Constantine's Donation and its relationship to the Acts of Sylvester

This rather complex problem was first exposed by Nicolaus von Kues, Lorenzo Valla and the English bishop Reginald Pecock (in his writing against the Lollards). The whole background story of the donation is dependent on the Acts of Sylvester, which narrates the baptism of Constantine by Sylvester after the victory at the Milvian bridge (cf. Wilhelm Pohlkamp, Textfassung, Literarische Formen und geschichtliche Funktion der römischen Sylvesterakten, in Francia 19/1 (1992), pp.115-196; digitally accessible in the Bavarian State Library). The validity of these actus Sylvestri is in turn assured by the pseudo-Gelasian decretum,  a Gallic index of permissible books from the 6th century (cf Erich von Dobschütz, Decretum Gelasianum, in the series Texte und Untersuchungen zur Altchristlichen Literatur, Bd xxxviim 3m  Leipzig 1911, digitally accessible at the Internet Archive) that eventually made its way into the Gratian judicial corpus.

The core problem was that Eusebius of Cesarea, though later condemned as Arian, had himself been the Church historian of choice of Constantin, as Reginald Pecock pointed out, and had narrated no baptism of Constantine in Rome (neither after the battle nor due to leprosy), but placed that even in Nicomedia toward the end of the Emperor's life.

Valla and the temporal Arrow

Thinking about interpretation of historical events for long will make one tend into the direction of increasing under-determination. But there are a few things that work like a hard pruning shear and that are not really debated. These have to do with some of the dimensions of our cognition, to put it in terms of Kantian categories, namely that temporally separate things only have one direction of dependence; and that the same macroscopic object cannot be at two locations (that share no spatial overlap) at the same point in time. 

That was basically all that Lorenzo Valla used to dismantle the claims behind the forged Donation of Constantine to Pope Sylvester. Valla argued that certain phrases were in use during the reign of Constantine and certain phrases were not. For example, during the time of Constantine, there were no satraps. Since the Donation assumes that there were satraps as a political title and role, the text shows no understanding of the time of Constantine and therefore cannot be from the time of the reign. 

What that means for an interpretation then is that we have a situation where we have run out of alternatives and ruled them out. As in the old Peanuts joke, there are no oceans (now) in Kansas, nor in North Dakota, nor in Colorado, nor in Arizona, nor in Utah, nor in Wyoming. Given that there is a finite number of states, we can eventually iterate over all of them and determine if they have oceans or not. Thus with the writings from the time of Constantine; eventually we can look through all of them and come up with something like word counts for satrap for each of them. And we can then make a positive statement of an absence: there are no documents from the time of Constantine that recognize satrap as a political title.

We of course immediately see the problem. How did we get this set of dated documents? By some method like Valla's, involving terminus ante quem and terminus post quem. Presumably involving the same logic that Valla just used. For clearly our set of documents cannot use the Donatio itself. There is then a petitio principii in the sense that we already need to exclude the document under consideration in order to make the determination.

But that may be overplaying the hand of the other side. Surely it is good cross-validation practice to go through a canon of writings and see how well, if one document is withheld during training, the separated document holds up when looking at all the other ones as the training corpus. Or perhaps one can cluster the documents by the language and find that the Donatio is an outlier along several dimensions. There is a way that this determination can be made that is not completely dependent on begging the question.

Perhaps the example of the satrap is not the best one either, because that term did exist before Constantine and had become part of the historical discourse since Herodotus (Book III, 89-93).

Modeling the under-determination

The most important change that we need to make in talking about historiographical interpretation is that we know what is true. We do not know what is true, what really happened, and similar.

At the same time, we have to insist that some interpretations are false. As Umberto Eco pointed out long ago, if no interpretation is false, then every text is the same text, and there is only one text. The phone book of Vienna from 1973 is the same thing as Lenin's writings. If we cannot reject an interpretation, then there is no way to differentiate them, and it is all the same.

That combination of there being no true one answer but many wrong answers must strike many people as strange because most people know that not-true is false and not-false is true. Due to this symmetry that setup is then confusing.

The first point to make then is that this switch from true to false using negation only works in the case of a complete disjunction. We already said that we want to assume that not all texts are the same text, so we have at least two interpretations. So if the competing interpretations A and B are up for discussion, and we can show not-A, then the disjunction allows us to conclude B. So if two people Alice and Bea are locked in a room with a hard piece of candy, and the candy is gone, and we can prove that Alice did not eat it, then Bea must have eaten it. 

For most historical events, however, this strategy fails because the disjunction of interpretations remains open. As David Hume pointed out in Dialogs concerning Natural Religion, some of these either-or arguments suffer from a lack of alternatives or become far from clear when other alternatives are considered (famously, that the world might be like a plant). The most obvious present day case is the restricted alternative between evolution and intelligent design, where the problems of evolution only can imply an affirmation of intelligent design if there are no competing interpretations.

So for the first measure of approximation, historiography cannot show what the true narrative is, only that there are false narratives because the disjunction of interpretations is not complete. Notice that psychologically, this may still be a problem, because a very large number of competing interpretations is almost an attack on conceptual resources, an interpretative denial-of-service strategy.

The next question then becomes however, how to show that an interpretation is false. Suppose that our hard candy contains a substance that some people have allergic reactions to. Suppose further that Alice has in the past shown allergic reactions. Then we can mount an argument that either Alice would have had an allergic reaction or that Alice did not eat the hard candy. Very quickly the devil shows itself in all the details as the tree of dependence and justification begins to extend downward into the minutiae of cellular biology, chemistry, and medicine of human food allergies. And that is just the natural science side of the problem. There are also other events that are historical in that chain, that have the same disjunction of interpretations intervening between the chemical processes, say, and the conclusions that we wish to draw for adjudicating between A and B. Perhaps Alice's prior episode was misdiagnosed; perhaps the reaction was caused by another allergenic substance; perhaps the evidence for that episode is suspect (Alice's grandmother told her, because Alice was too young at the time to remember herself). 

However to resolve the conundrum of the interpretative process, what should be clear though is that we need to be ready to accommodate a shift in the truth value of our supports at any point in time. Precisely because the supports of the sub-theories might shift with any new piece of evidence; precisely because none of these matters are monotonic in the logical sense of the word---truth maintenance as part of the ongoing process of rejustification in the face of discovery becomes paramount. 

David Reich and the effect of DNA research on Archeology

In his 2018 book, David Reich makes an important point when talking about the origins of the Indo-European language:

By tracing possible migration paths and ruling out others, ancient DNA has ended a decades old stalemate in the controversy regarding the origins of Indo-European languages.  

This is then the contribution that the DNA gene tracing can make. First, it can identify possible scenarios because of the markers. At the same time it also shows some paths to be impossible. 

In the particular case of the Indo-European languages, DNA analysis of ancient skeletons turned out to be lucky; the paths that Reich et al were able to rule out (prune in the search space view of the problem) axed all paths for a specific theory.

Notice that this does not say what happened. Reich and colleagues can say that the most likely remaining hypothesis points to south of the Caucasus, either Iran or Armenia, because the population DNAs there are the most similar to what they ended up being in the European heartlands:

... ancient DNA from people who lived there [i.e. south of the Caucasus Mountains, perhaps in present day Iran or Armenia, RCK] matches what we would expect for a source population both for the Yamnaya and for ancient Anatolians.

But as Reich had argued with respect to Colin Renfrew's agricultural hypothesis of language spread, that the populations who brought the agricultural revolution had brought Indo-European with them as well, 

... theory is always trumped by data ...

by which he means that new data will rule out previous paths. Data is the way to prune the search space.

