Warning: The following post is of a somewhat existential nature.
In friendly conversation, I often like to jestfully throw out a certain casual challenge to others' declarative statements. For example:
I think you get the idea.
But how can someone actually PROVE something? Can it be done? Is there any statement that all humans can agree is a true, provable idea?
Think of an idea. Anything at all.
Is it true? Can you prove it? Even with all the evidence you could gather in a lifetime, is there a possibility that someone out there exists who will still disagree with your statement?
In mathematics, we prove things by logically building on fundamental principles that both parties choose to accept as truth; e.g., 1=1, 1+1=2, 1+2=2+1, and so forth.
But what if we cannot agree on the fundamentals? In areas such as Politics and Religion, it is often possible for equally smart, rational people to vehemently disagree. Most often, such disagreements occur because people are basing their ideas on different assumptions.
In such cases (read: in most cases), we must assess an argument based on its logical goodness. An argument can be classified as
- Flawed: The conclusions do not follow from the assumptions
- Valid: The conclusions do follow from the assumptions
- Cogent: The argument is valid and convincing; it induces someone to believe in the conclusions.
Again, rational people can present equally valid arguments for conflicting ideas. Whether an argument is convincing, however, depends on the person that is receiving the argument. In this way, if we disagree on fundamental assumptions it is impossible to say which of any two valid arguments are more correct.
In science, we never talk about proving any theories to be true. The best we can manage is to consistently fail to reject an idea, with the understanding that future revelations may completely change things down the road.
The question then becomes less about what is true and what is untrue, and more about the nature of belief. Why do we choose to believe the things that we do? Why do some assumptions resonate with us more than others? And that will have to be the topic of another post.