Either true or false

To be, or not to be. That is the cliché. I haven’t even read Hamlet, which is where to be or not to be comes from. Apparently, the line is about suicide. It might have more interpretations. But on the surface, the statement is simple: either live or die. We are familiar with either/or phrases like this: have cake or eat it, my way or the highway, true or false. There are two states that Mister Hamlet is pondering, and he cannot choose both.

Logic sets out rules for arriving at truth. All white dogs are cute. My dog is white. Therefore, my dog is cute. If you believe the first and second statements, then the third is true. We call this deduction. The formal name is modus ponens, loosely method of affirming in Latin. Deduction is essential to logic and useful for working things out.

Suppose you are wanting to get a cute dog. You know the rule all white dogs are cute. When you see a white dog at the shelter, you easily conclude that she is cute. You did not have to pause and assess everything about her. You see she is white and therefore know she is cute. The rule helped you deduct it easily. Deduction saves you questioning everything and everyone at all times. You can immediately know truth now, based on truths from before.

To be or not to be invokes the law of noncontradiction. Hamlet cannot both live and die. You cannot say that the dog is white and the dog is not white without sounding ridiculous. And we all know not to contradict ourselves. Aristotle wrote noncontradiction down as a law of logic. He wrote down many such laws. The non-contradiction principle is foundational to logic. But even without reading Aristotle, the rule of noncontradiction is obvious to everyone.

Logic seems simple, but it quickly gets hairy. We know my dog is white. But suppose we take her on a walk, and she rolls around in the mud. The statement my dog is white is no longer true—she is more of a brown color now. What a fool I was to say she was white! I grumble as I struggle to get her back on her lead. I should have said my dog is currently white. But once I pull her out of the mud, I can shrug it off and say, semantics—you knew what I meant.

The law of noncontradiction means that I cannot say my dog is both white and not white. To be perfectly logical, I need to be more specific. The color of my dog at this point in time, as defined by this dog-shaped boundary, in this coordinate has fur constituted of all colors of the visible spectrum of light. If we were both dog owners in the park, and I told you this, you would quickly write me off as another weird, overly forward dog owner. And you would make an excuse to leave.

When talking with others, you make assumptions and use conventions. Assumptions are useful because you do not need to define everything upfront. Similarly, conventions let us agree on how things are done. Our heads all share these assumptions and conventions with other people. With them, successful communication becomes possible. Without having to follow formal rules of logic, we arrive at noncontradictory truths with each other. We operate logically without working through nauseating pedantry and logical proofs. Humans have a natural affinity for logic.

Logic is not only part of daily life, but a set of formal rules. You can follow these rules on paper and arrive at true conclusions. Logic is an object of study for scholars. For scientists, mathematicians, and engineers, logical rules are essential for developing advanced systems. Contradictions are not allowed, for if they were, nothing would work. Logic is a light, and noncontradiction is the switch.

Everyday people use logic to find truth and avoid contradiction. At least, we say we do. Famously, people are not completely logical. We lie to each other and close our eyes to the truth. The truth does not matter when it does not get what we want. We are also animals, and instinct can override logic. Logic allows people to live their lives and function in society. But we also live with contradictions. It’s not possible to live completely without them. Therefore closing one’s eyes to contradiction is vital.

Noncontradiction is at logic’s bedrock. Something cannot be both be true and false. Therefore drilling further into the rock seems impossible. If you agree that the rule stops here, that is good. I would mostly agree with you. Noncontradiction makes sense on first sight. But all can be questioned and investigated. And beyond the bedrock of noncontradiction lies even more mystery. I hope to go further.