# What is the origin of the truth table in logic?

Specifically for the material implication if possible. Who was the first to use a truth table for this and justify its validity?

• really, all a truth table is, is a definition. Jun 10 '16 at 0:52
• @robertbristow-johnson But it had to originate from somewhere, and have a justification behind it. Jun 10 '16 at 2:19
• the question of origin can be applied to anything. definitions don't require justification. they're axioms. Jun 10 '16 at 4:44
• @robertbristow-johnson The question of origin can be applied to anything, I don't see that as a problem. As for justification, there must be a reason for the definition. That is what I am looking for. Jun 10 '16 at 14:44
• @robertbristow-johnson In mathematics, definitions and axioms are not the same. Axioms are the foundation for a theory, while definitions are merelyhandy abbreviations. Jan 6 '18 at 9:07

You can see:

as well as:

Before Bertrand Russell (Harvard logic course: 1914) and Ludwig Wittgenstein (Russell and Wittgenstein's manuscript dated 1912; see also: Tractatus (1921), 4.31 and 4.442 for material implication), Charles Sanders Peirce and his followers must be credited.

See Christine Ladd-Franklin, “On the Algebra of Logic”, in Charles Sanders Peirce (editor), Studies in Logic (1883), page 17-on; see pages 61-62.

In Whitehead and Russell's Principia (page 115), we have a description of the truth-functional semantics of connective : not, if..., then..., and, or (but not in tabular form).

The modern tabular form is present in E.Post, Introduction to a General Theory of Elementary Propositions (1921), §2 Truth table development, with explicit reference to W&R's Principia (see footnote 6).

The verbal" description of conditional is in Frege's Begriffsschrift.

But it was already verbally stated in Ancient Stoic Logic with the so-called philonian conditional; see Sextus Empiricus, Πρὸς μαθηματικούς (Pros mathematikous) Book VIII, 113:

Philo, for example, said that the conditional is true when it does not begin with a true proposition and finish with a false one, so that a conditional, according to him, is true in three ways and false in one way. For when it begins with a true one and finishes with a true one, it is true, as in “If it is day, it is light.” And when it begins with a false one and finishes with a false one, it is again true – for example, “If the earth flies, the earth has wings.”