In logic, some statements can't be proven true, only proven false.
For example, the statement "the universe is infinite" can be disproven by discovering its bounds, say by launching a rocket that crashes into the all-encompassing, mysterious wall near a galaxy far, far away; but cannot be proven true, as the case of an infinite universe is observationally indistinguishable from the case of a universe "so large we haven't found its bounds yet".
The term I'm looking for could be viewed as equal and opposite to "unfalsifiable", in that I'm looking for a term roughly equivalent to "untruthable". Does such a term exist? Also, does the term "unfalsifiable" hold this strict interpretation of "provably true or unknowable" in logic, as I've only ever heard it used in the context of philosophy?
Best Answer
I think this is more traditionally a topic in philosophy (of science) rather than logic in mathematics. I don't know of a single word for it, but the standard phrase would be "falsifiable but not verifiable". For some references for this usage, see this encyclopedia entry, this blog post, or this youtube video.