 the same universe, that makes
&gt; the other true.
&gt; 
&gt; I presume that what John means is that the *intended*
&gt; intepreretations are different in the way he describes.
&gt; But the intentions of the writers of axioms have no place
&gt; in any kind of formal analysis of the meanings of those axioms
&gt; (other than by exclusion, in the sense that one can formally show
&gt; that the actual meaning does not correspond to the intended meaning,
&gt; cf. the previous paragraph.)  So this kind of example