Applying Peirce to Image Interpretation --- Part Two

If we look again at our four categories --- NONE, ALL, UNIQUE and SHARED --- we immediately realize that they are all grappling with a disjunction that is the enumeration of our sources. Recall that we said that Altdorfer is facing the following situation (in the single source case):

Rufus v Arrian v Justin v Schedel v Harlieb v Aventinus

(where v is the usual vel of classical logic, inclusive or): a big disjunction of choices.

Thus, if we see 32k as the number of battle participants on the flag of the Macedonian infantry, we know that it is either Justin or Schedel or Aventinus, but not Rufus, Arrian or Hartlieb.

The problem is that this representation is logically incomplete. What is missing is the precondition that these are in fact all of the possible sources on the Issos battle that Altdorfer could have consulted. So, the more correct logical form would be something akin to (now in sentential representation):

(and  (sourceUsedInCW Altdorfer-Alexanderschlacht-1528 ?X)
  (memberOf ?X (TheSet Rufus Arrian ... Aventinus))
  (not 
     (thereExists ?Y
        (sourceUsedInCW Altdorfer-Alexanderschlacht-1528 ?Y)
        (not (memberOf ?Y (TheSet Rufus Arrian ... Aventinus))))))

Since this construction is so awkward, we usually have syntactic sugar to make this more palatable.

(candidateSourceUsedInCW Altdorfer-Alexanderschlacht-1528 Rufus)

...

(candidateSourceUsedInCW Altdorfer-Alexanderschlacht-1528 Aventinus)

And then some meta-predicate that makes the same point

(completeExtentAsserted candidateSourceUsedInCW)

... most likely in a suitably restricted microtheory context.

While this is inferential successful and will allow us to conclude NONE in the case of the 12k killed Persian foot, or UNIQUE in the case Oxarthes and the Frauenzimmer, it is also historically false. We have in fact no way to know that there are no other historical sources that were available to Altdorfer at that time. In fact, any day a chance find in the Regensburg library, comparable to the one that recently uncovered the Quintus Rufus edition that Aventinus apparently used (cf Wagner-Jehle, Albrecht Altdorfer: Kunst als Zweite Natur, in: Regensburger Studien zur Kunstgeschichte, Bd 17, Regensburg 2012), might reveal another source.

This could directly affect our UNIQUE or NONE queries, or turn an ALL into a SHARED. It might also upend our source dependency analysis in the case of a former SHARED query. 

This is where truth maintenance comes into play. We must at all times be prepared to take this enumerated set extents and re-validate them against the latest state if historical research, and modify our claims accordingly. The specific transformations are as follows (if there is any change, rather than no change):

• NONE into UNIQUE if the new source contains the feature
• UNIQUE into SHARED if the new source contains the feature
• ALL into SHARED if the new source does not contain the feature

Only SHARED would continue as SHARED, albeit potentially influencing the dependency graph. For example, in a situation before Cord Meckseper's Iconography Paper, discussed in Part One, where only Justin's Epitome and Aventinus' Bavarian Chronicle might be in consideration as source for the 32k Macedonian foot, one might be tempted to think that Aventinus used Justin; but the insertion of Schedel's World Chronicle makes opens up new possibilities here.