Tuesday, February 18, 2020

Logical Foundations for Interpretation

The following discussion of Charles Sanders Peirce is based on the paper by Michael Hoffmann, Problems with Peirce's Concept of Abduction, published in Foundations of Science, Vol 4 (1999), pp.271-305. Hoffmann opens with a long quote from Peirce's mature work that clarifies the concept of abduction, deduction and induction (p.271):
... there are but three elementary kinds of reasoning. The first, which I call abduction ... consists in examining a mass of facts and in allowing these facts to suggest a theory. In this way we gain new ideas; but there is no force in the reasoning. The second kind of reasoning is deduction, or necessary reasoning. It is applicable only to an ideal state of things, or to a state of things in so far as it may conform to an ideal. It merely gives a new aspect to the premisses. ... The third way of reasoning is induction, or experimental research. Its procedure is this. Abduction having suggested a theory, we employ deduction to deduce from that ideal theory a promiscuous variety of consequences to the effect that if we perform certain acts, we shall find ourselves confronted with certain experiences. We then proceed to try these experiments, and if the predictions of the theory are verified, we have a proportionate confidence that the experiments that remain to be tried will confirm the theory. I say that these three are the only elementary modes of reasoning there are. (Peirce, 1905, ca., CP 8.209)

 And later (p275):
“Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea” (Peirce, 1903a, CP 5.171; cf. also Peirce, 1901–2/1911, CP 2.777)
This new idea is due to a form of creativity that Peirce describes as present in every act of perception (p282):

Looking out of my window this lovely spring morning I see an azalea in full bloom. No, no! I do not see that; .... That is a proposition, a sentence, a fact; but what I perceive is not proposition, sentence, fact, but only an image, which I make intelligible in part by means of a statement of fact. This statement is abstract; but what I see is concrete. I perform an abduction when I so much as express in a sentence anything I see. The truth is that the whole fabric of our knowledge is one matted felt of pure hypothesis confirmed and refined by induction. Not the smallest advance can be made in knowledge beyond the stage of vacant staring, without making an abduction at every step.

Perhaps the notion of abduction being present in any mode of perception is too closely stitched along Kantian interests in the distinction between Begriff und Anschauung (which, after all, it should not be forgotten, was developed to counter Humean scepticism, a book that famously had kept up Kant all night).

Perhaps a more productive mode of consideration would be to see this as a general way of hermeneutics. The issue of the circular nature of hermeneutics begins then to cash out more in the direction of iteration over the inductive supports that add plausibility to the initial abductive leap (and here, Alvirez Tucker is quite right, Bayesian modes of inference that explain how the probabilities of confirmation can be employed, can be plugged in quite readily).

For the purposes of the modeling of historical argumentation, this insight then can be translated as follows: We posit an event with Davidsonian structure and Schank-Abelsonian scripts associated at the type level. We then abduce these scripts in a forward fashion to generate our potential candidates for confirmatory verification. This forward generation may require the abduction of additional events, actors and materiel that have their own scripts associated with them.

All of this needs to be understood as embedded in a larger discourse that has participants and a pool of assumptions that function as "facts" in the discourse, i.e. we normally do not expect these to be called into question. Often these facts form the general basis upon which the abductive leap is even predicated (the things the abductive leap has to organize, as Peirce conceptualizes explanation), though Peirce is quite right that internally they are structured just as abductively. It is a convenience of the discourse and a simplification of the research tasks to hold them artificially as "understood", "agreed upon", "non-problematic" or "common knowledge" that need not be independently treated as up for grabs during the explanation phase. (However much later revisionism may expose that simplifying assumption as inaccurate.)

Notice that this model is left-recursive in so far as we can spend all of our time fleshing out the scenario into the minutest detail without ever getting to the point of verification. So some form of sensible heuristical iteration is required in practice, thereby limiting the accuracy of the reconstruction (we may never iterate to the winning posit).

Saturday, February 8, 2020

Alexander in Schedel's World Chronicle

In the World Chronicle of Hartmann Schedel (in German: Schedel, Hartmann / Alt, Georg / Wolgemut, Michael: Das buch der Cronicken vnd gedechtnus wirdigern geschichte[n], vo[n] anbegyn[n] d[er] werlt bis auf dise vnßere zeit, Nürmberg, 1493, digitised by the Bavarian State Library), reports on Alexander the Great as part of the Fifth Age of the World, beginning on sheet number LXXIV with his birth as the son of Philip Perdice.

