What do you believe to be true, but cannot prove?

The question was asked first on LinkedIn where other answers can be found. My answer was:

“Dear Guy, Very important question for all of us. While most of the other answers are aimed at answering the main question, i.e. what do we believe to be true even though we cannot prove it, please permit me to take a run at (A) the very notion of what we believe to be proof and what we may mean by it, (B) how proof is related to truth, and (C) what is the best way to determine what is true via a way of proving something using all of the forms of proof available.

(A) There are many kinds of proof. But, given your mathematical interests and such a theoretical question, I will assume that you are not interested in matters of proof involving liquor, for example. Let me suggest then three key types of proof: (1) mathematical proof; (2) scientific demonstration; and (3) commonsenical proof found in the laws of evidence used in courtrooms.

Each type of proof is founded on certain accepted starting points, usually assumptions or axioms, even beliefs.

Thus mathematical proof believes in the powers and scope of reason. It is therefore more idealistic and hypothetical. Scientific demonstration on the other hand believes in the powers and scope of sensory perception. It is therefore more materialistic and fact-bound. The law of evidence believes in both hypotheses and facts, but most often tests the credibility of the witness observer. It is therefore more realistic and fallacy-adverse.

I have written several blogs about counterfeit arguments. See, for example: "When you contend with others about judgments based on facts and reasons, what counterfeit arguments have you run into?"

(B) These differences in kinds and approaches to truth rely on different aproaches to how we know what we know and what we know when we claim to do so. In philosophy, it is called the study of epistemology. We reach the study of truth by what we know as a result of our approach to epistemolgy. But at bottom of every epistemology is again a starting point that closely resembles what everyone would otherwise recognize as a belief.

(C) Given this situation and your question about truth, arrived at without "proof," brings us to the issue of "How do you determine the truth?" I have written a blog on this as well as suggested that the source of the key insight that opens the door to the most satisfying proofs. See my blog: "Greatest invention/theory of all time and why?"

With this key in place, I have recommended a formal approach to "proof" in our time, based on what can be learned from the past. Please see my blog "DISPUTATION: Is disputation the best way to focus participants in change management? (Disputation)". I did this after writing two other related blogs, found here on LinkedIn as well, entitled: "Are efforts to manage change effectively limited by where the truth that lies in the plurality of the world's organized and institutional religions?" and "RELIGION: What's So Great About Christianity? (Disputation)."

Hope this adds to the discussion.

Thanks again for the question."

What do you think?

Please include your comment here or contact me to discuss.

Thanks.

John Darrouzet