Question
What is the difference between evidence and proof?
Evidence supports or weakens a claim. Proof is a stronger standard where the evidence is sufficient to justify accepting the claim as established for a given purpose.
Answer
Evidence is information that bears on whether a claim is true. It may include observation, documents, testimony, experiments, physical traces, patterns, statistics, expert analysis or logical argument.
Proof is a stronger idea. It means the evidence is enough to justify accepting the claim as established, at least within a particular standard. The standard may differ between mathematics, science, law, history and ordinary life.
This distinction matters because people often treat a small piece of evidence as if it were proof. A rumour may be evidence that someone said something, but not proof that the claim is true. A personal experience may be evidence that something was experienced, but not proof of the interpretation placed upon it.
Truth By Reason should use evidence carefully. A claim may have weak evidence, strong evidence, conflicting evidence or no good evidence. The strength of belief should follow the strength of evidence.
Evidence
Different fields use different standards of proof. Mathematics uses formal proof. Science uses evidence, testing and revision. Courts use standards such as balance of probabilities or beyond reasonable doubt.
In ordinary reasoning, evidence should be weighed by reliability, relevance, independence and explanatory power.
Alternative views
Some people use proof to mean absolute certainty. In many real-world questions, absolute certainty is unavailable, but strong evidence can still justify high confidence.