Logic

Spock_at_consoleIn the coming weeks, I want to look at some different arguments for the existence of God. But first, how can you know my reasons for believing God exists are legitimate? Maybe you don’t believe God exists, or maybe you simply don’t know. Likewise, how do I know if your reasons are legitimate? How do we discuss our opposing reasons (for this or anything else imaginable) on a level playing field? With that goal in mind, today let’s start out with a refresher (or introduction) to basic logic. Like a lot of foundational material, it may seem a little dry, but it really is the necessary foundation for any type of critical thinking. Underlined words are key terms in logic.

Let’s start with some clarification. An argument in logic is not a fight or quarrel, but rather a rational though process using a series of statements (or propositions) called premises and conclusions. As such, there are some rules for making sure the conclusions you draw are legitimate. Just like in sports, these rules help ensure that the winner really did win fairly.

Propositions are simply statements that may be either the premises or the conclusion of an argument. While you may be trying to determine a reasonable answer to a question with an argument, you can’t have a question or a command for a premise, so these are always declarative sentences. Not to bring up bad memories of diagramming sentences in grade school grammar, but these statements need a subject and a predicate. The subject is just what you’re talking about, while the predicate is what you’re saying about it. The premises are  propositions that each propose a basis for the conclusion. They give your evidence. Premises can be either true or false.  “The city of Houston, Texas is located in the country of Australia.” is a false premise, while “Mars orbits around the sun.” would be a true premise. These premises use terms that can either be clear or unclear. A term is clear if it can be understood in only one sense. For instance, a person can use the word “hot” to describe: temperature (“It’s hot outside”), attractiveness (“She’s hot!”), or questionable legality (“He wrote a hot check”).  In this case, “hot” has equivocal meanings and wouldn’t be a good term to use in a premise unless we either defined it first, or the meaning was clear from the context. Some terms are not so obviously different  in their meanings, and many a misunderstanding has happened because of this issue of equivocation (using the same term in different ways).

The conclusion either necessarily follows from the premises and the argument is valid, or it doesn’t follow and is invalid. “All men are mortal. Socrates is a man. Therefore, Socrates is mortal.” is a classic example of a valid syllogism. A syllogism is your most basic argument: 2 premises and 1 conclusion showing a clear relationship between 3 terms. If it is true that all men are mortal, and Socrates is indeed a man, then Socrates simply must be mortal. This is an example of deductive reasoning, which generally moves from a universal principle to a specific application. Inductive reasoning, on the other hand, typically moves from specific observations to a more general conclusion. Valid deduction provides certainty in its conclusion, while induction only provides a degree of probability. Just because you’ve observed many similar cases doesn’t mean all cases will be similar (the exception would if you’ve actually observed all cases). Science typically uses inductive reasoning based on specific observations, hence the tendency of scientists and engineers to always qualify what they say with disclaimers.

Understanding the principles of logic is advantageous regardless of your educational background, your culture, or your beliefs because it provides a framework for knowing that what you believe is true. If your terms are clear, your premises are true, and your deductive argument valid, then your position is necessarily true and there can be no argument against it. Likewise, if your opponent’s argument doesn’t have ambiguous terms, a false premise, or a logical fallacy, then, to be honest, you must admit he’s right. The same goes for me. And so we now have a level playing field, with the same rules applicable to and acknowledged by, both sides. Maybe you’ve listened to a talk show where two opposing guests simply stated their own views over and over again and ignored the other side. Or they simply talked past each other louder and louder? Did you walk away feeling like it was just pointless discussing some issues? There is hope, and this is where logic shines. I encourage you to not simply stop at this short  glossary of logic, but to dig deeper, learn it, and apply it in your own life.


Resources:

Socratic Logic, Edition 3.1, by Peter Kreeft, (St. Augustine’s Press, 2010), which served as a reference for much of this. This is an actual logic textbook.

Being Logical: A Guide to Good Thinking, by D.Q. McInerny, (Random House, 2005), is also an excellent and very concise introduction to logic, and well-suited for a first exposure to logical principles.