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Directory:Jon Awbrey/Papers/Inquiry Driven Systems (view source)
Revision as of 14:01, 17 December 2008
, 14:01, 17 December 2008→1.3.4.13. Formalization of OF : Objective Levels
| <math>y \gtrdot x : j.</math>
| <math>y \gtrdot x : j.</math>
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Assertions of these relations can be read in various ways, for example:
Assertions of these relations can be read in various ways, for example:
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In making these free interpretations of genres and motifs, one needs to read them in a ''logical'' rather than a ''cognitive'' sense. A statement like "<math>j\!</math> thinks <math>x\!</math> an instance of <math>y\!</math>" should be understood as saying that "<math>j\!</math> is a thought with the logical import that <math>x\!</math> is an instance of <math>y\!</math>", and a statement like "<math>j\!</math> proposes <math>y\!</math> a property of <math>x\!</math>" should be taken to mean that "<math>j\!</math> is a proposition to the effect that <math>y\!</math> is a property of <math>x\!</math>".
In making these free interpretations of genres and motifs, one needs to read them in a ''logical'' rather than a ''cognitive'' sense. A statement like "<math>j\!</math> thinks <math>x\!</math> an instance of <math>y\!</math>" should be understood as saying that "<math>j\!</math> is a thought with the logical import that <math>x\!</math> is an instance of <math>y\!</math>", and a statement like "<math>j\!</math> proposes <math>y\!</math> a property of <math>x\!</math>" should be taken to mean that "<math>j\!</math> is a proposition to the effect that <math>y\!</math> is a property of <math>x\!</math>".
:* In a cognitive context, if <math>j\!</math> is a considered opinion that <math>S\!</math> is true, and <math>j\!</math> is a considered opinion that <math>T\!</math> is true, then it does not have to automatically follow that <math>j\!</math> is a considered opinion that the conjunction <math>S\ \operatorname{and}\ T</math> is true, since an extra measure of consideration might conceivably be involved in cognizing the conjunction of <math>S\!</math> and <math>T\!</math>.
:* In a cognitive context, if <math>j\!</math> is a considered opinion that <math>S\!</math> is true, and <math>j\!</math> is a considered opinion that <math>T\!</math> is true, then it does not have to automatically follow that <math>j\!</math> is a considered opinion that the conjunction <math>S\ \operatorname{and}\ T</math> is true, since an extra measure of consideration might conceivably be involved in cognizing the conjunction of <math>S\!</math> and <math>T\!</math>.
:* In a logical context, if <math>j\!</math> is a piece of evidence that <math>S\!</math> is true, and <math>j\!</math> is a piece of evidence that <math>T\!</math> is true, then it follows by these very facts alone that <math>j\!</math> is a piece of evidence that the conjunction <math>S\ \operatorname{and}\ T</math> is true. This is analogous to a situation where, if a person <math>j\!</math> draws a set of three lines <math>AB\!</math>, <math>BC\!</math>, and <math>AC\!</math>, then <math>j\!</math> has drawn a triangle <math>ABC\!</math>, whether <math>j\!</math> recognizes the fact on reflection and further consideration or not.
:* In a logical context, if <math>j\!</math> is a piece of evidence that <math>S\!</math> is true, and <math>j\!</math> is a piece of evidence that <math>T\!</math> is true, then it follows by these very facts alone that <math>j\!</math> is a piece of evidence that the conjunction <math>S\ \operatorname{and}\ T</math> is true. This is analogous to a situation where, if a person <math>j\!</math> draws a set of three lines, <math>AB,\!</math> <math>BC,\!</math> and <math>AC,\!</math> then <math>j\!</math> has drawn a triangle <math>ABC,\!</math> whether <math>j\!</math> 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, consider the predicate <math>P : J \to \mathbb{B} \}</math> defined by the following equivalence:
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| <math>P(j) \quad \Leftrightarrow \quad j\ \text{proposes}\ x\ \text{an instance of}\ y.</math>
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Then <math>P\!</math> 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 <math>J\!</math>. And yet all of these expressions are just elaborate ways of stating the underlying assertion which says that there exists a triple <math>(j, x, y)\!</math> in the genre <math>G (:\!\lessdot)</math>.
=====1.3.4.14. Application of OF : Generic Level=====
=====1.3.4.14. Application of OF : Generic Level=====