And this pruning works both way, because it is a recognition function. It recognizes what it can accept (the prediction view) and it therefore knows what to filter. Sometimes these functions are couched positively and sometimes they will be couched negatively and that can muddle up the issue too. 

 

2020 Joseph Smith Papers Conference

The Church History Library in Salt Lake City is hosting its 2020 conference.

Panel 1: Interpreting

Spencer McBride: James Arlington Bennett as a supporter and future vice-president for his candidacy. Butterfield as representative of Joseph Smith Jr, original attorney for the US govt during the bankruptcy hearings. The core problem is avoiding the 2nd extradition request from Missouri.

Shannon Kelly Jorgensen: George Bachmann (sp?) in Carthage, Illinois, against John C Bennett.

Stephanie Steed, Brett D Dowdle, Angela Thompson and Stephanie Steed also participated.

Q&A:

• focus on JSJr is broadened by connecting him to women, people of color
• it's a tough place to start with the people being so many
• Joseph Smith Jr did meet with Indians in Nauvoo as they passed through

Panel 2: Power Networks

Paul Reeve, "I Dug the Graves" 

Afro-American Jane Elizabeth Manning was baptized 1842, followed by her brother Isaas Lewis Manning (+1913) that same December baptized, in Connecticut, but went to Nauvoo in 1843, eventually joined the RLDS in London, Ontario, then moved to Utah, rejoining Jane, and switched back to LDS, became baptized again.

Recollections about Nauvoo''s Mansion House, where they had lived during the first days in Nauvoo, gave them new clothes lost, hired to work at the Mansion house (laundress & cook), but called him a prophet and would have laid their life down for them.

Sister Sarah also joined, as well as brother Peter, but also mother and aunt.

About 25 black people were in Nauvoo at this point in time, in a city of almost 12,000 people. Smith Jr was convinced that blacks only had worse socio-economic situations, not genetic. But Smith Jr was not a racial abolitionist, later suggest reimbursing for freeing of slaves. Separation of the races in marriage had his support. Priesthood Ordination was rare, but it was not systematic back then and roughly 1/3 held that of the white men.

Manning dug fake graves for Hyrum and Joseph; the actual bodies of the two were in the basement of the Nauvoo Mansion house. Manning then helped Emma move the bodies to the old log house of the river.

"Uncle Isaac" and "Aunt Jane" was their names in the later articles in the Salt Lake Herald of 1899 in Utah ("First Negroes to Join Mormon Church"). Brigham Young had defined Manning's race as cursed theologically; but Manning's personal connection with the Prophet somehow undercut that notion.

Brian Stutzmann, Conflict with Warsaw

Warsaw, Hancock County, Illinois was the nemesis of Nauvoo. Demoine Rapids in the Mississippi required lightening the road. Thomas Sharp initially supported that railroad, as the cost was about 500k$ a year at that time. Nauvoo refused to participate because of the economic depression, after effects of 1837, Isaac Galen had only sold them on land only because of the no-money down; the railroad did not have such conditions.

Wrote a history of Warsaw, Illinois, quite hostile to Thomas Sharp, editor of the Warsaw Signal, an anti-Mormon newspaper.

Derek Sainsbury, Cadre for the Kingdom

Joseph Smith Jrs electioneers. Smith Jr advocated aristarchy (-> Council of 50) and theodemocracy.

Editorial in Times and Seasons, The Government of God July 15 1842 (Friday) in Nauvoo.

The Campaign, the Kingdom and the Assassination. Smith Jr wanted to be president in the US, or in Texas, California or Mexico, if necessary.

600 electioneer missionaries went out. Example Joseph A Stratton, electioneered in the East, hopefully thereafter England.

William I Appleby former judge, democratic Whig, saw in Smith Jr the solution to injustice and corruption, believed that the Mormons had been predicted by Daniel, published 2,000 copies of a 24-page book interpreting this.

Franklin Richards made a pillar of stone as a testimony to God's plans.

Q&A

• Smith Jr had to distance himself to abolitionism and race mixing initially (1836), but by the presidential platform was supporting open racial vision (1844), the former in AT and the latter in the NT; Brigham Young 1852 speech is racist, no doubt
• Smith Jr's attempt at presidency is a move for religious freedom, gave the president power to intervene if religious freedom was not protected; context of the Bible riots of Philadelphia, Wenton letter of 1842 was supportive but in 1844 the Mormons had been let down
• Sharp tried to recruit support for the Expositor (June 1844), supports a call to arm to defend the press in Nauvoo; almost every issue he was arguing against Smith Jr; the Warsaw library has the complete Warsaw Signal newspaper issues digitally online
• Marshall, Turning point of Thomas Sharp
• Century of Black Mormons (.org), first temple endowed of mixed-racial ancestry in 1845, probably passing as white

Panel 3: Financial Networks

Elizabeth Kuehn: Was JSjr bad at business?

Admits that the shares were HUGE for the time

Sharalyn Howcroft: The Red Store Book

Oct 1842 and Oct 1843 Emma Smith worked as a clerk at the store

Jeffrey Mahas: Labor Disputes and building of Nauvoo Temple

People who were exploiting build the temple were still happy to be exploited

No single critical question; all hunky-dory; so much for science 

Correlating Population with Bank Solvency

In the previous post we discussed two assumptions about Hill et al's 1977 argument regarding the prudence of opening a savings society in Kirtland in 1836. Recall that they had used Coover's enumeration of Ohio banks to conclude that the population in Kirtland should have been sizeable enough to support a modest bank. The presupposition of this claim is, as I noted

• Population size is a good predictor for bank success.

In this post I want to break down the claim that is wrapped in this statement into its constituent parts. The current formulation, though not an inappropriate assumption based on the data that Hill et al had used to make their case, sounds too statistical in nature, while the argument that Hill et al had in mind was in all likelihood more qualitative.

The basic observation is that banks require specie to operate. Specifically, they have to have specie to have their bank notes accepted and to make loans to customers (where the interest charged is part of the income that the bank produces). The way banks obtain specie, other than by accepting deposits, is to take down payments for subscribed stock that they issue. In my dissertation I detail some of the rules of how subscriptions worked and how much of the stock value had to be paid in as specie by what point during the subscription period by the subscribers [RCK15, 230-238] and I replicate the information from Coovers' research in the appendix [RCK15, 425f]. 

Since there is no residency requirement for subscription, subscribers can come either from 

• within the community wishing to have a bank; 
• or can be American financiers, usually at that point in time from the East Coast, 
• or Europeans engaged in trade with the US who wish to park their profits from their trade within the Americas within the US of A. 

Europeans here means wealthy non-Americans and in the majority, British traders. Though the world economy was rapidly moving toward integration---Joseph Smith Sr had been exporting East Coast Ginseng root to China in the years before Joseph Smith Jr had been born [RCK15, 79]---the wealthy traders from Africa, India or the Far East were not involved in American frontier banking.

As Charles Clifford Huntington showed in his 1915 thesis, A History of Banking and Currency in Ohio before the Civil War (available at the Internet Archive), there was much concern about capital flight in Ohio in the 1830s, due to the large number of financiers from the East Coast and even from outside the country proper that were involved in buying Ohio banking stock (Hunt15, 137f). In fact they owned over 70%, US$3.35 million of the US$4.73 million in capital stock in the state, before March of 1834 [RCK15, 233], as researched by the Cincinnati Republican.

