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By way of anticipating the nature of the problem, consider the following examples to illustrate the contrast between logical and cognitive senses:

By way of anticipating the nature of the problem, consider the following examples to illustrate the contrast between logical and cognitive senses:

1. In a cognitive context, if j is a considered opinion that S is true, and j is a considered opinion that T is true, then it does not have to automatically follow that j is a considered opinion that S and T are true, since an extra measure of consideration might conceivably be involved in cognizing the conjunction of S and T.

# In a cognitive context, if ''j'' is a considered opinion that ''S'' is true, and ''j'' is a considered opinion that ''T'' is true, then it does not have to automatically follow that ''j'' is a considered opinion that the conjunction "''S'' and ''T''" is true, since an extra measure of consideration might conceivably be involved in cognizing the conjunction of ''S'' and ''T''.

# In a logical context, if ''j'' is a piece of evidence that ''S'' is true, and ''j'' is a piece of evidence that ''T'' is true, then it follows by these very facts alone that ''j'' is a piece of evidence that the conjunction "''S'' and ''T''" is true.  This is analogous to a situation where, if a person ''j'' draws a set of three lines ''AB'', ''BC'', and ''AC'', then ''j'' has drawn a triangle ''ABC'', whether ''j'' recognizes the fact on reflection and further consideration or not.

Some readings of the staging relations are tantamount to statements of (a possibly higher order) model theory.  For example, the predicate ''P''&nbsp;:&nbsp;''J''&nbsp;&rarr;&nbsp;'''B'''&nbsp;=&nbsp;{0,&nbsp;1}, defined by ''P''(''j'') &hArr; "''j'' proposes ''x'' an instance of ''y''", is a proposition that applies to a domain of propositions, or elements with the evidentiary import of propositions, and its models are therefore conceived to be certain propositional entities in ''J''.  And yet all of these expressions are just elaborate ways of stating the underlying assertion which says that there exists a triple (''j'',&nbsp;''x'',&nbsp;''y'') in the genre ''G''(<font face="system">:<s>&lt;</s></font>).

 

Some readings of the staging relations are tantamount to statements of (a possibly higher order) model theory.  For example, the predicate P : J -> B = {0, 1}, defined by P(j) <=> "j proposes x an instance of y", is a proposition that applies to a domain of propositions, or elements with the evidentiary import of propositions, and its models are therefore conceived to be certain propositional entities in J.  And yet, all of these expressions are just elaborate ways of stating the underlying assertion which says that there exists a triple ‹j, x, y› in the genre G(:<).

=====1.3.4.14.  Application of OF : Generic Level=====

=====1.3.4.14.  Application of OF : Generic Level=====