Undecidable

Whether this difference is only perspectival or whether we deal with an interactive many-worlds "world" even at the global level may remain undecidable, too. ❋ Unknown (2001)

We should remark that this problem is non-trivial since deciding whether a finite set of equations provides a basis for Boolean algebra is undecidable, that is, it does not permit an algorithmic representation; also, the problem was attacked by Robbins, Huntington, Tarski and many of his students with no success. ❋ Portoraro, Frederic (2005)

But the "undecidable" stuff needs a lot more care. ❋ Unknown (2009)

Viewed as a first-order theory, sentences in Quantum Mechanics are undecidable. ❋ Gordon McCabe (2009)

However, undecidable statements which are free from self-reference have been found in various branches of mathematics. ❋ Gordon McCabe (2009)

Crucially, however, whilst the theory of a model, Th (M), may be undecidable, it is guaranteed to be complete, and it is the models of a theory which purport to represent physical reality. ❋ Gordon McCabe (2009)

Moreover, whilst Peano arithmetic is axiomatizable, there is a particular model of Peano arithmetic, whose theory is typically referred to as Number theory, which Godel demonstrated to be undecidable and non-axiomatizable. ❋ Gordon McCabe (2009)

However, even if a final Theory of Everything is incomplete and undecidable, the physical universe will be a model M of that theory, and every sentence in the language of the theory will either belong or not belong to Th (M). ❋ Gordon McCabe (2009)

I have found that its assumed use of the square root of minus one is logically independent from the theory's axioms: a subset being the Field Axioms, under which the square root of minus one is a well known and proven undecidable sentence. ❋ Gordon McCabe (2009)

What matters is that the winner deserves it, not the undecidable question of whether the most deserving wins. ❋ Unknown (2011)

It transpires that the theory of arithmetic (technically, Peano arithmetic) is both incomplete and undecidable. ❋ Gordon McCabe (2009)

But what do you mean by scientifically undecidable? ❋ Unknown (2008)