There were examples of banks completely supported by the community, such as the infamous Owl Creek bank; or the Bank of Wooster that failed in spite of $150,000 paid-in stock and a leverage of 1.29 [RCK15, 245]; but the more typical case was the Ohio Life Insurance & Trust Company, who had only three residents of Ohio among its twenty board members and was held, in the words of the Ohio Monitor of March 14, 1836, "by the Wall Street gentry of New York" [RCK15, 234]. The company had given loans totalling almost US$2 million in 67 counties of Ohio, which were secured with some US$4.34 million worth of real estate---a very different league from the banks of Wooster mentioned above or of West Union, which had $20,000 of species at 2.42 leverage when it failed.

With this information at our fingertips, we can now note two things:

• For the successful banks, the majority of the capital stock was held by out-of-state financiers.
• Banks that were predominantly funded from within the community failed during the banking crisis of 1837.

Again, the Bank of Wooster is the most interesting example. Its was chartered in February of 1834 with US$100,000 and immediately oversubscribed by its population by 25% [Hunt15, 141]. In 1837, with a leverage of 1.29, it was almost stellar, $150,221 paid in for a circulation of $194,289 notes. Perhaps the easiest way to explain this is the lack of expertise? 

Population and Bank Support

In their 1977 paper, Hill et al. The Kirtland Economy Revisited (BYU Studies Vol 17, 4, Article 2) argued that the idea of founding a bank such as the Kirtland Safety Society was an appropriate idea based on the size of Kirtland and the number of other banks in existence in other communities.

Kirtland at this time was one of the larger communities in northern Ohio---a number of smaller communities already possessed banks. Judging from the successful experience of other banks in Ohio, one with as little as $20,000.-- in paid-up capital, Kirtland probably could have supported a modest bank. (433)

In a footnote they go on to enumerate some of the locales with banks that Hill et al had in mind.

... smaller banks in northern Ohio included Warren (3), Ravenna (2), Canton (2), Salem, Youngtown, Elysia, Ashtabula, and Cuyahoga Falls. Cleveland, which had perhaps twice as many people [as Kirtland, RCK] had eleven [sic RCK] banks. (433 Fn 61)

In my dissertation,  where I discuss this argument (246), I argued that this exposition was misleading on multiple grounds. But in order to fully counter the claim by Hill et al, one needs to first explicate the argument structure. And in order to explicate the argument structure, we need to make clear that this argument is trying to support the larger notion that the creation of a bank, as endeavored by the Church leadership in 1836 was a reasonable thing to undertake and had all of the appearances of success on its side. 

So the argument structure goes something like this:

• Warren had a smaller population than Kirtland.
• Warren had three banks.
• Raven had a smaller population than Kirtland.
• Warren had two banks.
• Canton had a smaller population than Kirtland.
• Canton had two banks.
• Salem (Ohio) had a smaller population than Kirtland.
• Salem had one bank.
• Elysia had a smaller population than Kirtland.
• Elysia had one bank.
• Ashtabula had a smaller population than Kirtland.
• Ashtabula had one bank.
• Cuyahoga Falls had a smaller population than Kirtland.
• Cuyahoga Falls had one bank.

The inductive leap of this assumption then is that towns with smaller populations than Kirtland had between one and three successful banks in 1836. We will call this argument Min1-3

(Note: The bank of West Union, which is the one of $20,000 capitalization, is not in this list. Perhaps it was not possible to arrive at population data for West Union?)

The argument in the case of Cleveland goes in the other direction.

• Cleveland had double the population of Kirtland.
• Cleveland had twelve banks.

The inductive leap here is that Kirtland should be able to support six successful banks. We will call this argument Max6.

Combining these two inductive leaps Min1-3 and Max6, we can now create another inductive leap, to wit:

• Kirtland's population sized should have supported at least one to three banks (Min1-3) and possible as many as six banks (Max6).

We will call this argument Kirtland-1-3-6. 

Hill et al are arguing that the Church leadership made this same sequence of inductive leaps. They have no documentary proof for this, but it is a reasonable imposition: the members of the Church leadership were well connected with political leaders and the legislature; furthermore, they had taken out loans before and engaged in real estate speculation, a task that required banking connections during the boom times of the federal land sales [RCK15, 248f]. Assuming Kirtland-1-3-6 and the absence of any banks in Kirtland in 1836, at all, it was a reasonable idea to found one and to expect it to succeed.

The first problem is that the argument is prefixed by the assumption that Hill et al interpreted the data given in Coover correctly. Unfortunately, as I argued in my dissertation [RCK15, 247], that is not the case. Coover's list gives all the banks known for Ohio between 1803 and 1866, not just the banks operating in 1836 time. In fact, since Coover was a collector of banknotes, all that can be said is that at some point someone issued a note with the name of a bank located in one of these cities (and some people made notes for non-existent banks, as Coover pointed out). 

As I pointed out in my dissertation [RCK15, 247], the following banks have to be removed from the list, because we know nothing about when and how successfully they operated:

• Two of the three banks in Warren.
• Both banks in Ravenna.
• One of the banks in Canton.
• The bank in Salem.
• The bank in Youngstown.
• The bank in Elysia.
• The bank in Ashtabula.
• The bank in Cuyahoga Falls.
• Ten of the twelve banks in Cleveland.

In terms of inductive evidence that is a slaughter. 

But there are further problems. There are two key unstated assumptions in this argument:

1. Population size is a good predictor for bank success.
2. Past success is a good predictor for future success.

The first is wrong on the observation, as spelled out in my dissertation, that a lot of the money in Ohio banking was from out-of-state, both financiers of the East Coast [RCK15, 244] as well as Europeans doing import/export business with the United States. In the 1830s, the United States was effectively a third-world country, running a huge trade deficit on its import of goods and export of raw and somewhat processed materials. Because these problems were common to all of the frontier states, the situation was the same in Michigan for example.

The second one seems like a reasonable slogan, but one could only have agreed to that assumption with respect to a bank if one was ignorant of the then-brewing storm regarding small bills in general (New Jersey and Maine in 1835 forbidding small bills, Virginia & Maryland & Pennsylvania purging small bills from their monetary system at the same time). Furthermore, the no-bank Democrats had just won dominance in the legislature of Ohio, they had been cool on charters for bank for a while now, and they had passed no charters in 1836 by the summer, pointing to the unused potential for capitalization in the existing charters [RCK15,234f]. Ohio was also pressuring its bank during the spring of 1836 with threats of taxation should they not strive to remove the small bills from circulation, with all $3 bills phased out by July 4, 1836. 

Perhaps even more importantly, President Andrew Jackson on July 11, 1836 had issued his famous specie circular via the Treasury, which eliminated local banknotes as method of payment for purchasing federal lands and insisted on hard specie. Professional cashiers left the frontier banks after this circular, unless their fianciers promised additional monetary support, as Henry Dwight of Massachusetts did to H.K. Sanger, who was cashier at the Bank of Michigan [RCK15,244].

Post Scriptum

It is not entirely clear when the Church leadership decided to go ahead with the plan for the Kirtland Safety Society. Oliver Cowdery was already traveling to New York to inquire into credit for printing plates in August of 1836. The revelation promising resolution to the financial plights (v5) that is now Doctrines & Covenants 111 was given in Salem, Massachusetts, August 6th, 1836. The letter that reports the decision was printed in the Messenger & Advocate in September 1836.  

