Formal Logic 101 – Part 15: Introduction to Predicate Logic

As promised, this time we will be beginning our discussion of predicate logic. So what is predicate logic? Why does it exist? Well to answer that first question: 

I’m assuming most of you remember back in grade school, your teacher telling you that sentences have a subject and a predicate. I can already hear 95% of you being like “Yeah… I mean I was told that but it’s been… HOW many years now?”, and the other 5% of you saying “Yeah of course I know that, I’m an English major.”

So, for the benefit of you Non-English-Majors out there, the subject is the person, place or thing that you’re talking about. If I say “Leo Tolstoy was a Russian”, I’m talking about Leo Tolstoy, he’s the subject. The predicate tells us something about the subject (e.g. “he’s a Russian”). To help separate subjects and predicates, I tend to imagine a conversation like this:

Me: Hey, you know Leo Tolstoy?
You: Yeah, what about him?
Me: He’s a Russian.

“The kid threw a ball.”
Me: Hey, you see that kid?
You: Yeah, what about them?
Me: They threw a ball.

“War and Peace is a novel.”
Me: Hey, you know War and Peace?
You: Yeah, what about it?
Me: It’s a novel.

The part of the sentence that tells us who or what we’re talking about is the Subject, and the part that answers the question “what about it?” is the predicate.

So instead of doing logic on full sentences now, we’re going to also be symbolizing the predicate parts of sentences.

“Ok, interesting. But why?”
I’m so glad you asked that question!

Consider the following statements: Leo Tolstoy was a Russian. All Russians write Sad stories. Therefore, Leo Tolstoy wrote sad stories.

Using what we know so far, we would symbolize these statements as follows:
1. L
2. R→S

And be left with nowhere to go in our hopes of reaching a conclusion. Do note that if we tried to rephrase our first premise to “L→R”, then we’re left with something akin to “If he’s named Leo Tolstoy, then he’s a Russian”. So we’ve walked back our assertion that “Leo Tolstoy was a Russian” back to kind of “hypothetical territory” where we’re not saying he was a Russian… we’re just saying “if that’s his name, then he would be a Russian”. So we haven’t maintained our meaning, and we’re not able to reach our conclusion, despite the argument being obviously valid when viewed in plain English.
We need predicate logic because there is sometimes simply no way to symbolize a perfectly valid argument only using propositional logic.

Now that we’ve had a broad overview of why predicate logic is necessary, next time we’ll come back and discuss symbolization. Don’t worry, it’s basically just some tweaks to the symbolization for propositional logic. Like I said last time, we’re not starting from scratch, we’re building on what we’ve already learned.

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