Explanatory Residue: A Paper from the AHDH
The central claim of the paper is brief enough to fit on a card: every explanatory act generates explanatory residue. The AHDH published it without a named author, without a date of submission, and without an abstract, on the grounds—recorded in the editorial notes—that an abstract would itself require explanation, and the editors considered this a conflict of interest.
The paper runs to thirty-one pages. The bibliography runs to forty-four. Several of the works cited do not appear to exist independently of their citations, which the editors describe, in a footnote that constitutes the entirety of the methodological section, as “a known feature of the field rather than a defect of this particular entry.”
The claim itself is not, on first encounter, controversial. Anyone who has explained anything to anyone else will recognise the phenomenon: the explanation produces questions. The questions require answers. The answers generate further questions. A person who set out to explain why the train was delayed arrives home three hours later having covered ground they did not intend to cover, holding positions they did not know they held, and having failed, in any meaningful sense, to explain why the train was delayed. This is the ordinary experience of explanation.
What the AHDH paper proposes is that the residue produced by explanation is not a failure of the explanation but a structural property of the act itself—that explanation does not reduce confusion but redistributes it, and that sufficiently rigorous explanation increases the total quantity of confusion in the system while reducing its local density at the point of application. The train delay is explained. Everything adjacent to the train delay becomes slightly more mysterious.
The paper’s vocabulary is careful. It distinguishes between primary residue, which it defines as the questions directly produced by an explanation, and secondary residue, defined as the questions produced by the act of answering the primary residue, and tertiary residue, which it declines to define on the grounds that “the reader who has followed the argument to this point will have already generated sufficient tertiary residue to constitute a working example.” This is either elegant pedagogy or a refusal to do further work dressed as elegance, and the paper does not invite the reader to determine which, presumably on the grounds that the invitation would itself generate residue.
Professor Anya Solberg of the University of Oslo, who reviewed the paper for the Nordic Journal of Explanatory Theory in what the journal describes only as “a recent volume,” wrote that “the AHDH has here identified something that philosophy of language has circled for decades without naming. The concept of explanatory residue gives us the vocabulary to describe why every academic field is larger at the end of each year than it was at the beginning, regardless of how much ground the field has covered. We are not discovering new things. We are generating new residue from old explanations, and calling the residue progress.”
Solberg adds, with a confidence that may itself be a contributing variable: “Von Entenbraten, characteristically, saw this coming. His refusal to define Boulderdash was not obscurantism. It was prophylaxis. He declined to explain in order to avoid the residue.” She does not acknowledge that this interpretation is itself an explanation of von Entenbraten’s silence, and therefore generates residue, and therefore illustrates the corollary she is attempting to describe. The Nordic Journal published the review in full. The paper cites it in a subsequent edition as external confirmation of its central claim, noting in a parenthesis that “the reviewer’s contribution is duly appreciated and has, predictably, expanded the literature.”
When the AHDH submitted the paper to the Department of Ontologenodynamology Research for independent assessment—a procedure the Vorpel Foundation requires for any paper making structural claims about the nature of enquiry—DOOR’s response arrived after fourteen months and ran to six pages, five of which concerned the procedure for inter-departmental referral and one of which addressed the paper itself.
The substantive page invoked the Germoglio Corollary to Recursive Clarification, which states: each successful clarification increases the total quantity of material requiring subsequent clarification. DOOR offered no further commentary, noting that any further commentary would constitute a clarification and would therefore, under the terms of the Corollary, expand the problem it was attempting to address. DOOR’s departmental head, Dr Bernardo Cisternino, signed the response personally and added a handwritten note at the bottom that read: “We considered saying more but thought better of it.” The note has been reproduced in every subsequent AHDH discussion of the paper as a primary source document, a decision that has generated, by the AHDH’s own count, eleven secondary sources and what the Department describes as “a promising quantity of tertiary material.”
