Truth, proof, and evidence
We encounter all manner of statements, beliefs, facts, and claims which we assert are either true or not true, or might be true or might be false. If a statement is true, how do we know it. Can we prove that it is true or false? Do we have evidence that it is true or false. What does it mean to say that we have proof or that we have evidence?
Truth is our ultimate objective as seekers of knowledge and wisdom. Whether we ever achieve truth is usually a matter of debate.
A proof or our ability to prove a statement, belief, fact, conclusion, assertion, or claim is some collection of knowledge and artifacts which when viewed by an independent, objective, competent observer with the necessary expertise would lead that observer to conclude that the claim is "true beyond all doubt." That's quite a tall order. In fact, except in pure mathematics or particular bureaucratic institutions, it is essentially an impossible objective. In truth, the best we can usually hope for is to approximate a proof of a claim. Each of us and each of our social and political institutions has a subjective right to define our own criteria for what standards we wish to accept for proof of any particular claim. Different individuals and institutions can differ on what proofs they accept as fact.
Evidence is basically anything, such as an observation, measurement, calculation, document, physical object, reasoning, knowledge, etc. that supports a claim, or, alternatively, anything that undermines a claim. Generally, evidence by itself does not necessarily prove (or disprove) a claim, but can help to guide us in the direction of strengthening or weakening our confidence in a claim. If we collect enough evidence of enough strength, we may in fact eventually be able to confidently assert that we are able to prove or disprove a claim beyond our own doubts. Maybe, but not necessarily. Evidence does not per se have to be able to prove or disprove a claim for us to assert that it supports or undermines a claim. Evidence does not have to be strong and convincing; it may merely be weak and flimsy, or maybe even irrelevant. The only real requirement is that evidence is offered to support or dispute a claim.
We could use the analogy of a destination and a journey to that destination. We seek to arrive at a proof. Evidence is the collection of individual steps along the way to that destination. We can, to some degree, measure our progress on our journey. At some point we may be able to confidently conclude that we have in fact arrived at the destination, that truth has been obtained.
As a final note, even an accepted proof may not necessarily be the definitive achievement of truth. People may in fact justifiably believe in a proof, but there may be a flaw in their assumptions, observations, measurements, analysis, calculations, or reasoning. People may not initially be aware of any such flaws, but as our minds, knowledge, and technology advance, flaws may become apparent. Then, suddenly, our knowledge and its proof may be overturned. Much of the evidence itself may still be just as valid as before, but our interpretation, integration, and induction of conclusions based on that evidence may be different.
In short, constantly seek evidence that supports or undermines claims and be careful to leap too quickly to conclusions and acceptance of proof, and always be ready for the sudden appearance of new evidence or new ways of thinking about and working with existing evidence that may undermine an existing proof or in fact support a new proof.