Points that I did not make clear with reference to this argument in my dissertation include that the Kirtland Safety Society was anything but modest [RCK15, 250], and the number of Cleveland banks in the research by Coover on Ohio Banking Institutions from 1913, on which the observations were based, is twelve not eleven.

Argument Structures around the Kirtland Safety Society

While historians want to be both educated and corrected by their sources, it is often difficult to pin down that that exactly means. In the following, I want to look at a few examples of how this plays out in the case of the economic history of the Kirtland Safety Society (this is Chapter 10 in my dissertation).

The backbone of course is the chronology. Many narratives already fall apart due to not aligning with the basic chronology of the matter. Of course the selection of what elements to include in the chronology brings us back to the problem of enplotment.

It is important to realize that a chronology is not a sequence of dates, but a sequence of dated events. The distinction is crucial, because dates are just chronometric units, while events have actors and properties and are enmeshed in a event sequence, as well as a geometric positioning. The chronometric units have a canonical order, but it is independent of all semantic contents---which is precisely what makes them units.

Perhaps it is best to first to tease apart the pieces that can go into a historical argument. For an intentional action, we have to presuppose some kind of script, that is, a codification of the "usual" way to do this. This would be the usual way from the point of view of the contemporaries, of course, not from the point of view of the historian. 

The "usual way" is typically distilled in some form from another event that has a similar structure. As Eduard Meyer pointed out (1912) [cited in the dissertation], it is this compare-and-contrast operation that is at the root of the historical research effort for distinguishing the common from the unusual. In the Kirtland case, I used the Owl Creek Bank, which did occur in Ohio about two decades before the Mormon arrival, as well as the Old Bank of Michigan, in which Joseph Smith~Jr's uncle Stephen Mack had participated. In the end it was the cross-comparison between these three instances that provided the fodder for the historical reconstruction.

These three elements were underpinned on the one hand by a history of banking in Ohio, mainly a sequence of state legislature actions and bank foundations (which had to be chartered by the legislature), and a history of the more global economic settings both in Ohio proper and in the US. This was the place for wealthy East Coast magnates and European importers, mainly from England, that had a strong influence on the money supply. This was also the place for Jacksonian interventionism at the national level and the ins and outs of the federal land sale that had such an impact on the monetary supply. All of these lines had their own event sequence with its own "arc" so to speak, mostly expressed as supporting or blocking specific aspirations on the legislative side and injecting or removing money on the financiers' side. 

The final element was the chronology of the creation and dissolution of the Kirtland safety (anti-)banking society itself. The comparison with the other banking charters in Ohio as well as with the Owl Creek Bank highlighted the inversion of the order of steps (charter last) as well as the enormous leverage that had been prototypical of other bank failures in the past and would eventually be outlawed in 1839 by the legislature, requiring 1:3 at the most.

For all of these elements, the observation of the overdetermined asymmetry of causation was in effect. For example, only a small fraction of the notes issued by the Kirtland society survived, supporting reconstructive efforts such as simulations how many bills of which type might have been issued. Also, the stock subscription book survived, allowing to determine which families of the Mormon elite had taken out the most stock and subscribed how much of their money. Some newspaper editorials and similar statements survived, but many other actions and their direct and indirect effects remain inaccessible, lost to time.

Some Birthday Stories

Consider this story template to generate yes/no questions:

On May 12, [2020//1930/1890], [Emma/Charles] celebrated their [10th/20th/40th/80th] birthday in London. When their sibling [Charles/Emma] ate the [cake/pony/Faberge egg/iPhone], the birthday child cried. Does that surprise you?

Stories are surprising when the mix of ingredients does not go together. Some of these incongruencies would be temporal: An iPhone in 1930 (or a dodo bird at any of the offered points in time, having become extinct in the 16th century already). 

Some of these incongruencies would be structural: eating a pony or a Faberge egg is hard work and could not be accomplished quickly. 

Some of these would be social conventions surrounding emotions: a 40-year old man in 1890 London, that is Victorian society, would be expected not to cry over the loss of a birthday present, but a 40-year old woman may well be expected to. 

Some of these might be unusual but acceptable: though a Faberge egg cannot be eaten (despite what it name seems to imply to a noun tagger), it is also an odd present for a 10-year old (possibly excepting upper aristocracy). Eventually, as the age of the celebrated person increases, the presence of a sibling itself becomes unlikely without additional information.

Meandering and the Asymmetry of Overdetermination

The meandering nature of historiographical reconstruction has occurred to anyone who has worked in that field at all. One starts out at a general topic, such as the sources of a historical painting or the origins of Mendelian experimentation, and finds oneself, a couple of units of effort later, in the middle of contemplating the household receipts and textual editions (not to mention X-rays of the painting under consideration) or computing the total number of pea plants that the Moravian monetary garden (plus glass house) might have held or the names and origin of Mendel's four assistants (mostly lay brothers).

How did one get there?

Perhaps the most straightforward suggestion is afforded by David Lewis and his observation on the asymmetry of overdetermination of actual worlds (1973). The observation here is the plurality of traces that causal events leave and the point is to allow the philosopher by comparison to establish the causal relationship with respect to the effects. 

At issue is not the correctness of Lewis' observation per se but the proposal that actions in the real world that are causal leave a plurality of traces that extend into the historical record in a bewildering variety of ways. (The image of ripples on a pond is usually exercised at this point in the discussion.) All the same, time is the great destroyer and as the spans increase and other ripples chase across the pond, the traces become effaced. The artist's studio has disappeared, and so have his tools, materials and assistants; the Mendelian fields and glasshouse, should they have survived at all, were preserved only due to the conservative nature of the institution where he experimented. The historian is thus faced with "temporal cluster bombing" that works counter to the very tracing of the effect chains the historian wishes to undertake. At the same time, if the event was "big" enough (the extinction of the dinosaurs by meteorite comes to mind) the large number of traces prevents the erasure of every single detail---too much shocked quartz, too much iridium, too little volcanic activity in the Deccan traps.

My mother still remembers where she was and what she was doing the day John F. Kennedy was assassinated in Dallas, even though she was then an Austrian teen. It would be difficult to erase all traces, to spill damnatio memoriae on all the causal lines, that reverberated through the global village of modern media when that US president died. Diaries, letters, mementos, not to mention an avalanche of conspiracy theories all take their origin in that event. 

It is this situation that is both the possibility of performing historiographical research over the ages and the impossibility of focusing the ontology of investigation up front, as the lack of readier-made traces and the ability to decide between competing interpretations will push the historian farther and farther down the causal chain to refute some of the interpretations (and herein lies the underdetermination of historical reconstruction, as Tucker pointed out) and strengthen the others (where the notion of strengthening may be related to Lewis' similarity metric, a point that needs further analysis). Here Lewis' points of world become relevant again. 

Life of Aventinus

In the first volume of the Collected Works of Aventinus (actually Johannes Turmair), there is a biographical sketch that provides interesting tid-bits that are worth noting.