Schedel reports that Alexander the Great brought 32k foot and 5.5k horse with him (LXXV c1), which Dareios opposed with 300,000 foot and 100,000 horse (LXXV c2). When Darius flees toward Babylon, 62,000 foot have been killed, ten thousand horse, and 40,000 captured. Of the Macedonians, 130 foot and 150 horse were killed. Alexander not only captured the camp with much gold, but also the mother, wife, sister [= which should be the same as the wife, RCK], and two daughters.

Schedel reports that Bersanem and Alexander had a child named Hercules (LXXV c2).

After Darius' flight toward Babylon, then prepares another 400k foot and another 100k horse for the final battle, which Alexander also wins (LXXV c2). Darius first is persuaded to flee, then killed by his own people, and Alexander eventually settles down in Babylon, where he is poisoned.

Schedel makes a mess of the chronology, however, having Alexander in Jerusalem and Sidon before battling Darius, even building Alexandria first (LXXV c1).

Aventinus on Alexander

The Bavarian Chronicles of Aventinus, one of the texts that Albrecht Altdorfer used for his Alexander-Schlacht, one way or another, was published in German in 1526. At this point, Aventinus was already living in Regensburg, having fled there from the anger of the Bavarian duke with assistance of the Bavarian chancellor.

The Digital Library of the Munich Center for Digitalisation of the Bavarian State Library has the scans of the Bavarian Chronicle, based on the edition of Vol IV of the Sämtliche Werke, edited by Sigmund von Riezler and Matthias von Lexer.

For the discussion of Alexander, the important parts are in Book I and range from Chapter 153 to 159.

The important points are as follows:

  • Aventinus gives Arrianus and Quintus Curtius Rufus as the main sources, mentioning the Patrons of these editions as Emperor Sigmund for Arrianus and Duke Ernst of Bavaria for the Rufus edition that Erasmus of Rotterdam had overseen (Bk I, Cpt 153, p.337)
  • Aventinus disparages Johannes Harlieb's rendition of the Alexander romance, though its patrons had been the Bavarian Duke Albrecht and his wife Anna of Braunschweig, criticizing its adding and deleting as well as its lack of Latin skill (Bk I, Cpt 153, p.337)
  • Aventinus gives the number of 32,000 foot soldiers and 4,000 men cavalry both in his overview (Bk I, Cpt 153, p.337) as well as in his description of Alexander defeating the satraps of Darius Bk I, Cpt 157, p.346)
  • The role of Alexander in the prophecy of Daniel regarding the four empires is both given at the summary beginning (Bk I, Cpt 153, p.336) as well as reiterated at the end of his biographical sketch (Bk I, Cpt 153, p.340).
  • The battle with Darios at Issos is described in Cpt 158 as the First Battle (Bk I, Cpt 158 pp.346-347).
  • Aventinus only gives 10,000 horse for Darios, not 100,000, as do many others (Rufus' numbers add to 62k horse, Justin gives 100k, which Schedel probably copied from there), though he agrees with the 300,000 Persian foot that Schedel gave in his Weltchronik (250k if you sum Rufus, 400k in Justin) (Bk I, Cpt 158 pp.347).
  • Aventinus does not describe the women at the battle, nor how many men Darius flees with, nor how many were killed, but has Darius escape to Babylon (Bk I, Cpt 158 pp.347).
  • Aventinus reports the sack of the camp, the "Wagenburg" as he puts it (Bk I, Cpt 158 pp.347).
  • Aventinus does report the capture of the women and family of Darius (Bk I, Cpt 158 pp.347).
    • "Captured also Dareios' mother, house wife, son, daughters, the whole women's quarters, maintained it well until his end." (Bk I, Cpt 158 pp.347)
  • The "Other Battle" with Dareios at Arbela (Gaugemala) is recounted in Bk I, Cpt 159, pp.350ff. 
  • Aventinus reports Alexander's becoming sick and then recovering ((Bk I, Cpt 159 pp.350), then wins the battle and Darios is killed during the retreat, while Alexander takes Babylon (Bk I, Cpt 159 p.352).
Among the more curious points are:
  • Aventinus reports that Alexander fought German tribes ("Teutsche") on his northern border of Macedonia, including some Bavarians, who apparently were scared of having the sky fall on their heads only (Bk I Cpt 154-157 pp342-345).
  • In reference to Rufus, Aventinus claims that 4k Suebians (with Suabia running all the way down to Poland and Hungary) were at the battle ((Bk I, Cpt 159 p.351).
Because the number of Darios horse was so low, I cross-checked them against an edition from 1580 printed in Regensburg, but the number was the same.