Sometimes the answer to “is X true or false?” can only be a shrug. The answer might be unknowable, or perhaps unknowable without an impractical amount of work. Jaina seven-valued logic offers an interesting perspective on (or alternative to) the problem.
Consider the halting problem in computer science. The question is: “Can you write a program Oracle that takes any other program and answers whether that other program will halt for a given input?” (If not, it falls into an “infinite loop.")
The answer is: “no, you can’t.”
You can react to that answer in at least two different ways:
-
“Well, determining whether an arbitrary program will halt is impossible, so I’ll go do something else.”
-
“Okay, fine, there’s no universal answer, but what special cases can I write an
Oracleto handle?”
The halting problem doesn’t prevent you from writing a perfectly useful Oracle that reports, for a given program:
- “It will always halt, because it contains no loops.”
- “It will definitely not halt on any input less than zero because of the way this loop right here at line 2383 is written.”
- …
- “Sorry, boss, you’ll have to do a lot of program-specific work to determine if the program might loop forever on some input. Does the answer really matter?”
This example shows why standard boolean logic is inadequate. We almost never, in daily life, solving today’s problems, care about ∀-claims (claims that are always either true or false). We care about specific examples, or classes of examples.
Ordinary true/false logic very radically simplifies the world into one where “dunno, beats me” is not an acceptable answer. That is unacceptable.
One alternative is Jaina logic. Crudely put, it has three basic truth values: true, false, and unassertible. (That last is the “beats me, boss” answer.)
However, Jaina logic is extra neat because it specifically includes context. The Jain use a Sanskrit word that can be translated as “from a certain standpoint” or “within a particular philosophical perspective.”
With that said, there are seven truth values in Jaina logic. My own rough gloss:
- From a certain standpoint, P is true.
- From a certain standpoint, P is false
- From a certain standpoint, P is true. From another, it is false
- From a certain standpoint, there’s nothing you can say about the truth or falsity of P
- From a certain standpoint, P is true, but from a (different) standpoint, there’s nothing to say about P.
- From a certain standpoint, P is false, but from a (different) standpoint, there’s nothing to say about P.
- From one standpoint, P is true. From another, P is false. From another, there’s nothing to be said about P.
I find that a refreshing system, especially because it demands the question “from what standpoint?” It’s not something I use rigorously, but I find the “from what standpoint?” question a good one when confronted by confident claims about a Universal Truth.
Sources
“Taking Perspective: the Jain Theory of Standpoints” - a podcast episode, but the page has a wealth of (non-clickable) links.