The Universe of Discourse

Universe of discourse:

When I started getting into database logic, I often came across the expression “universe of discourse”. When I tried to understand what exactly it is really, most answers I found referred to it as “a set”. Well it didn’t help much to me understanding one concept by naming it another. So after studying the subject thoroughly, here’s what i found : The universe of discourse is at its core really is a set (wait...what?...but..), but before we dive right into it let's take a step back for a second: the term “universe of discourse generally refers to a collection of objects being discussed in a specific discourse. The concept universe of discourse is generally attributed to De morgan (1846) but the name was used for the first time by George boole (1854). ( boole's definition ). So now after we know that a universe is a “collection” so to speak, let’s take it up a notch. To understand best what the universe” is we can bring an example from predicate logic. In predicate logic we have propositions which are the “sentences” in the predicate. For instance, x lives in y is a proposition without values (predicate). But now that we know that a universe is a collection we’re able to assign those parameters a range of values that will make the propositions in the predicate a statements in the objects of the universe. This method is called “quantifying” a predicate. a real life example would be Suppose P(x) is the sentence “x has fur” and the universe of discourse for x is the set of all animals. In this example P(x) is a true statement if x is a cat. It is false, though, if x is an alligator}). So really a universe is a collection of objects that defines a range of the values. We can use it to resolve predicates. But there’s still one more important thing to know. And that being a “set”. Now I know that this can get a little confusing, especially because a set in natural language is a very general broad term, so what is a “set” in logic?. A set is any collection of objects or symbols. The objects in a set will be called element or a number of the set. Sets are usually described using ”{}” and inside these curly brackets a list of the elements or a description of the elements of the set. If a is an element of a set A, we use the notation a ∈ A and often say ”a in A” instead of ”a an element of A”. The notation a ∉ A indicates that a is not an element of A and is often read as ”a is not in A”. So to summarize a universe is a collection of sets of interest (discourse). A set is a collection of well defined and distinct objects, considered as an object in its own right. Enjoy!