Propositions and connectives in natural language

We just noted that the sentence "If Ignat passes the class, Ignat is eligible for graduation" is a complex sentence built out of two simpler sentences. The two simpler sentences are connected, by "if ___then___" so logicians call the words which do the connecting connectives or operators. (The term "operator" is a bit broader than "connective.") We'll see right away that some complex sentences which are formed out of simple sentences don't connect two sentences.

What are some of the operators or connectives in English? Here are some examples:

	sentence	connective
1.	I'm happy and you're sad.	"and"
2.	Fred went to the store but Mathilda stayed home.	"but"
3.	You can have the cookies or the cake.	"or"
4.	I'll see to it that you finish the project.	"I'll see to it that"
5.	If you miss the train I'm on, then you'll know that I have gone.	"If__, then__"
6.	Fred is not here.	"not"

How can you tell whether a sentence has connectives? Just see whether you can find sentences imbedded within the sentence, connected by some word or phrase, or look for a phrase which modifies a sentence which could stand alone. Sometimes that may mean rewriting the sentence. For example, in sentence 3, "or" connects two sentences, but the second sentence is not explicitly stated. To make it explicit that "or" connects two sentences, we need to rewrite "the cake" as "you can have the cake". In sentence 6, we can rewrite "Fred is not here" as "It is not the case that Fred is here." in order to see how "It is not the case that" operates on the simple sentence "Fred is here."

In the following exercise, you'll be asked to make up some sentences with connectives and state the connective.

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List of Exercises