The Whole Truth about Partial Truth Tables

TLDR: This essay explains what a partial truth table is and shows how such a table is constructed, and applies the partial-truth-table technique successively to arguments, individual propositions, and sets of two or more propositions.

Abstract: Partial truth tables have two salient virtues. First, like whole truth tables, they are algorithmic (i.e., effective). If you construct them correctly, you will get an answer to your question whether a particular argument is valid; whether a particular proposition is tautologous, self-contradictory, or contingent; or whether a particular set of propositions is consistent. Second, they are less time-consuming and tedious to construct than whole truth tables. No partial truth table has more than three rows, and many have only one. A whole truth table, by contrast, may have as many as 32, 64, 128, or 256 rows (or more). In this essay, I explain what a partial truth table is and show how such a table is constructed. I then apply the partial-truth-table technique successively to arguments, individual propositions, and sets of two or more propositions. I conclude by evaluating the most widely used logic textbooks, showing what they do well and where they fall short.