Sentential Logic Overview

In this module, we work with another “deductive logic” — a sentenced-based approach to deductive logic—Sentential Logic. While Sentential Logic has different methods and techniques than those we encountered with Aristotelian Logic, it shares the same goal — to evaluate deductive arguments to determine whether they are valid or invalid.

Given the connection between argument form and validity, Sentential Logic, too, must identify precise criteria for the logical form of arguments, and it must handle the preliminary task of cleaning up the natural language.

We will explore how Sentential Logic uses structures parallel to  but different from the techniques of Aristotelian logic to perform the three essential tasks:

1. Tame natural language by removing imprecision and unruliness (task 1).
2. Define form by making arguments precise and suitable for evaluation (task 2).
3. Devise a way to test logical forms for validity (task 3).

To accomplish these tasks, Sentential Logic steps outside natural language entirely. It constructs an artificial language and only evaluates arguments expressed in its terms. A  systematic relationship between the artificial language and our natural one (English) allows translation between the two. We will refer to the artificial language of Sentential Logic as “SL”  for short.

Module 4 Roadmap

• Section 4.1: We look at the advantage that Sentential Logic offers when compared to some shortcomings inherent in Aristotelian Logic, to gain an appreciation for why this logic is helpful.
• Section 4.2: In this section, we learn about the syntax of Sentential Logic, its own special set of symbols, and rules that govern its structure.
• Section 4.3: We use simple truth tables to dig into truth value meaning for symbols and other bits and pieces that were defined in the material on syntax.
• Section 4.4: In this section, we work on translation between our ordinary English usage and the symbolic language of Sentential Logic.
• Section 4.5: In the final section, after reiterating the rules for ‘form’, we work with truth tables to test for the validity of arguments expressed in sentential form.

Key Terms

• antecedent
• biconditional
• compound sentence
• conditional
• conjunction
• consequent
• disjunction
• logical form (Sentential)
• main operator
• necessary condition
• negation
• semantics
• simple sentence
• sufficient condition
• syntax

Definitions for these terms are available in the course Glossary.