What Is God According To Science – Who would have thought that God would be a suitable topic for an essay on mathematics? Don’t worry, the discussion below is still firmly grounded in an understandable scientific framework. But the question whether God can be proved mathematically is a thorny one. In fact, over the centuries, many mathematicians have repeatedly tried to prove the existence of the divine. They range from Blaise Pascal and René Descartes (in the 17th century) to Gottfried Wilhelm Leibniz (in the 18th century) to Kurt Gödel (in the 20th century), whose writings on the subject were only published in 1987. And perhaps most surprising of all: In a pre-press study first published in 2013, an algorithmic proof wizard tested Gödel’s chain of logic—and found it to be undoubtedly correct. Has mathematics finally disproved all atheist claims?
As you probably already suspected, it is not. Godel was able to prove its existence
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, which he defines as divine, certainly follows certain assumptions. But it may be doubted whether these assumptions are justified. For example, if I assume that all cats are tricolor, and I know that tricolor cats are almost always female, then I can conclude: Almost all cats are female. Even if logical thinking is correct, it is obviously not valid. Because the belief that all cats are tricolor is wrong. If someone makes a statement about something that can be observed in our environment, such as cats, it can be verified by scientific research. But when it comes to proof of divine existence, things get a little more complicated.
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While Leibniz, Descartes, and Gödel relied on an ontological proof of God, in which they logically deduced the existence of a divine being from its mere possibility, Pascal (1623–1662) took a somewhat different approach: he analyzed the problem. From this point of view what can be considered today as game theory and developed the so-called Pascal’s Wager.
To do this, he considered two possibilities. First, God exists. Second, God does not exist. He then examined the consequences of believing or not believing in God after death. If there is a divine being and one believes in him, he will go to heaven; Otherwise you will go to hell. On the other hand, if there is no God, nothing else happens – whether you are religious or not. The best strategy, Pascal claims, is faith in God. At best, you end up in heaven; In the worst case scenario, nothing happens. On the other hand, if you don’t believe, the worst you can do is go to hell.
Pascal’s thoughts are understandable – but they relate to theological situations and do not constitute proof of the existence of a superior being. They simply say that one should approach faith based on opportunism.
Ontological approaches dealing with the nature of existence are more persuasive, even if atheists are unlikely to change their minds. The theologian and philosopher Anselm of Canterbury (1033-1109) proposed his ideas at the beginning of the last millennium. He described God as beyond whom nothing superior can be conceived. But if God does not exist, then something greater can be imagined: that is, a being beyond which nothing can be imagined. But like God, this entity also exists and exhibits the attributes of supreme greatness. This, of course, is nonsense: nothing can be greater than the greatest thing one can imagine. Therefore, the assumption that God does not exist must be wrong.
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It took several centuries for this idea to be revisited—except for Descartes (1596–1650). Apparently unaware of Anselm’s writings, he provided an almost identical argument for the divine existence of the Absolute Being. Leibniz (1646–1716) took up the task a few decades later and found a flaw: Descartes, he argued, had not shown that the “perfect properties” of certain entities, from the triangle to God, were consistent. Leibniz further argued that perfection cannot be properly investigated. Therefore, it can never be denied that the absolute attributes are united in one being. Therefore, the possibility of God’s existence must be real. So, based on the arguments of Anselm and Descartes, it is necessary that God exists.
However, from a mathematical point of view, it was only because of Gödel’s efforts that these thought experiments became truly serious. This is not very surprising: the scientist already showed at the age of 25 that in mathematics there are always true statements that cannot be proved. In doing so, he used logic. This reasoning allowed him to prove the existence of God. Check out these 12 steps made up of a set of axioms (Ax), theorems (Th) and definitions (Df).
At first glance they seem confusing, but one can go through them step by step to follow Gödel’s thinking. It begins with an axiom—a presupposition, in other words: if φ has property P and φ always follows from ψ, then ψ also has property P . For simplicity, we can assume that P stands for “positive.” For example: If a fruit is delicious, has positive attributes, it is also fun to eat. So enjoying eating is also a positive trait.
The second axiom sets the framework for P . If the opposite of something is positive, then that “something” must be negative. Therefore, Gödel divided the world into black and white: something is good or bad. For example, if health is good, disease must necessarily be bad.
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With these two premises, Gödel can derive his first theorem: if φ is a positive property, then it is possible that x exists with the property φ. That is, it is possible for positive things to exist.
Mathematicians now turn for the first time to the definition of divine existence: x is divine if it possesses all the positive properties of φ. The second axiom ensures that God defined in this way cannot have negative characteristics (otherwise a contradiction would result).
The third axiom states that divinity is a positive characteristic. This matter is not disputed because the deity combines all the positive characteristics.
The second theorem now becomes a bit more concrete: by combining the third axiom (divinity is positive) and the first theorem (it is possible for something positive to exist), there can be an entity x that is divine.
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Gödel’s goal now is to show in the next steps that God must exist within a definitely set framework. To this end, he introduces in the second definition the “essence” φ of the object x, the characteristic property that determines all other characteristics. An illustrative example is “Puppy, if something has this attribute, it must be cute, fluffy, and clumsy.
The fourth axiom doesn’t seem very exciting at first. It simply states that if something is positive, it is always positive – no matter the time, situation or place. For example, whether it’s day or night in Heidelberg, Germany or Buenos Aires, being a puppy and having good taste is always a positive.
Gödel can now formulate a third theorem: if x is divine, then divinity is its essential property. This makes sense because if something is divine, then it has all the positive properties – and therefore the properties of x are fixed.
The next step deals with the existence of a specific entity. If somewhere at least one organism y has the property φ, which is a necessary property of x, then x also exists. That is, if something is like a puppy, then puppies must exist.
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According to the fifth axiom, existence is a positive property. I think most people would agree with this.
From this we can now conclude that God exists because this entity has every positive attribute and existence is positive.
As it turns out, Gödel’s logical conclusions are correct – even computers were able to prove them. However, these findings are also being criticized. Apart from the axioms, which can of course be questioned (why would the world be divided into “good” and “bad”?), Gödel does not elaborate on what positive properties mean.
But all this does not ensure that these sets are unique. There may be multiple collections that meet the requirements. For example, as logicians have shown, it is possible to make the case that, according to Gödel’s definition, there are more than 700 divine entities that differ in essence.
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This does not ultimately resolve the question of the existence of one (or more) divine beings. The question is whether mathematics is really the right way to answer this question – even if it is exciting to think about.
. She mainly covers mathematics and computer science and writes the column Fabulous World of Mathematics. Bischoff studied physics at the Technical University of Darmstadt in Germany and then worked as a researcher at the Johannes Gutenberg University in Mainz, Germany.
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