I'm trying to find out who invented truth-tables. Here is what I have so far.
Leibniz 'invented' binary arithmetic, or at least is the first one recognized to have codified and explained a base 2 system for arithmetic (there's no doubt that there are vague priors from China; Leibniz himself mentions 'Fohy' and goves a figure that looks like 'I Ching').
Boole, in his Laws of Thought, essentially created boolean algebra (notice that the name of the thing is not the same as the thing).
Peirce and Frege separately introduced symbolism that treated boolean things functionally (that's a roundabout way of saying they were the first to use the notation of functions on booleans, i.e. boolean functions).
Schroeder and later Post also are mentioned in connection with truth tables, but I'm having a hard time substantiating that more than just by repeating that other people collocate those names with 'truth table'.
Wittgenstein, in Tractatus Logicus-Phiosophicus, chapter 5, discusses boolean functions using that terminology and -graphically- expresses these functions in tabular format, calling them 'truth tables' (in German).
Shannon is famous for introducing boolean logic in his master's thesis (1936) for use in design of computers. (his primary references being Couturat, The Logic of Algebra (1905), and Whitehead, Universal Algebra (1898).
It is taken by philosophers that Wittgenstein is the inventor of truth tables: (Stanford Encyclopedia of Philosophy entry on Wittgenstein). But with a background more in cs and math, I find that it doesn't fit with my preconceived notions of intellectual culture – I just wouldn't expect scientific/mathematical types to trace the usage history of something so technical back to someone (Wittgenstein) so humanities-oriented (to be frank, I can't believe that people who built the first digital computers learned truth tables directly or indirectly from TLP).
It is the introduction of a tabular format called 'truth table' that I am looking for the provenance. Since boolean functions were well known before then, it is simply the distinctive visual device of laying out the function in a table with all the possibilities for the arguments next to the value of the function for those arguments. To me this seems like who invented 'FOIL' for teaching how to multiply binomials, in that a name was given to something that people had been doing anyway already (or not even bothering to do).
So, really, where did the use of truth tables really come from, and is there any indication in the history that follows, where the mathematicians and engineers got it from? So maybe Wittgenstein 'popularized' it among the philosophers (I don't have any doubt there), but maybe he was (or maybe wasn't) the source for later use by the engineers.
So, whoever was the first to have invented truth tables (Peirce is definitively the first one there is evidence for), who popularized the use of truth tables in elementary mathematical logic? Wittgenstein certainly popularized it among philosophers, but he (and the Wiener Kreis by extension) doesn't have much influence on mathematicians, so I find it unlikely that mathematicians learned it there.
Best Answer
Well, Aristotle qualifies as quite "humanities oriented" according to the modern way of classifying subject areas, but up until recently plenty of usage history can get traced back to him. Actually, there still exists some usage history traceable back to him.
That said, you might want to see this page, which indicates that perhaps no real inventor existed. Shosky tried to argue that Russell did so. Anellis, though, if his evidence is correct clearly enough indicates that C. S. Peirce had them before that. So, unless historians have missed something in Frege, Peirce gets the prize here:
One might also ask here, "who first used numbers for truth-values in the context of truth tables?" I'm not so sure here, but I would think Łukasiewicz did that first, though when he wrote a truth table he wrote them horizontally instead of vertically. ${}$