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Is there anything or phenomenon in the universe that scientists think or deduce that it exists but cannot prove it scientifically?

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A snake can (try to) eat anything, but not itself. — personal reinterpretating the Genesis[1]

An eye can (try to) see anything, but not itself. Fire can't burn itself. A knife can't cut itself. — Zen sayings

Knowledge can (try to) know everything, but not itself. — personal

Mathematics can (try to) prove everything, but not itself. — Gödel[2]

“true” and “real” are one and the same. If something is true then it's real, and if it's real then it's true. Nothing true has no reality, and nothing real isn't true. — personal, and Jed McKenna[3]

You can't know yourself. There can't be knowledge without a knower and there can't be a knower without knowledge, therefore if knowledge and the knower are inseparable, they are the two ends of one single entity, and so this entity is the only thing that is real! So it's where the self is. — Alan Watts[4]

If the universe had a border, because borders separate two entities, then there would exist something bigger than it, which would invalidate the definition, if by “universe” we mean “all that there is”, therefore the universe can't have a border, and that's how having a size is a property of a contained thing, and not being able to have a size is a property of a container (let's call the container “a dimension”), that's equally how being a container invalidates its own existence (dimensions don't exist because they don't exist “somewhere”), and only being contained validates its existence (something can only exist in a dimension), therefore the universe and dimensions don't exist, so that we can't do any science on them. — personal

Footnotes

[1] Serpents in the Bible - Wikipedia

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