Reading Notes

• Aventinus had contact to Conrad Celtis circle in Vienna and their Danubian society during his studying in Vienna.
• In 1516, Aventinus founded a similar society in Ingolstadt which included Bavarian chancellor Dr Leonhard von Eck, who was the "head and protector" (p.XV) of that association. However, the association was only active until 1520, and the authors blame the rabies theologica of the theologian Dr Eck in Ingolstadt for this (ibid).
• 1517, wie Herzog Ernst becoming the bishop of Passau, Aventinus was elevated to court historian for the Dukes Wilhelm and Ludwig (p.XVI).
• After two years of data collection (1517-1519) for his Historia Baiorum, Aventinus spent 1519 to 1521 in Abensberg, where his sister took care of him, to write the first draft, immediately followed by a second draft (p.XVIII). Occasionally he interrupted his work, for example, to meet with Chancellor von Eck in Regensburg (ibid).
• November 1522 he begins with the translation of the Historia into the vernacular (p.XIX)
• Aventinus makes another influential friend in the Cardinal and Archbishop of Salzburg, Matthaeus Lang, who keeps him at Salzburg for two months in the Spring of 1523 and will remain his friend even into the 1530s (p.XX).
• In 1524, the dukes raised his salary from 60fl, which he had received already for tutoring Ernst, to 100fl annually, provided he gave them control over the printing of the chronicle and would not accept offers from other dukes without notifying them (p.XXI).
• Aventinus managed to glide through the Peasant Revolt of 1525, which the dukes quickly battered down, and enjoy life in Abensberg in 1526, now with the official order to translate his work into German (p.XXII).
• In 1527, he began to frequent Regensburg, because there was no one in Abensberg that he could discuss matters with (ibid); the authors suggest it was the beginning of Aventinus being pulled into the question of the Reformation (p.XXIII).
• Unsurprisingly, as the Introduction of his work shows, he thinks of history as a moral and political effort (p.XXVI).
• In his moral crusade, his preferred enemies are the clericals, and especially the monks, and his warning against them extends even into Anti-Semitism: "Beware with equal care vis-a-vis a preacher, a Jew and a wolf." (Sigh ... :P) (p.XXIX).
• In his crusade against the church Aventinus also reveals a crusade for German Nationalism, even though he is employed by Bavarian dukes, for the German empire and the emperor (p.XXXI). "Deutschland ist nach seiner Ansicht in das Erbe des römischen imperium mundi eingetreten, "die vierte und letzte Monarchie der Daniel'schen Weissangung, an deren Fortbestand die Weltdauer geknüpft ist" (ibid).
• "Sonderinteressen zu verfolgen und eigene Politik zu treiben verurtheilt [sic] er stets als Unrecht und Untreue gegen die Gesamtheit." (p.XXXII) 
• For this reason, Aventinus criticizes the aristocracy for their focus on their special interests and advantages (p.XXXIII), leading him to demand public justice and free discourse (p.XXXIV).
• The three external enemies are the Pope, the French and the Turks (p.XXXV).
• For Aventinus, Religion is primarily about Justice, and he can praise the Romans and the Ancients for being just (p.XXXVII) --- including Alexander the Great.
• In the discussion of his historiographical achievements, the overly strong dependence on the forged Chaldean book of Berosos of Annio of Viterbo (Giovanni Nanni) is a black mark (p.XLI). His friend Beatus Rhenanus exposed the work as a forgery, but Aventinus either did not share his convictions or died before he could (p.XLII).
• The publication of his works was blocked by the two dukes (p.XLVI) since 1522, when they had forbidden the departure from the old faith, as supportive as they had been of reformatorical writings earlier, and there was just too much critical writing in Aventinus' books.
• Dr Eck of Ingolstadt got the dukes to execute tough punishments for the lapsed, which cost several anabaptists their life (ibid).
• 1528 was a troublesome year for Aventinus, the Turks were back in Hungary and Carinthia and were sending people into slavery (p.XLVII).
• Aventinus had friends in Regensburg, two of the cities' Stadtschreiber, as well as the Abbot Minzer, and there had been both the Jewish pogrom as well as the beginnings of the Reformation, both related to Dr Balthasar Huber, the preacher at the cathedral (p.XLVIII).
• But then (ibid) the preacher Nicolaus Georgius Fabri, a friend of Aventinus, was arrested in Landshut, where he was the chaplain of Duke Ludwig, and this struck fear into Aventinus, who fled to Regensburg. More preachers were imprisoned, 
• Aventinus himself was imprisoned on October 7th, 1528 (p.XLIX), but the Chancellor Leonhard von Eck quickly intervened to free him again, eleven days later, from jail, and Aventinus quickly returned to Regensburg (ibid).
• Aventinus had been an active Catholic during his time as tutor of Prince Ernst, and he prayed the breviary every day with him in 1513 (p.L).
• Aventinus knew too much history to believe in the indulgences and was too much a critic of the clergy and the monks, but he may not have ever left the Faith, comparable to Dr Konrad Peutinger and other supporters of Church reform (p.LI).
• During this time, he was sick and deeply discouraged and only found comfort in his work on the Germania Illustrata (p.LII).
• Aventinus tried to influence the matter by marrying Barbara Fröschmann, a Suebian girl from Niederrieden, December 1529 (p.LIII), but the expectation for this marriage as a source of calm in these confused times apparently did not materialize. However, the evidence for Aventinus being unhappy with his wife comes only from his biographers (p.LIV), and they had two children (two of which died quickly), and were able to buy a house in Regensburg for 150fl without selling the Abensberg estate. So clearly it was not a financial problem. And the inventory at his death (middle of the long footnote on p.LV-LVII) of old books, some from the 9th century, is impressive.
• In 1530, Aventinus was looking for a new position, and Philip Melanchthon suggested to him to try his friend Matthaeus Lang in Salzburg (p.LVII), instead of going to Saxony or even Wittenberg.
• His old friend Chancellor Dr von Eck helped him out and hired him as the tutor for his son Oswald at Ingolstadt (p.LVIII), a task he kept up until Christmas 1533, when he caught cold on his way back to Regensburg (ibid) and died January 9th, 1534.
• The publication of his main works was suppressed for many years after his death (p.LIX): the German Chronicle's Book I was printed in Nuremberg in 1541, and the Bavarian Chronicle in 1566 in Frankfurt am Main. 

Discussion

• When the authors write: "Wie unverständig es war, seine Mahnworte zu verachten, zeigte die schon im Jahre 1529 erfolgte Belagerung Wiens durch die Türken." (p.XXXVI) then this skips the fact that the pamphlet against the Turks was reworked in 1529.

Aventinus on why God lets the Turks defeat the Christians -- Part 1 and 2

Among his smaller writings is a pamphlet in which Johannes Aventinus (Turmeyr) reports on his musing about why God allows for the Turks to defeat the Christians and what the Christians can do in the face of so much suffering.

Aventinus notes that his thinking began with the death of Ludwig, King of Hungary and Bohemia, on the battlefield of Mohacs (though he cites the event, not the locale) [172] but that the context of publication is the Turkish emperor besieging Vienna in 1529. Aventinus complains that he had warned people in high places of the impending dangers but had been ignored due to the unpopularity of his message (depicting the truth as a coarse farmer's wife that cannot bribe and speak after people's wishes) [172]. Similarly, the emperors, Friedrich II, Henry VII, Sigismund and Maximillian had written against the problems with the estates and the popes, but no one seems to read them [173]. Aventinus could have ignored these warnings as well, but his friends E.W. (Ernst and Wilhelm, the dukes of Bavaria?) pressed him, given how the present danger of the Turks in Austria makes the matter urgent ("the water is reaching the mouth"), and so he composed the pamphlet in four parts [173]. The first will explain the causes, the second the indicators for worst parts to come, the third what the Ancients---Christians, Jews and Pagans had done---and the fourth proposes reforms that will prevent this from happening in the future [174].

