The terms "(epistemological) possibility," "certainty," and "probability" all characterize one's state of knowledge.
- A positive hypothesis is possible if there is some
evidence (within one's context of knowledge) for the
proposition, while no evidence contradicts it. To assert the
possibility of something is to make a positive claim,
requiring supporting evidence. (If we took the opposite view,
saying that "anything is possible," then the term "possible"
would no longer pertain to any differences of kind among
hypotheses—and hence would be cognitively useless.) If
the hypothesis is not possible, we say it is
impossible.
- A hypothesis is probable if the preponderance of
evidence supports it and no evidence contradicts it.
- It is certain if the evidence supports it conclusively.
Exactly when this point of certainty is reached is a complex
problem in logic.
The above concepts are all dependent on one's context of knowledge. Mathematicians understand well that a hypothesis can become more or less probable as more information is acquired. The terms "possibility," "certainty," and even "knowledge" must likewise be interpreted in a given context. For if these concepts are to have any meaning relevant to our experience, they must apply to humans, who are finite beings whose judgments are always made in a context of limited awareness. 
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