"Present your case, says the Lord; bring forward your arguments, says the King of Jacob." (Is 41:21)In the last post, we considered what a proof isn't. Our current goal is still to comprehend the term "proof" and distinguish between types of proofs. This is another of our foundational terms -- another brick in the beginning of the wall:
Going back to dictionary.com, a proof is "evidence sufficient to establish a thing as true..." One way to establish a thing as true is to establish it as certain. Let's start with that.
1. Some things we accept as true because of empirical (observed, experienced) evidence. I don't have to take anyone's word that water boils at sea level at 212°F. I can try it out, and I can have other people try it out with the same result.
2. Some things we accept as true because of logical (deductive) evidence. The premises are true and necessarily entail the conclusion. The conclusion is inescapable, then. The best known example is: "Socrates is a man. All men are mortal. Therefore, Socrates is mortal." If I agree with the two premises, the conclusion is inescapable. I don't need to go around testing people's mortality (your welcome) or take someone's word for it that Socrates died. He must have because of the impeccable logic.
3. Some things we accept as true because of internal covert knowledge. I know my wife loves me – not because of any test that can be performed on her, nor because of how many people tell me so. Even if she's mad at me (not that that ever happens) and not showing it, I know she loves me. Similarly, I know what I am thinking with certainty. It cannot be tested and retested, nor can it be corroborated by other people, but it is still certain.
In these cases we have (or can have, if we want) personal experience of the proof. We can see the truth with our own eyes or encounter it in our own mind.
So, what do we get out of this?
- Proof is sufficient evidence for belief.
- That evidence can come directly from seeing and testing directly, logical thinking, or introspection - depending on what we're looking for evidence of.
Are there other sources of evidence beside those three? Next time, we'll look at the seemingly-contradictory idea of a probable proof.
proof. Dictionary.com. Dictionary.com Unabridged. Random House, Inc. http://dictionary.reference.com/browse/proof (accessed: November 24, 2013).