Permalink Submitted by maarten on September 3, 2011

I don't think I put in an explicit definition for "ex contradictione quodlibet" either.

The three concepts "falso" (or "falsum"), "contradictione" and "absurdum" are three concepts which are classically equivalent. Paraconsistent logics make distinctions between these ideas. "Absurdum" is anything which is absurd in the sense that only the trivial theory (which gives a proof of every statement, true, false, or otherwise) can be paraconsistently (and classically) derived from an absurd statement. "Contradictione" is simply a (local) contradiction, such as the Russell set, which need not infect the rest of the theory. "Falso" is a logical constant, whose definition is in a sense up for grabs and isn't very meaningful. The role that "falso" plays in this article is that the principle is classically called "ex falso quodlibet" and interchangeably used with the other two. (In fact, if you search Wikipedia for "falsum", it points you at the "contradiction" page demonstrating how ingrained this interchangeability is!)

So in short, "ex absurdum quodlibet" means "from an absurdity, conclude anything" (the trick being that "absurdity" in paraconsistent theories is really just a placeholder for "everything is true")

## re: ex absurdum quodlibet?

I don't think I put in an explicit definition for "ex contradictione quodlibet" either.

The three concepts "falso" (or "falsum"), "contradictione" and "absurdum" are three concepts which are classically equivalent. Paraconsistent logics make distinctions between these ideas. "Absurdum" is anything which is absurd in the sense that only the trivial theory (which gives a proof of every statement, true, false, or otherwise) can be paraconsistently (and classically) derived from an absurd statement. "Contradictione" is simply a (local) contradiction, such as the Russell set, which need not infect the rest of the theory. "Falso" is a logical constant, whose definition is in a sense up for grabs and isn't very meaningful. The role that "falso" plays in this article is that the principle is classically called "ex falso quodlibet" and interchangeably used with the other two. (In fact, if you search Wikipedia for "falsum", it points you at the "contradiction" page demonstrating how ingrained this interchangeability is!)

So in short, "ex absurdum quodlibet" means "from an absurdity, conclude anything" (the trick being that "absurdity" in paraconsistent theories is really just a placeholder for "everything is true")