Building Blocks of Logic

Proposition

$$``\text{Today is Wednesday}"$$

When writing this very lesson, the simple sentence above was true. But is it also true when you’re reading this? Is it Wednesday today? Maybe, maybe not. But one thing we can safely say is that no matter which day of the week it is, this sentence is strictly going to be either true or false.

Predicate and proposition

The simplistic structure of the sentence above points our attention toward something. Its subject (“today”) associates a claim about it or assigns a property to it. This property is termed as the predicate (“Wednesday”). All such sentences that a) have a subject and predicate, and b) resolve to either true or false are called propositions. Propositions are the fundamental building blocks of logic.

Exercise

Create a simple sentence that’s not a proposition.

How about this sentence itself: “Create a simple sentence that is not a proposition.” While we can clearly understand its meaning, the meaning isn’t strictly reducible to true or false. It’s a command and a call for action.

Simple and compound sentences

“Today is ...