Interpreter and Interpretant • Selection 9

Posted on January 27, 2025 by Jon Awbrey

Transfer

Let’s examine how the transfer of knowledge through the analogy of experience works in the case of Dewey’s “Sign of Rain” example.

For concreteness, consider a fragment K_\mathrm{pres} of the reasoner’s knowledge base which is logically equivalent to a conjunction of two rules.

K_\mathrm{pres} \Leftrightarrow (B \Rightarrow A) \land (B \Rightarrow D).

K_\mathrm{pres} may be thought of as a piece of knowledge or item of information allowing for the possibility of certain conditions, expressed in the form of a logical constraint on the present universe of discourse.

It is convenient to have the option of expressing all logical statements in terms of their models, that is, in terms of the primitive circumstances or elements of experience over which they hold true.

  • Let E_\mathrm{past} be the chosen set of experiences, or the circumstances in mind under “past experience”.
  • Let E_\mathrm{poss} be the collective set of experiences, or the prospective total of possible circumstances.
  • Let E_\mathrm{pres} be the current experience, or the circumstances immediately present to the reasoner.

If we think of the knowledge base K_\mathrm{pres} as referring to the “regime of experience” over which it is valid, then the sets of models involved in the analogy may be ordered according to the relationships of set inclusion or logical implication existing among them.

In logical terms, the analogy of experience proceeds by inducing a Rule about the validity of a current knowledge base and then by deducing a Fact, the applicability of that knowledge base to a current experience.

  • Step 1 is Inductive, abstracting a Rule from a Case and a Fact.

\begin{array}{lll} E_\mathrm{past} \Rightarrow E_\mathrm{poss}, & \text{Chosen events fairly sample Collective events.} & \text{Case} \\ E_\mathrm{past} \Rightarrow K_\mathrm{pres}, & \text{Chosen events support the Knowledge regime.} & \text{Fact} \\ \hline E_\mathrm{poss} \Rightarrow K_\mathrm{pres}, & \text{Collective events support the Knowledge regime.} & \text{Rule} \end{array}

  • Step 2 is Deductive, admitting a Case to a Rule and arriving at a Fact.

\begin{array}{lll} E_\mathrm{pres} \Rightarrow E_\mathrm{poss}, & \text{Current events fairly sample Collective events.} & \text{Case} \\ E_\mathrm{poss} \Rightarrow K_\mathrm{pres}, & \text{Collective events support the Knowledge regime.} & \text{Rule} \\ \hline E_\mathrm{pres} \Rightarrow K_\mathrm{pres}, & \text{Current events support the Knowledge regime.} & \text{Fact} \end{array}

References

  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  Archive.  Journal.  Online (doc) (pdf).
  • Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA.  Reprinted (1991), Prometheus Books, Buffalo, NY.  Online.

Resources

cc: Academia.edu • BlueSky • Laws of Form • Mathstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

This entry was posted in C.S. Peirce, Hermeneutics, Interpretation, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization and tagged , , , , , , , , , , , . Bookmark the permalink.

4 Responses to Interpreter and Interpretant • Selection 9

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