The properties and relations of sentence and propositions that are subject matter of deductive logic can be arranged in three groups.
1.4.1. A closer look at entailment
Entailment will be at the heart of our study and we will begin by looking in some detail at a couple ways of formulating its definition.
1.4.2. Laws for entailment
One way of getting a feel for the character of entailment is to see what general principles can be stated for it.
1.4.3. Equivalence and tautologousness
Like entailment, equivalence and tautologousness concern conditional or unconditional guarantees of truth and both can be defined in terms of entailment.
1.4.4. Absurdity and inconsistency
Absurdity is one of another group of concepts that all concern guarantees of falsity. The chief one among them is the idea of a number of sentences being inconsistent, a guarantee that they are not all true.
1.4.5. Exhaustiveness
A final group of concepts involve exhaustiveness, a guarantee that a group of sentences are not all false.
1.4.6. A general framework
Although a conditional guarantee related to exhaustiveness is not a concept in ordinary thought about deductive reasoning, it subsumes the others we have seen and provides the basis for seeing a certain kind of connection among the laws for them.