<p><pre><code>  Z is designed to loop through its 7918 instructions forever, but if it did eventually stop, it would prove ZFC inconsistent. Mathematicians wouldn’t be too panicked, though – they could simply shift to a slightly stronger set of axioms.
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Am I correct in thinking that this is completely wrong? Strengthening a set of inconsistent axioms -- taking a &quot;stronger&quot; set of axioms to be a set of axioms that can prove more statements -- will just produce another inconsistent set of axioms. (The inconsistent set &lt;A, B-&gt;~A, B&gt; cannot be salvaged by extending it to &lt;A, B-&gt;~A, B, C&gt; -- no matter what C is, you can always derive &lt;A, ~A&gt; from the original three axioms.)<p>Incompleteness is a whole other thing, of course.