecidable than logically decidable.

3.) However, if God does exist, then the ‘unknowable’ aspect of God would make ‘God exists’ more likely to be logically undecidable than logically decidable.

4.) So because ‘God exists’ is likely to be logically undecidable, I conclude that God is more likely to exist than to not exist.

Unfortunately this argument also applies equally well to any other primitive concept with an unknowable aspect – so if two of these primitive concepts are differing concepts of God, we must conclude that more than one God is likely to exist! This is especially troubling if both concepts include the idea of there being only one God. So what started as an argument for the likely existence of God has led to heresy for the Abrahamic religions, or perhaps a paradox. Once again logic has failed to yield a tenable conclusion about God – which is precisely what Kant and others argued would always happen.

The British physiologist J.B.S. Haldane (1892-1964) made what may be the most perceptive general observation ever made about the Universe: “Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose.” (Possible Worlds and Other Papers, p.286, 1927.) I have a similar suspicion about the existence of God: The existence of God is not only more unknowable than we suppose, but more unknowable than we can suppose.

© Roger McCann 2012

Roger McCann was a professor of mathematics for seventeen years, then spent fifteen years at the research lab of the ExxonMobil Corporation. He currently consults on the statistical assessment of pipeline corrosion.