No, you misunderstand. I am such a witness, but my testimony, like most similar testimonies, while they are no secret and public, was not verified publicly, but privately. There are however, written, historic testimonies that were verified publicly...they are recorded in the bible.
But what you are purposing is unreasonable. Even in a court of law, one cannot actually reconstruct what they have witnessed...just so you as the jury of their peers can have the same verification. Be reasonable.
The problem is that the term "reasonable" introduces a subjective (and individual) set of personal choices. It also highlights the difference between a purely empirical standard of evidence (as atheists apply to the topic of God and nowhere else) vs. a "scientifically reasonable" standard of evidence.
Evidence if it's empirical in nature is fantastic, optimal in fact. On the other hand "science" has never technically been limited to studying, exploring, or testing 100 percent empirical models. There's even a certain amount of 'faith' required to study concepts like quantum gravity theory, since no carrier particle called a graviton has ever been observed in the lab. Likewise M-theory is requires 'faith' in 7 additional dimensions of spacetime, none of which have been observed in a lab. Scientists still study, explore and devote their entire professional lives to such concepts.
"Reasonable" in the context of "science" has never actually been limited to empirically demonstrated cause/effect relationships. Empirically demonstrated cause/effect relationships are ideal when possible, but a full 95 percent of mainstream 'scientific' cosmology theory remains devoid of empirical cause/effect justification in a lab.
Atheists tend to only apply a 100 percent empirical standard of cause/effect justification when it comes to the topic of God, whereas they don't apply such limitations in the realm of particle physics or cosmology. That's not even "reasonable".
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