Rationale behind truth values I originaly asked a question on Programmers.SE to know why $0$ was consider $\text{false}$ and all the other [integral] values were considered $\text{true}$. That was a huge debate and many said it was a legacy from Boolean algebra where $0$ is indeed $\text{false}$ and $1$ is $\text{true}$.
Somebody suggested I go further and ask here why this is actually the case in Boolean algebra. So here is the question: what is the rationale for $0$ to be $\text{false}$ and $1$ to be $\text{true}$ and not the other way around in Boolean algebra?

I wouldn't be surprised if a version of this convention goes back to Boole himself, in his algebra of classes.  I believe he used $0$ for the empty class and $1$ for the class of "everything".  (This was before the set-theoretic paradoxes made people queasy about the class of everything.)  Under the natural correspondence between classes and functions to "true" and "false" (where a class $C$ corresponds to the function sending elements of $C$ to "true" and "everything" else to "false"), these would be the constant "false" function for $0$ and the constant "true" function for $1$.  So it was natural and convenient to identify the truth values with these numbers.
