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Can you, please, give me an example of a nonconstructive mathematical concept that's close to what you linked?

• jessriedel 10y ago
  You said > Suppose God doesn't exist. Then ... middle, middle, middle,...Contradiction. Thus by "excluded middle", God does exist. I have never seen theology do that. Here is a summary of Anselm's argument for the existence of God: > 1. It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined). > 2. God exists as an idea in the mind. > 3. A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind. > 4. Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist). > 5. But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.) > 6. Therefore, God exists. (Emphasis mine.) https://en.wikipedia.org/wiki/Ontological_argument#Anselm https://en.wikipedia.org/wiki/Ontological_argument#Anselm But really, you don't even need something with such a close 1-to-1 mapping for fpoling's comment to be reasonable. Consider the Banach–Tarski paradox. In both cases, you're talking about "something that cannot be experimentally observable or constructable" -- a perfect being, or a certain disjoint decomposition of the 3-ball -- "and then apply logic".