Changes

Another way to formalize the defining structure of an OG can be posed in terms of a ''relative membership relation'' or a notion of ''relative elementhood''.  The constitutional structure of a particular OG can be set up in a flexible manner by taking it in two stages, starting from the level of finer detail and working up to the big picture:

Another way to formalize the defining structure of an OG can be posed in terms of a ''relative membership relation'' or a notion of ''relative elementhood''.  The constitutional structure of a particular OG can be set up in a flexible manner by taking it in two stages, starting from the level of finer detail and working up to the big picture:

1. Each OM is constituted by what it means to be an object within it.  What constitutes an object in a given OM can be fixed as follows:

1. Each OM is constituted by what it means to be an object within it.  What constitutes an object in a given OM can be fixed as follows:

a. In absolute terms, by specifying the domain of objects that fall under its purview.  For the present, I assume that each OM inherits the same object domain X from its governing OG.

a. In absolute terms, by specifying the domain of objects that fall under its purview.  For the present, I assume that each OM inherits the same object domain ''X'' from its governing OG.

b. In relative terms, by specifying a converse pair of dyadic relations that (redundantly) determine two sets of facts:

b. In relative terms, by specifying a converse pair of dyadic relations that (redundantly) determine two sets of facts:

i. What is an instance, example, member, or element of what, relative to the OM in question.

i. What is an instance, example, member, or element of what, relative to the OM in question.

ii. What is a property, quality, class, or set of what, relative to the OM in question.

ii. What is a property, quality, class, or set of what, relative to the OM in question.

 

The last and likely the best way one can choose to follow in order to form an objective genre G is to present it as a triadic relation:

The last and likely the best way one can choose to follow in order to form an objective genre G is to present it as a triadic relation:

G = {‹j, p, q›} ?  JxPxQ, or

:<p><math>G = \{ (j, p, q) \} \subseteq J \times P \times Q ,</math></p>

 

: or

G = {‹j, x, y›} ?  JxXxX.

:<p><math>G = \{ (j, x, y) \} \subseteq J \times X \times X .</math></p>

For some reason the ultimately obvious method seldom presents itself exactly in this wise without diligent work on the part of the inquirer, or one who would arrogate the roles of both its former and its follower.  Perhaps this has to do with the problematic role of ''synthetic a priori'' truths in constructive mathematics.  Perhaps the mystery lies encrypted, no doubt buried in some obscure dead letter office, due to the obliterate indicia on the letters "P", "Q", and "X" inscribed above.  No matter - at the moment there are far more pressing rounds to make.

For some reason the ultimately obvious method seldom presents itself exactly in this wise without diligent work on the part of the inquirer, or one who would arrogate the roles of both its former and its follower.  Perhaps this has to do with the problematic role of ''synthetic a priori'' truths in constructive mathematics.  Perhaps the mystery lies encrypted, no doubt buried in some obscure dead letter office, due to the obliterate indicia on the letters "P", "Q", and "X" inscribed above.  No matter - at the moment there are far more pressing rounds to make.