Quote from Teleologist:
Show me a reference that says inference is based on overwhelming evidence. Show me a reference that says inference is the same as proof. If you look up synonyms for inference you won't find proof listed. Nor will you find inference listed as a synonym for proof.
What, you didn't even read z10's post?
Here's the link again (copied from z10):
http://faculty.ncwc.edu/toconnor/308/308lect01.htm
A PRIMER ON INFERENCE
"In the end, there are usually more correlates than causes, and one cannot control everything.
Causality is always an inference. This particular type of relationship must be inferred from the observed information, and then related back to known information. Inference demonstrates itself in hypothesizing, sampling, designing, and interpreting. It is the basis for scientific generalization, especially those having to do with the explanation of causality. It is
never the final proof, but because final proof is itself never possible, inference is the best substitute. It enables ways to advance science, debunk mistaken beliefs, and is always mindful of its own limitations. Certain safeguards are built into the process which protect against unwarranted generalizations. The process of generalizing in an explicit and scientific manner is inference." (emphasis in the original text)
Repeat: "because final proof is itself never possible, inference is the best substitute."
From the part that discusses sampling (not quoted here), you can understand why the evidence needs to be overwhelming. You want to minimize spurious variables.