There comes a time in most games of chess (those not doomed to end in a draw) where one king can no longer evade the opposing forces and stands checkmated. This position can be expressed with mathematical precision and is undeniable for anyone who accepts the current rules of the game.
Nothing quite so clear-cut exists when it comes to logical arguments, but there can be cases where it comes close. For instance, if there are two theories about what is causing some effect, testing can be used to develop strong confidence about which cause explains it. If my computer will not turn on and the problem could be either that the hard drive has been removed or there is no electricity, I can undertake trials to determine the cause. I can check that the power cord is plugged in. I can test the socket by putting something else into it. I can open up the computer case. I can try booting from a DVD or a network drive.
Similarly, it is possible to forcefully rebut a logical argument on the basis of logic itself. This mostly applies to very narrow computer-science-type problems, but it is still worth recognizing. For instance, we can evaluate self-contained logical statements like: “Object X is either part of Group A or Group B. It is part of Group A. Therefore, it is not part of Group B.”
More often, we combine logic with factual claims about the world. The patient cannot be having an allergic reaction to the antibiotics, because they have not been administered yet. My keys cannot be in my apartment, because they are here in my hand. The atomic bomb cannot detonate, because the plutonium pit has been removed.
To me, it seems that there are some large and important questions where we have basically achieved checkmate, when it comes to how certain we can be that one perspective is correct and another is not. For example, the claim that the universe is 6,000 years old is demonstrably false. The case is closed. We know the universe to be billions of years old. The same goes for the fact that evolution takes place.
Less certain, but still very close to checkmate, are positions including: “The Earth’s climate is being altered by human activities.”.
Then there are positions that are very certain, but which involve less concrete claims, such as: “There is no evidence the universe was created by a sentient being.” and “There is no evidence of any kind of divine being that cares about human behaviour.”. The only real rebuttal to these arguments is that people have strong feelings or intuitions that contradict them, but feelings are neither logic nor evidence.
Ultimately, it is important to keep proving and re-proving claims that we believe to be true. Oftentimes, we find that we were basically right but that there was more complexity than we expected. Other times, we discover that we have been more comprehensively wrong. Awareness of our own fallibility is a critical part of the advancement of knowledge.
At the same time, we should not allow ourselves to be paralyzed with uncertainty, especially when it is those last lingering wisps of uncertainty that remain alive only because people have strong feelings about a subject. Every human decision involves dealing with some level of uncertainty, and yet it is demonstrably the case that it is better for people to act once they have done their due diligence than it is for them to dither forever while evaluating evidence and arguments. When one is in checkmate, the only sensible thing to do is to accept it and start thinking about what the lessons of the game have been. It is frustrating for me – then – that there are still vast numbers of people who believe that the planet is 6,000 years old, all the world’s land animals were once on one big boat, every organism was created in its current form and doesn’t change, or that all the climate change we are observing is caused by natural forces. How can we continue to improve humanity’s understanding of the world when there are people who will never accept that they have been checkmated, no matter how many times you point out the pieces blocking every possible avenue of escape for their king?