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.
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