Christ alone is the throne of grace, powerful, self-ruling lord in heaven, hell and on earth, the eternal, just, natural pope and emperor, our doctor, salvation and justice; .... [174]

Part I 

Aventinus [175] discusses the great abuses of the masters, of the Church and of the world, that lead to this calamity. Because God is merciful, He would not be punishing Christianity if there was not a reason [175]. Concilia and Diets have not figured out why the Turks have grown so strong [175];  the Knights of St-John wrote to the emperor when Rhodos was under attack, that the Turkish Sultan was not afraid of the Empire, much less the Germans, because they are divide, focused on physical pleasures, cannot tell top from bottom and practice no justice [176]. And since, as Aristotle argued, all things in nature are naturally good [177], it must be the government that is the problem. Aventinus reminds his readers that even the pagans know that the love of money, avarice and the own advantage is a source of injustice [177]. The rapacity of the bureaucracies and the knavery of the judges amplifies this and was the death of the Roman empire [177]. Even worse than the unfair and impatient prince is the money fool ("geltnarr"), who only focuses on increasing his profit while showing neither mercy nor understanding for the lower orders [178]. Even the pagans handle this situation of the poor being oppressed by the rich better [179], how the office holders steal from the rulers even:

The office holders grow rich; the rulers rot away together with the lands and their people. [180]

Vox populi vox Dei is here taken to mean that the protest of the poor is the accusation of God [180]. Aventinus includes the hanseatic organizations in these, and how the money-fools press the last bit of bloods from everyone else [180], worse than any tyrant in the history of the world. They think themselves to be good Christians but are not even good pagans [181]. Since bringing life is the hard part, not bringing death, God cannot be react or He would stop being God [181].

If you punish the heretics, why do you not punish the bishops, pastors and the monks? [181]

Aventinus now refers to Maximillian's pamphlet against the German estates, calling himself a king of kings, because all of the rules of Germany want to be their own master and do not suffer the emperor [182]; the money fools take it from everyone and no one pursues unity. This is the core of the problem (though coin, toll and customs association could be mentioned as well, since they weigh down the people and anger God) [182].

But the Christian and the Jewish authors teach, that such abuse has its root in the wrong worship of and service to God [183]. God is infuriated and he uses one people to punish another:

Always one people has to punish another, eliminate and exterminate them [183]

The one form of this blasphemy is to exhibit outwardly proper religious behavior and long prayers while stealing from the widows and stiffing the poor [183]. This is especially galling in the case of the barfeeted monks [183], who sell their prayers and will end up like the stupid virgins, without any [184]. Aventinus sees the mendicant orders as the source of much of this, and compares the light of their churches to the darkness of their hearts [184]. Mendicant orders are like whore houses and equally forbidden by God [184]. They take and never give and the preaching orders are no better [185]. And the female orders are worse than the Amazons attacking the Greeks ever were; did StPaul and StJerome not say that the women should be quiet in church and not sing loudly? [186] And the auxiliary bishops (Weihbischof) the same, who pay for the bishopric of a far-off land that the Turk now controls, swear to go there and preach but never mean that, perjuring themselves? [187] This was the kind of thing that the reformation of Emperor Sigismund was planning to fix [187]. Aventinus compares the pastors unfavorably to the Good Shepherd, who are unwilling to sacrifice anything for their sheep.

They take leave of absence, eat the sin and drink the evil of mankind, preach nothing, do not earn a farthing, place vicars like themselves over the poor, don't inquire into the salvation of the poor people. [187]

The religious lords were supposed to be poor but now they are rich:

It was forbidden that bishops, prelates and clergy own any worldly good, no churches nor feudal estates, to pull toward them, had to get by on the Tenth. ... Now they own cities, markets and castles, and do not want to do anything for it. [188]

The once who have to support this are the poor, and Aventinus again points to Emperor Sigismund's reformation [188]. Now, with the Turks near Vienna again and threatening Bavaria, people still refuse to see the signs and recognize that God is getting ready to punish them for their sins [188].

The other blasphemy [189] is the way in which both clergy and laymen live openly in violation of the laws of God [189]---but especially the clergy, who will not marry but practice whoring, will not be honorable but are traitors and knaves. Again Aventinus refers to Emperor Sigismund's attempts of reform in the face of such simony that put them into imperial banishment in the empire of God [189]. For anyone who wants to live in agreement with the word of God, they are the worst traitors [190]. If their deeds happen without intent, they lack diligence, if they happen on purpose, they are knaves of the worst kind [191]. Adultery, weakening the virgins and abusing the widows, those are worse crimes than thievery in the eyes of God, but the only thieving that is punished is that of the poor, and the highers ones simply add it to their pile [191]. David was punished for his adultery, and Troy destroyed over adultery [192]. It would be better to have no order at all than one that is not enforced [192]. Even if by now all have fallen short, the only way to remedy the matter is to start at the head, because once the head is cured, the whole body will already be doing better [193]. A concilium needs to take place [193], as Pope Hadrian allowed at the last Diet, and as Emperor Maximilian I had demanded in his writings against Pope Julian [193].

 But the Pope fears a free concilium of the church like the devil fears holy water .... [194]

And Constanz and Basel have shown them that this is where popes are removed from office [194]. In the face of all these pointless consultations, the Turks say [195]:

The Christians consult much and have many diets, in the mean time I conquer land and people. [195]  

When they meet in Hungary, the Turk invades Friaul and beats the Venetians; they meet in Worms and the Turk wins Greek-Weissenburg; they meet in Nuremberg and the Turks take Rhodos; they meet in Speyer and the Turk invades Hungary and kills the king [195].

Nobody wanted to come and help [the King of Hungary, RCK], however much he kept writing for help; they [Herzog Ernst of Bavaria, RCK] had to help the Bishop of Salzburg against his own poor people at the same time instead. [195]

That year, they met in Speyer again, and the Turk invaded Austria and besieged Vienna, an no one knows how the story will end [195].

Part II

Aventinus now turns to other signs of coming disaster [196]. Aventinus now enumerate learned men who have prophesied that the Turks would come up to Cologne, that the Papacy will suffer and eventually be destroy, and that the Roman Empire before the Judgement Day will return to Asia [196],

The sundown will be suppressed again, the sunrise will rule again. [197]

Equally, Ezechiel had prophesied that the peoples Gog and Magog would come and cover the faithful [197]. 

Now many interpret Gog and Magog as meaning the Turks and the Saracene Belief [i.e. Islam, RCK]. [197]

Aventinus reminds them that at the Diet of Speyer, Philip Melanchthon had published a book that warns about how the Turks will fulfill the prophecies of Daniel, and things would have been better if the powerful had listened to him [197]. Also there were many signs in the heavens, but people only make fun of them [197]. As King David warned in his psalms, the godless do not recognize the anger of God [198]. Did God not embarrass the pope and have him called the antichrist in the streets? [198] Does anyone still fear his banishments?

I see no one who still fears him or gives much [for his opinion, RCK], except for those, that benefit from it, if they did not anymore either, they'd be his worst enemies. [198]

But Rome was sacked by the German Landsknechts [198], and the powerful French king embarrassed [1525 at Pavia, RCK], and now they write stupid pamphlets [199].

If the heads do this, there is no need to ask nor wonder, why the Turks are coming: they must punish the evil, as the scourge and rod commanded by God. [199]

The Franks and the Suebians have been attacked by their own farmers [199]. Even CharlesV, the powerful emperor, sees his siblings in danger, and the death of his brother-in-law Ludwig, king of Bohemia and Hungary [during the battle of Mohacs, 1526, RCK] [200]. Aventinus sides with Luther against Georg of Saxony and the Emser Testament, complains, that the lords do not understand Greek but want to help the clergy with their knavery [201]. God is ready to punish them, after several century of difficulties with the Turks [the crusades? RCK] [201].

