A student in my introductory logic course expressed some frustration with the course this evening asking, “Does logic speak in terms of the English language??” Another student amplified that frustration. She replied, “Apparently not. I rather thought Philosophy was not all formulas.” I took both of their comments as a frustration with the relevance of logic. What good are all these formulas and terms and how do they relate to “real life?” Below is my response.

What do you think of how I answered them?

Symbolic logic is a system that symbolizes the structure of thought. A formal language (like English) symbolizes things in the world. So for example, the word "tree" is a symbol for a class of things in the world, namely, all trees. The sentence "That tree." is meant to specify a particular tree when used by a speaker to pick out an object in the world. It’s still symbolic. Of course a formal language can be used to symbolize other things including other symbols (think of poetry here).

But logic symbolizes how ideas should relate to one another. So modus ponens for example symbolizes how two things should properly relate to each other in thought. If p then q, p, therefore q essentially is a symbolic representation for the relationship p ought to stand to q in order thought. Just like a formal language has a grammar ("a singular subject takes a singular verb, while a plural subject takes a plural verb"), ideas have a grammar and that’s captured in logic.

Ideally, as you learn the grammar of ideas, you’ll become better at seeing and using those relationships to make arguments. Here’s an example.

Suppose you want to get me to believe that Apple makes the best computers on the market. I ask you why. You could say, "I dunno, they just do." or "You’d have to be stupid not believe that." or "Because apples grow on trees and that’s what makes them good." You’ve given me no reason why I should believe Apple computers are better than other kinds of computers. So, in a sense, our conversation really can’t go anywhere.

But suppose you give me a modus ponens argument. You say, "If a computer maker uses the highest quality materials in their workmanship, their computers will be better than everyone else’s. Apple uses the highest quality materials in their workmanship. So Apple computers are better than everyone else’s." Now we have something to discuss. I can disagree that highest quality materials are the only factor in "being the best" (your first premise) or that Apple uses the highest quality materials (your second premise) etc.

For this to work you don’t have to think to yourself, "I must now give a modus ponens argument." just like you don’t generally think, "In order to write a complete sentence, I must have a noun, a verb, and an object." Once you learn English grammar well enough, you just write complete sentences. The same should be true of logic. Once you master the rules, the "proper" formation of arguments will just come naturally.

So in once sense, you can think of early studies in logic as an elementary grammar for ideas. If it feels odd or "fake" and disconnected from the real world, it might be because you’re learning a new grammar. If you just started studying English grammar for the first time (without knowing another language) it too would most likely feel fake (what does noun, verb, and object have to do with anything? you might think in a sort of non-linguistic way—assuming that’s possible). If you invest in this though and stick with it, it will pay off.