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What does unprovable mean?

Looking for the meaning or definition of the word unprovable? Here's what it means.

Adjective
  1. That cannot be proved or verified by any test
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Examples
That some scientists confuse the unprovable with the nonexistent does not justify the deliberate attempt of IDists to substitute sophistry for science in our public schools.
He proved, to borrow from the course outline: There are true statements that are unprovable within the system.
Juries sometimes contain the teachers of some of the contestants, raising damaging, but unprovable, doubts about their impartiality.
Is this just another example of academics talking up unprovable dangers to draw attention to themselves?
Moreover, the whole point of Godel is that any first order system has true but unprovable statements.
The US and its allies need to focus on the strengths of their case rather than draw attention to flights of fancy or unprovable points.

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