5. Conditionals

5.1. If: trimming content

5.1.0. Overview

The last connective we will consider is an asymmetric one whose asymmetry gives it an important role in deductive reasoning.

5.1.1. Conditions
In its simplest form, the conditional trims the content of one component by limiting the worlds it rules out to ones that the other component leaves open.

5.1.2. The conditional as a truth-functional connective
The trimming of content is naturally described by an asymmetric truth table.

5.1.3. Doubts about truth-functionality
The truth table just associated with the condition has been controversial since antiquity because the conditional is closely associated with certain implicatures that can seem to add further content.

5.1.4. Examples
The chief task in analyzing the English conditionals marked by if alone is to assign the correct order to the components.