A Final Word

You now have a working toolkit: how to distill an idea into a clause, how to quantify and negate it, how to combine claims into conjunctions, disjunctions, implications, and equivalences, and how to test arguments built from these by trying, deliberately and systematically, to make them fail. That is no small thing. Most people go through an entire education without ever being handed a repeatable method for asking whether an argument actually proves what it claims to prove.

But the notation, symbols, and truth trees were never really the point. The deeper habits are simpler: What exactly is being claimed? Have I represented that claim fairly? What does it commit us to? What would follow if it were true? What assumptions are being made? Is there some coherent way for the premises to be true while the conclusion is false? If you have learned to ask questions like these naturally—even when no symbols ever appear on paper—then you have learned the most important part of this volume.

One further distinction is worth carrying with you: Logic can tell us whether a conclusion follows from its premises. It cannot, by itself, guarantee that those premises are true. A perfectly valid argument can begin from a mistaken understanding of the world, an incomplete description, an ambiguous word, or a false premise. That is why careful representation has mattered throughout this book. Time, context, qualification, point of view, governing assumptions, and the situation about which a claim is made are not nuisances to be discarded so that reasoning becomes easier. Sometimes they are exactly what determine whether we have represented the idea correctly at all.

Many real-world arguments are invalid—not the carefully constructed arguments you encounter in a logic textbook, but the things we hear from coworkers, pundits, friends, relatives at holiday dinners, and, honestly, from ourselves. People often state conclusions, impressions, suspicions, or deeply held opinions and expect agreement without ever making the supporting structure clear. This usually is not malicious. Most people have simply never been taught to examine reasoning in this way. Expect it, and it becomes less discouraging and more simply a feature of ordinary human conversation.

You will also rarely convince anyone of anything important very quickly. Minds change slowly, and often not primarily because of one decisive argument, but because of trust, relationship, experience, reflection, and time. For that reason, use these tools first and most rigorously on your own beliefs. We are all inclined to be skeptical of positions we already dislike and much more charitable toward positions we already hold. One of the disciplines of reasoning well is refusing to grant ourselves that advantage.

Have an attitude of ongoing self-correction. Discovering that you were wrong about something—or even that you were considerably more confident than the evidence justified—is a genuinely good outcome, although it seldom feels like one in the moment. It means that you are now standing a little closer to what is actually true than you were before. This applies to the tools in this book as well. Philalethic Logic is a method for seeking and testing truth; it is not itself the truth, nor should any formal system be treated as beyond examination. The same habits of clarity, fairness, and willingness to revise that we apply to other claims must also be applied to our methods of reasoning about them.

Approach other people with good will, humility, and openness, even—especially—when you are confident that you are right. Most of the people you meet will not have had this particular training (or anything even close to it). Keep your explanations simple, your questions genuine, and your listening real. Before criticizing someone's position, make sure you have understood the position they actually hold rather than a weaker version that is easier to defeat.

Be willing to “steelman” the other side—to state it, at least to yourself, as strongly and fairly as its best defenders would. And whatever degree of scrutiny you are tempted to apply to a position you dislike, apply at least that much scrutiny to the position you already hold.

You will encounter people who use reasoning, rhetoric, and argument for domination rather than truth. Some may do this deliberately. Many more do it defensively, because a challenge to an important belief can feel like a challenge to one's identity, community, or entire understanding of the world. Develop a thick enough skin to endure this without allowing it to harden into contempt. The fact that someone reasons badly or has mistaken beliefs does not necessarily make that person your enemy. We all make mistakes.

There is also no requirement that everything you have learned here remain on paper. You do not need to construct a formal truth tree every time someone says something questionable. With practice, much of the discipline becomes habitual. You begin to notice an unstated premise. You hear that two apparently identical claims actually concern different times or situations. You recognize that a conclusion is stronger than anything the premises warrant. You instinctively ask what a counterexample would look like. Formal analysis trains the mind so that clearer informal reasoning becomes increasingly natural.

And this volume is only a foundation. Human reasoning is richer and more complicated than the fragment we have developed here. There are further kinds of relations, identity, more complex quantified structures, richer modal questions, and many other matters still to explore. But nothing that comes later makes these foundations unimportant. The discipline of identifying the idea, preserving its meaning, exposing its commitments, and looking honestly for a way in which one's reasoning could fail remains fundamental.

Above everything else in this book, remember that people are moved toward truth far more often by love, patience, and honest example than by winning arguments. Whatever skill you have built here, keep it in service of a genuine, humble, and persistent search for what is real—for yourself first, and then, gently, for whoever else is willing to walk that road with you.

Practice on the news. Practice on advertisements and political speeches. Practice on the arguments in your own head. Practice on the next serious disagreement you have with someone you love. Ask not merely, How can I prove my position? but What is actually true? What would show me that I am mistaken? Have I understood the other person? Am I seeking truth, or merely victory?

And remember why the search matters.

All of this truth-seeking is most worthwhile when it is undertaken in a context of genuine love—in willing and seeking the good of others, and ultimately their salvation. Truth without love can easily become a weapon. Love without truth can become sentimentality, indulgence, or deception. We need both.

Veritas in caritate.