Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001). In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid. In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on 'The Philosophy of Logical Atomism' truth table matrices. The matrix for negation is Russell's, alongside of which is the matrix for material implication in the hand of Ludwig Wittgenstein. It is shown that an unpublished manuscript identified as composed by Peirce in 1893 includes a truth table matrix that is equivalent to the matrix for material implication discovered by John Shosky. An unpublished manuscript by Peirce identified as having been composed in 1883–84 in connection with the composition of Peirce's 'On the Algebra of Logic: A Contribution to the Philosophy of Notation' that appeared in the American Journal of Mathematics in 1885 includes an example of an indirect truth table for the conditional. A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001). In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid. A truth table has one column for each input variable (for example, P and Q), and one final column showing all of the possible results of the logical operation that the table represents (for example, P XOR Q). Each row of the truth table contains one possible configuration of the input variables (for instance, P=true Q=false), and the result of the operation for those values. See the examples below for further clarification. Ludwig Wittgenstein is often credited with inventing the truth table in his Tractatus Logico-Philosophicus, though it appeared at least a year earlier in a paper on propositional logic by Emil Leon Post.