(continued in next post)

Justins Epitome of Trogus and Hartmann Schedel

The story at Justin's Bk 11, Chapter 8, reads almost like Hartmann Schedel.

But there is also proximity to Aventinus too, bringing the siege of Tyre before the mentioning of the return of Darius to Babylon.

Aventinus' simile for the big wall

When Aventinus describes the stone blocks that Alexander used to fill in the moat around the city of Tyre during its investure, Aventinus thinks of Regensburg and its old city wall:

Then Alexander thought of an unbelievable thing, had no one for that, who could have suggested this: mobilized land and people, let them bring there big trees, that is with their branches still, the same big stones, square mined pieces (just as they are in Regensburg at the old wall) || from an old broken city nearby, sunk them in the sea, banked up from the land to the city, so that he would be able to move dry and straight from the land toward the city with the might of his army. (own translation)

Da unterstuend sich Alexander eines ungleublichen dings, het niemant darfür, das es geratten solt: pot land und leuten auf, lies zuehin pringen groß päum also ganz mit esten, dergleichen gros stainene vierecket außgehauen stuk (wie zu Regenspurg an den alten mauern sein) || von einer alten zerprochen stat daselbs, versenkts in das mer, macht vom land pis in die stat ein beschüt, das er truckens und ebens fues auf dem land mit herskraft für die stat mocht ziehen.

(Bavarian Chronicle, Bk I, Cap 158; p.347 and p.348 in the Academy edition)

Aventinus complains about the Turks in Alexander Depiction

I missed this on the first reading of Chapters 153 and 158, but when Aventinus gives the context for the Battle against Darius (Book I, 158 of the Bavarian Chronicle), he complains in Chapter 157 about how the Alexandrian Empire had been converted to Christianity by St Paul and then lost to the Turks (Aventinus began the translation "at Abensberg on Saturday evenings in the year 1526").

Nach obgenanter schlacht [i.e. mit den kaiserischen hauptleuten, RCK] viel zu im von den Persiern das ganz clain Asia, so vom nidergang gegen Constantinopel und Kriechen über ligt, an mitternach an das mer, darein die Thonau felt, von süd an das mer, darin gegenüber Rhodis und Cypern ligen, stöst; und von osten schaidet's von gros Armenien der wasserflues Euphrates und das pirg, so man den Taurn und Aman nent. Hat grosse mechtige geweltige (ân die grossen insel Cypern, so auch ein künigreich ist, Rhodis und ander vil mêr) künigreich: Pontus, Bithynia, Paphlagonia, Galatia, Cappadocia, clain Armenien, Phrygia, Mysia (pêde, gros und clain), Troia, Meonia, Lycaonia, Aeolia, Jonia, Caria, Lydia, Lycia, Isauria, Pisidia, Pamphilia, Cilicia. Die land hat s. Pauls alle pekert zum glauben und alda prediget; ietzo hat der Türk alles in, haist die gros Türkei. 

My own translation:

After the aforementioned battle [with the imperial diadoches, RCK] fell to him from the Persians all of Asia Minor, vom the lowlands toward Constaninople across from the Greeks, toward Midnight [i.e. North, RCK] from the sea into which the Danube empties, toward the south to the sea in which Rhodos and Cyprus lie; and from the east it separates from Greater Armenia the waterflowing Euphrates and the Mountains, which are called Taurus or Aman. It has mighty powerful (in the large island of Cyprus, which is also a kingdom, in Rhodes and in many others) kingdoms: Pontus, Bithynia, Paphlagonia, Galatia, Cappadocia, Armenia Minor, Phrygia, Mysia (both, the Greater and the Lesser one), Troy, Meonia, Lycaonia, Aeloia, Jonia, Caria, Lydia, Lycia, Isauria, Pisidia, Pamphilia, Cilicia. These lands had St Paul convert all to the [Christian, RCK] Faith and preached all over there; now the Turks control it all, now called Turkey Maior.

Jouko Väänänen's Short Course on Finite Model Theory

Jouko Väänänen, who also authored the higher-order logic page at the Stanford (Internet) Encyclopedia of Philosophy, published his lecture notes as an introduction to finite model theory, based on his teaching them in Lissabon in 1993 and Helsinki in 1994.

His remarks are extremely helpful in following the basic gist. After disproving the compactness theorem (as Fagin had done in 1993), he comments:

It is only natural that the Compactness Theorem should fail, because its very idea is to generate examples of infinite models. (5)

In the lecture notes, the Trakhtenbrot Theorem of 1950 is proven, namely that the set of finitely valid first order sentences is not recursively enumerable (by mapping it onto the halting problem, which is also undecidable).  From the fact that Sat is recursively enumerable but undecidable, it follows that its "complement" cannot be recursively enumerable. This has the consequence that neither the Completeness Theorem nor the Dowardward Löwenheim-Skolem Theorem hold.

Some notes on Finite Model Theory

It was with great appreciation that I began to read Ronald Fagin's explicitly personal introduction to Finite Model Theory of 1993. Fagin was then working at the IBM Almaden Research Center in San Jose, California, and presented his thoughts at the 3rd International Conference on Database Theory in 1990. Fagin bemoans that so many results are for infinite structures, when databases are all finite. Logic, developed to deal with the hard part of mathematics, the infinite (Gurevich) [p4], but too many of the results for infinite structures do not hold for the finite [ibid]. In practice, finite model theory mostly found application in computability with its connection to algorithmic questions of complexity [p4], which Fagin devoted a whole section (5) to, showing that the class of generalized spectra from his thesis work are the class NP (non-deterministic polynomial time), while spectra are the NE (non-deterministic exponential time) [p.10].

But Fagin correctly pointed out that databases are finite structures [4].

As an aside: The Humanities are in a very similar situation. Even the analysis of an absurdist play like Ionescu's mathematics Lesson with its ridiculously huge numbers does not require an infinite domain of discourse like ℕ. The number of humans and objects and locations and years that matter for Humanities research are all finite. Yes, time and distance are reals, but for the purposes of most arguments, nano-seconds and angstrom provide more resolution that our sources possible allow us to handle anyway. (In fact, the Humanities have the opposite problem that the amazing accuracy of GPS and Google Maps belies knowledge about the exact location of past events on our present-day maps that misleads; but that is a separate rant.)

For example, Fagin shows that taking ℒ to be a "recursive, finitely controllable set [i.e. either unsatisfiable or finitely satisfiable] of first order sentences", then the decision problem is decidable, because each sentence p is either finitely satisfiable or its negation (¬p) is, via the completeness theorem (3.1).

Is weak second-order logic sufficient for Humanities research?

In the process of reading Jouko Väänänen's article on "Second-order and Higher-order Logic" in the Stanford (Internet) Encyclopedia of Philosophy, I came across the question of whether weaker forms of second-order logic are decidable or not.

One interesting paper in this regard is Michael O. Rabin's paper from July of 1969, where he shows the decidability of some second-order theories (using the automata on infinite trees, a reduction of a Turing machine that can only read but not write to the tape).

Perhaps most promising seems to me to be that both linearly ordered sets (Corollary 2.2) and countable well-ordered sets (Corollary 2.3) is decidable. The result that Rabin seems to be especially proud of, that the second-order theory of a unary function in a countable domain is decidable (Theorem 2.4), seems to be unhelpful for the knowledge representation needs of the Humanities.

