Changes

Ordinarily, it is desirable to avoid making individual mention of the separately indexed domains, ''P''_''j'' and ''Q''_''j'' for all ''j'' ∈ ''J''.  Common strategies for getting around this trouble involve the introduction of additional domains, designed to encompass all the objects needed in given contexts.  Toward this end, an adequate supply of intermediate domains, called the ''rudiments of universal mediation'' (RUM's), can be defined as follows:

Ordinarily, it is desirable to avoid making individual mention of the separately indexed domains, ''P''_''j'' and ''Q''_''j'' for all ''j'' ∈ ''J''.  Common strategies for getting around this trouble involve the introduction of additional domains, designed to encompass all the objects needed in given contexts.  Toward this end, an adequate supply of intermediate domains, called the ''rudiments of universal mediation'' (RUM's), can be defined as follows:

:{| height="100" width="90%"

:<p><math>\begin{matrix}

| ''X''_''j'' = ''P''_''j'' &cup; ''Q''_''j''&nbsp;,

X_j = P_j \cup Q_j ,

| <p>''P'' = <font size="+2">&cup;</font>_''j'' ''P''_''j''&nbsp;,

& P = \bigcup_j P_j ,

| ''Q'' = <font size="+2">&cup;</font>_''j'' ''Q''_''j''&nbsp;.

& Q = \bigcup_j Q_j .

\end{matrix}</math></p>

Ultimately, all of these ''totalitarian'' strategies end the same way, at first, by envisioning a domain X that is big enough to encompass all the objects of thought that might demand entry into a given discussion, and then, by invoking one of the following conventions:

Ultimately, all of these ''totalitarian'' strategies end the same way, at first, by envisioning a domain X that is big enough to encompass all the objects of thought that might demand entry into a given discussion, and then, by invoking one of the following conventions: