1.2. What is said: propositions

1.2.0. Overview

In 1.1.5, we saw the close relation between two properties of a deductive inference: it is a transition from premises to conclusion that is free of any risk of new error, and the information provided by its conclusion is already present in its premises. The relation between these properties points to a way of understanding the content of a sentence, the information it provides.

1.2.1. Truth values and possible worlds
First we look more closely at the concepts of risk and error involved in the idea of risk-free inference.

1.2.2. Truth conditions and propositions
We can use these ideas to give an account of the content or the meaning of a sentence, an account of what it says.

1.2.3. Ordering by content
When there is a risk-free inference from one sentence to another, the first may say the same thing as a second or it may say more by ruling out some possibility the second leaves open.

1.2.4. Tautologies and absurdities
Two extremes in the ordering of sentences by content are sentences that say nothing and sentences that say too much to distinguish among possibilities.

1.2.5. Logical space and the algebra of propositions
Deductive logic can be seen as the theory of the meanings of sentences in the way that arithmetic is the theory of numbers.

1.2.6. Contrasting content
Other logical relations between sentences concern differences rather than similarities in content. Together with implication, these provide a complete collection of logical relations between two sentences, so sentences related in none of these ways can be described as logically independent.