Changes

: ''G'' = {''G''_''j''} = {''G''_''j'' : ''j'' ∈ ''J''} with ''G''_''j'' ⊆ ''P''_''j'' × ''Q''_''j'' for all ''j'' ∈ ''J''.

: ''G'' = {''G''_''j''} = {''G''_''j'' : ''j'' ∈ ''J''} with ''G''_''j'' ⊆ ''P''_''j'' × ''Q''_''j'' for all ''j'' ∈ ''J''.

Here, J is a set of actual (not formal) parameters used to index the OG, while Pj and Qj are domains of objects (initially in the informal sense) that enter into the dyadic relations Gj.

Here, ''J'' is a set of actual (not formal) parameters used to index the OG, while ''P''_''j'' and ''Q''_''j'' are domains of objects (initially in the informal sense) that enter into the dyadic relations ''G''_''j''.

Aside from their indices, many of the Gj in G can be abstractly identical to each other.  This would earn G the designation of a ''multi-family'' or a ''multi-set'' according to some usages, but I prefer to treat the index j as a concrete part of the indexed relation Gj, in this way distinguishing it from all other members of the indexed family G.

Ordinarily, it is desirable to avoid making individual mention of the separately indexed domains, Pj and Qj 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:

Aside from their indices, many of the ''G''_''j'' in ''G'' can be abstractly identical to each other.  This would earn ''G'' the designation of a ''multi-family'' or a ''multi-set'' according to some usages, but I prefer to treat the index ''j'' as a concrete part of the indexed relation ''G''_''j'', in this way distinguishing it from all other members of the indexed family ''G''.

<pre>

Ordinarily, it is desirable to avoid making individual mention of the separately indexed domains, ''P''_''j'' and ''Q''_''j'' for all ''j'' &isin; ''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:

Xj = Pj U Qj, P = Uj Pj, Q = Uj Qj.

 

</pre>

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

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

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

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

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: