There's a difference between an absence of evidence, vs. evidence of absence.

A medical test is performed on a person and comes out positive for cancer. The doctor presents this diagnosis and prescribes medical treatment. After the treatment is completed, the test is run again. This time the test comes out negative, the test offers an absence of evidence for cancer.

However, after the test results the doctor will sometimes say: "You are cancer free!" That declaration suggests the test is evidence for an absence of cancer. It is not. The tests are an absence of evidence for cancer. What?

Imagine a large room. You illuminate part of the room with a flashlight (the cancer test). The first time you turn on the flashlight, you see cancer. So you do the cancer treatment, then turn on the flashlight (cancer test) again. This time you don't see cancer. Does that mean the room doesn't contain ANY cancer? No, it only means you can't see it with your flashlight. Yet the doctor, with his "You're cancer free!" statement interprets the results as if the entire room (patient's entire body) is cancer free.

But it's deeper than that. Actually, you can NEVER prove something does not exist, right? As with swans, for centuries, Europeans thought all swans were white. It took on sighting of a black swan to refute that "fact." You can never prove all swans are white. You can also never prove your body is entirely disease free.

The Black Swan: The Impact of the Highly Improbable by Nassim Nicholas Taleb

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