What seems unclear at this point is whether weak second order logic allows the relating of sentences as well as contextualization. That seems to be the crux of the matter for the Humanities, after all. Väänänen writes:

In weak second-order logic we have no function variables and the relation variables range over finite relations only. The resulting logic is in many ways similar to the extension of first order logic by the generalized quantifier $Q_0$. 

The inability to iterate over the functions seems acceptable, as we can turn all finite function applications into terms anyway.

Perhaps it will require a look at finite model theory to make progress on this question.

Addendum: Notice that Daniel Leivant's Higher Order Logic discussion also emphasises that the key features of weak second-order logic is that the relations variables "range over finite relations" [p44], which is later clarified to mean that the relation variable "R is ranging over finite sets" [p.45] and that there are not function variables [p44]. Among the noteworthy results, Leivant mentions that

• Though the upward Skolem-Löwenheim property does not hold, the downard Skolem-Löwenheim property does [p.45]
• The set of f-valid second order formulas is PI-1/1 [p.45].
• Linear ordering and one function are both decidable [p.45].

Some details on the relation between 2nd Order Logic and Set Theory

For Humanities researchers, who relate sentences to sentences, 2nd Order Logic seems more unavoidable than perhaps to knowledge engineers, who prefer to remain decidable. This tension forces me to revisit the precise ways in which 2nd order and first-order formalisms influence expressivity.

Now I found a nice quote in the Stanfard Encyclopedia Of Philosophy article on Higher-Order Logic about the relationship between 2nd-order logic and set-theory that illuminates some of the puzzlement about that connection:

Perhaps this [result of comparing the model hierarchy and the Levy hierarchy, RCK] would not be so puzzling if we thought of set theory as a very high order logic over the singleton of the empty set. After all, set theory permits endless iterations of the power set operation, while second-order logic permits only one iteration.

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.

Applying Peirce to Image Interpretation --- Part One

The basic notion of Charles Sanders Peirce's, that the positing of an abduced structure of some sort (e.g. a Schankian script in a Davidsonian representation world) can organize a set of disparate pieces into an explanation, is sound. The problem is how to play that through for the specific case of, say, Albrecht Altdorfer's Alexanderschlacht.

The start of the story must be the flags and the labels, because they give specifics. We also need to hold the inscription aside, because there is a strong suspicion that it is not by Altdorfer himself, but later (possibly by Jean De Pay in 1658, whose restauration receipt is already mentioned by Franz von Reber's Catalogue of the Old Pinakothek's collection of 1900 in the 8th edition, though Buchner in the 1938 Katalog for the 400th anniversary exhibition in Munich seems first to suggest that this included a reworking of that inscription).

There is a list of possible sources that Altdorfer could have used for obtaining the details of the battle. That list includes Arrianus, Quintus Curtius Rufus, Justin's Epitome of Trogus, Aventinus, the Alexander Romance of Johannes Hartlieb, Schedel's Nuremberg Chronicle, and Plutarch. (For some of Aventinus' views on this matter, see this post here.)

Per CSP's recommendation, we can now construct alternate worlds of various forms. The basic idea would be that Altdorfer used exactly one source. For example, as Cord Meckseper did in his article on the iconography of the battle (Zeitschrift des Deutschen Vereins für Kunstwissenschaft, XXIII, 3/4, 1968, 178-185), one might assume that Schedel's Weltchronik might suffice.

The point is to expand what »suffice« might mean in terms of a strategy of mechanical interpretation. We assume that the narrative (it is not very long in Schedel) is summarized in a suitable Davidsonian event representation. This instantiation then identifies actors, actions, matériel and similar.
We also need a similar instantiation of the content of the painting itself, as an event, describing the various discernibles. Here, we can simplify the problem by delineating (e.g. with TEI standard bounding boxes) and describing at the action level (moving, turning, etc.) all those entities that any of the art historic works we have considered have identified, i.e. the superset of the interpretation constituents. Recall that we wish to model the argumentation, not automate the argumentation.

But if we have the description of the picture, and the description of the events as reported in the various sources, what then is the abduction doing for us? It is the mapping between these components, a representational correspondence. The picture has a golden-armored man riding a white horse. The story has Alexander leading a charge (say, not all sources go into that detail). The abduced mapping then says that the man on the white horse is Alexander (and by one step of inference that leads us beyond the sources, the horse is Bukephalos).

Consider the battle flag for a moment, which consist of the following pieces of information:

• the army to which the troops are attached (Greek/Macedonian or Persian, often mentioned pars pro toto via the commanders Alexander and Darius III)
• the type of troops we are talking about (here, mostly foot vs horse, i.e. infantry vs cavalry)
• the number of men present at the beginning
• the cardinalities of the categories at the end of the battle
• killed (presumably this includes missing in action, in modern parlance)
• captured (e.g. 40k Persians in Justin and Schedel)
• escaped (1k horse w/ Darius in Quintus Curtius Rufus, 4k in Arrian)

Here we are matching not against actors or roles in the script, we are matching against event statistics, so to speak, or statistics of sub-events (e.g. the troop numbers at the beginning and at the end of the battle). The flags visually represent the battle statistics (which are abstractions and therefore not visible per se).

In all of these representational mappings, we can run into four situations:

• NONE: there is something in the image that is in none of the sources (the scythes on the fleeing chariot, the chariot driver felled by the arrow, the boats on the sea), 
• ALL: there is something in the image that is in all of the sources (Alexander, Darius)
• UNIQUE: there is something in the image that is only one of the sources (the women, Oxarthes)
• SHARED: there is something that is in some, but not all of sources (the 32,000 Macedonian foot in Aventinus, Justin's Epitome of Trogus and Schedel's Weltchronik)

We have different reactions to these situations, then, as they give us different information about the question of which sources were used.

• NONE means that Altdorfer invented the matter himself
• ALL means that we cannot distinguish between the different source theories based on this piece of information
• UNIQUE means that the specific source was definitely used

SHARED has a special status, as it is often an indication of the genealogy of the sources themselves. For example, Altdorfer was not the only one working from sources, both Aventinus and Schedel had to use ancient reports to underpin their reconstructions. We may not be able to separate out Justin from Trogus, since Trogus did not survive the ravages of time as an independent source. But since Justin  (200-400 AD) is temporally before Schedel (1493) and Aventinus (1526), it is likely that Schedel used Justin (in the particular case of the 32k Macedonian foot). There are other cases were Schedel agrees with Justin, such as the number of 40k captured Persians.

The problem is trickier in the case of Aventinus, whose Bavarian Chronicle was published in 1526 when Aventinus was already living in Regensburg. Since Schedel predates Aventinus by over 30 years, and Aventinus only discusses Quintus Curtius Rufus as well as Arrian (Bk I, Cpt 153, p.337), as well as disparaging Hartliebs Romance. So perhaps Aventinus used Schedel and not Justin; unfortunately he mentions neither.

One more point about the NONE category, because Alexander's horse Bukephalos falls into it. None of the source I have looked at specifically mention that Alexander was riding Bukephalos at the battle of Issos. But Bukephalos is not invented in the same way that the chariot driver pierced by the arrow is, and not in the same way that the scythes on the carriage are. So we will have to return to the problem of this category at a later point.

But before that, we have to look at the problem of dealing with the open-ended disjunctions.

Links to the Griffin Warrior

Not sure how this escaped my notice earlier, but the World of the Griffin Warrior is of course supremely fascinating, especially the battle gem.

The article in Archeology by Andrew Curry of 2019 is here, and the later news item on the trade links exemplified by Hathor is here.

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).

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.