These last several postings are exactly why i quit taking Philosophy Courses.
It's like modern art. There was once a time when Art was becoming increasingly exciting and realistic ... and then color photography was invented.
And all of a sudden, millions of budding artists decided they needed to try their hand at representing non-reality. And the dead body was found right there ... with a circling "eagle" above, showing the world its location.
Since there are many standards of Evidence, a "proof" that meets a pre-stated standard of evidence does not preclude the possibility that the proof is still in error.
a. Audit Samples - These are statistical short-cuts used by auditors to roughly approximate the nature of the population being sampled.
b. Preponderance of Evidence - This is a courtroom benchmark which requires merely to have more evidence than the opposing argument, with additional options including which side does "a tie" favor, or to adjust the consequences in the event of a tie.
c. Beyond a Reasonable Doubt - This is the usual standard for capital trials where the accused could be executed if found guiltty.
d. The Reasonable Man Standard - where evidence doesn't have to be "beyond a reasonable doubt", but what most "reasonable people" would accept as sufficient evidence.
e. Circumstantial Evidence - the standard where nobody has actually witnessed who the perpetrator was, but the circumstances of the evidence are such that only one person could have committed the crime (etc). While most trial lawyers believe Circumstantial Evidence is actually better than Eye-Witness evidence, some critics consider Circumstantial Evidence (or some uses of it) to be no more than a variant of the "Reasonable Man Standard".
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The distinctions made (or not made) in the posts above make the assumption that if something "is proved", there is no possibility of being in error. This seems likely only when we are discussing "a priori" proofs.
I can have a "proof" and still "believe". And think how many people are offered valid "proofs" and still do not believe !!!
oh, and @T_aquaticus, when it comes to beliefs, a Believer only comes under obligation to provide adequate evidence if he proposes that you should agree with his belief.