Heavy lifting here but a fun lift. I've excerpted only part of the Gödel discussion.
Can God Be Proved Mathematically?
Who would have thought about God as an apt topic for an essay about mathematics? Don’t worry, the following discussion is still solidly grounded within an intelligible scientific framework....
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Has mathematics now finally disproved the claims of all atheists? As you probably already suspect, it has not. Gödel was indeed able to prove that the existence of something, which he defined as divine, necessarily follows from certain assumptions. But whether these assumptions are justified can be called into doubt.
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From a mathematical point of view, however, these thought experiments became really serious only through Gödel’s efforts. This is not too surprising: The scientist had already turned the subject on its head at the age of 25 by showing that mathematics always contains true statements that cannot be proved. In doing so, he made use of logic. This same logic also enabled him to prove the existence of God. Take a look at these 12 steps made up of a set of axioms (Ax), theorems (Th) and definitions (Df).
It’s true that by means of the definitions and axioms, one can describe the set P mathematically:
As it turns out, Gödel’s logical inferences are all correct—even computers have been able to prove that. Nevertheless, these inferences have also drawn criticism. Besides the axioms, which of course can be questioned (why should a world be divisible into “good” and “evil”?), Gödel does not give more details about what a positive property is
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For example, as logicians have shown, it is possible to construct cases where, by Gödel’s definition, there are more than 700 divine entities that differ in essence.
...
This does not settle the final question of the existence of one (or more) divine beings. Whether mathematics is really the right way to answer this question is itself questionable—even if thinking about it is quite exciting.
...
Can God Be Proved Mathematically?
Who would have thought about God as an apt topic for an essay about mathematics? Don’t worry, the following discussion is still solidly grounded within an intelligible scientific framework....
...
Has mathematics now finally disproved the claims of all atheists? As you probably already suspect, it has not. Gödel was indeed able to prove that the existence of something, which he defined as divine, necessarily follows from certain assumptions. But whether these assumptions are justified can be called into doubt.
...
From a mathematical point of view, however, these thought experiments became really serious only through Gödel’s efforts. This is not too surprising: The scientist had already turned the subject on its head at the age of 25 by showing that mathematics always contains true statements that cannot be proved. In doing so, he made use of logic. This same logic also enabled him to prove the existence of God. Take a look at these 12 steps made up of a set of axioms (Ax), theorems (Th) and definitions (Df).
It’s true that by means of the definitions and axioms, one can describe the set P mathematically:
- If a property belongs to the set, its negation is not included. The set is self-contained.
- The fact that the essence of the set has only the characteristics of the set is itself an element of the set. The set always has the same elements—independent of the situation. In this case, the situation is the mathematical model in which the set is contained.
- Existence is part of the set.
- If φ is part of the set, then the property of having φ as the essence of the set is also contained in the set.
As it turns out, Gödel’s logical inferences are all correct—even computers have been able to prove that. Nevertheless, these inferences have also drawn criticism. Besides the axioms, which of course can be questioned (why should a world be divisible into “good” and “evil”?), Gödel does not give more details about what a positive property is
...
For example, as logicians have shown, it is possible to construct cases where, by Gödel’s definition, there are more than 700 divine entities that differ in essence.
...
This does not settle the final question of the existence of one (or more) divine beings. Whether mathematics is really the right way to answer this question is itself questionable—even if thinking about it is quite exciting.
...