Proof is, by definition, being able to determine something with absolute certainty. Things are proven if their existence is self-evident. For example, it is proven that consciousness exists. Things are proven false if they can be shown to be contradictory. For example, it is proven that no circular squares exist, because circles and squares have properties that are mutually exclusive.
Conservative view on proofEdit
There really is no such thing as "liberal proof" because liberals are too wishy-washy to take a firm stand on anything. All real proof is conservative.
Conservative proof consists of insisting that the Bible agrees with your point of view. It may require some intellectual gymnastics, as when proving that there were dinosaurs on Noah's Ark. This can be accomplished by pointing out that there were two of every kind of animal on the ark, and that the Bible doesn't actually mention dinosaurs because the word was not coined until after the Bible was written. One can prove that the Speed of light was a great deal faster at one time because the Bible says the Earth is only 6,000 or so years old, so the light from distant Stars and Galaxies must have traveled much faster at one time to have reached us so soon, see Starlight problem.
Alternatively, conservatives can also prove a point by pointing out that this is what people have always believed so it must be true. Hard to beat that Logic.
Liberals are more likely to find some "Grey areas" to talk about, or whine that most important problems are so complex that there can be no real proof of the matter. Liberals are more likely to fall back on accepting the consensus of the scientific community, for example, that the Universe is Billions of years old. They are willing to accept a mass of supporting data as an indication that something is "true" rather than insist on "proof." This is known in conservative circles as Atheism.