Simple Propositions

Simple propositions  are declarative sentences which do not contain a connective.  The restriction to declarative sentences is important. In propositional logic each proposition, simple or complex, must be capable of being either true or false.  So we won't count questions or commands, for example, as simple propositions.  The reason for this is not hard to find: We're interested in figuring out which arguments are truth-preserving and which aren't. That means that the premises and the conclusion of arguments must be propositions which can be either true or false.

To determine whether a sentence is simple or complex, look for the simplest form of the sentence which can be true or false, and then look for a phrase that connects that form to another such form, or find a phrase that operates on our modifies the form. So, for example, in the sentence "It is possible that snow is green", we can find the simple sentence "Snow is green" and the operator "It is possible that".

A wrinkle in what we've just said about simple vs. complex sentences is that some sentences which have full sentences within them have to be treated as logically simple. For example, the sentence:

Ignatious likes apples with tartar sauce.

contains the sentence "Ignatious likes apples" as a part, but "with tartar sauce" does not operate on, or modify the embedded sentence. Rahter, it modifies the non-sentence fragment, or term, "apples." Therefore we must treat the sentence as a simple sentence. Contrast that with a complex sentence such as:

It's not the case that Ignatious likes apples.

In this case, the operator "It's not the case that" modifies or applies to, the entire sentence.

Sometimes you need to rephrase a complex sentence to find its complex structure. In sentence "Lobsters are fierce but tasty." we need to see that "but" means "and", and we should rewrite the sentence as "Lobsters are fierce and lobsters are tasty." This is a complex sentence conjoined by "and". The two simple sentences are "Lobsters are fierce" and "Lobsters are tasty."

In the following exercise you'll determine whether propositions are simple or complex.