Method
Truth table
Overview
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. 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, A and B), and one final column showing the result of the logical operation that the table represents (for example, A XOR B). Each row of the truth table contains one possible configuration of the input variables (for instance, A=true, B=false), and the result of the operation for those values.
A proposition's truth table is a graphical representation of its truth function. The truth function can be more useful for mathematical purposes, although the same information is encoded in both.
Ludwig Wittgenstein is generally credited with inventing and popularizing the truth table in his Tractatus Logico-Philosophicus, which was completed in 1918 and published in 1921. Such a system was also independently proposed in 1921 by Emil Leon Post.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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Now this requires that the number of events concerned should be infinite in any finite period of time. If this is to be the case in the world of one man's sense-data, and if each sense-datum is to have not less than a certain finite temporal extension, it will be necessary to assume that we always have an infinite number of sense-data simultaneous with any given sense-datum. Applying similar considerations to space…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
States what Truth table is; the author is tied to Truth table in the knowledge graph.
But whether valid or not, the argument has been very widely advanced in one form or another; and very many philosophers, perhaps a majority, have held that there is nothing real except minds and their ideas. Such philosophers are called 'idealists'.
Bertrand Russell, The Problems of Philosophy
States what Truth table is; the author is tied to Truth table in the knowledge graph.
Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
States what Truth table is.
Philosophers who discussed Truth table
Related ideas
- Exclusive or
- Integer
- If and only if
- Propositional variable
- Negation
- Truth value
- Logical equivalence
- Ludwig Wittgenstein
- Logical conjunction
- Propositional logic
- Exponential growth
- Logical NOR
- Validity (logic)
- Logical biconditional
- Stephen Cole Kleene
- Sheffer stroke
- Commutative property
- Tractatus Logico-Philosophicus
- Bit
- Emil Leon Post
- Bertrand Russell
- Tautology (logic)
- Logic
- Boolean algebra
Place in the tradition
Part of Analytic philosophy.