The Germoglio Corollary itself has a history worth examining, not least because its own history illustrates it. Ottavia Germoglio, whose institutional affiliation appears in different sources as the University of Bologna, the Free Institute of Trieste, and simply “continental Europe,” published the Corollary in 1934 as a footnote to a paper on legal definitions. The footnote read, in full: “It should be noted that every successful definition of a term in law immediately generates a class of cases the definition did not anticipate, requiring further definition. This process does not converge.” The footnote attracted more attention than the paper, was extracted and discussed in three subsequent publications, was named the Germoglio Corollary by Professor Max Ehrfeld of Frankfurt in 1951 without Germoglio’s knowledge or apparent consent, and by 1970 had accumulated a secondary literature that Germoglio herself, writing in a short memoir published privately in 1978, described as “an excellent demonstration of the principle, except that I no longer recognise my own footnote in what people say it means.” She added: “I intended to describe a problem in legal drafting. I have apparently described the structure of knowledge itself. This is more than I meant to do in a footnote.” The memoir runs to forty pages. It has generated its own secondary literature. Germoglio died in 1982, before the process had converged, which it has not subsequently done.
Professor Dieter Schloss of the Berlin Academy for the Theory of Theoretical Frameworks, whose monograph The Self-Defeating Explanation: Toward a Unified Account appeared in 2004 and achieved the distinction of being cited more often than it is read—a condition Schloss describes in the preface as “statistically inevitable for any book whose title accurately describes what it does”—devoted his third chapter to the relationship between the AHDH paper and the Germoglio Corollary. He concluded that they described the same phenomenon from complementary positions: the AHDH paper approached explanatory residue from the perspective of the explanation’s producer, while the Corollary approached recursive clarification from the perspective of the definition’s consumer.
“Together,” Schloss wrote, “they constitute a complete account of why the production and consumption of knowledge are equally futile, which is either a unified theory or a reason to go outside.” He then devoted three more chapters to elaborating the unified theory, which expanded to fill the remaining two hundred pages of the book, a fact that Schloss either did not notice or chose not to address. The monograph received strong reviews.
Professor Helena Vance of the London School of Epistemics described it as “the most rigorous demonstration of its own thesis I have encountered in twenty years of the field,” and Schloss quoted this on the cover, which involved removing the word “rigorous” from the sentence in a way that subtly changed its character. The full review is in the AHDH archive, filed under “External Endorsements: Nuanced.”
The practical implications of the AHDH paper, if implications can be considered practical when they concern the structure of explanation itself, run in several directions simultaneously, none of which the paper follows to a terminus. It notes that educational systems consistently produce more questions per student than they receive, suggesting that teaching, understood as explanation applied systematically, generates residue at industrial scale.
It notes that legal systems expand their own scope with each clarifying judgment, a point Germoglio would have recognised immediately and which the paper acknowledges in a citation that describes her footnote as “the founding document of the field,” a description Germoglio would likely have found alarming. It notes, with a brevity that functions as a kind of mercy, that scientific papers generate more papers than they resolve questions, and that the scientific literature is therefore not an archive of conclusions but a compounding ledger of residue, each entry producing interest in the form of further entries.
Von Entenbraten appears in the paper three times. The first appearance cites his observation that “the dimension most frequently omitted is the interesting one” as evidence that he understood explanatory residue intuitively—that the interesting dimension is omitted precisely because including it would generate more explanation than any given account can contain.
The second appearance quotes his Notes Toward the Correction of Obvious Mistakes on the subject of depth, where he wrote that “excavation reveals further appearances, which is not a reason to stop digging. It is a reason to revise one’s estimate of the depth.” The paper presents this as anticipating the Germoglio Corollary by forty-seven years. Whether this is accurate depends on whether Germoglio’s footnote was anticipated by von Entenbraten’s remark or simply consistent with it, a distinction the paper declines to make.
The third appearance is a single footnote, number thirty-one of thirty-eight, which reads: “Von Entenbraten’s refusal to define Boulderdash may represent the only methodologically sound response to the problem described above. The editors are not recommending this approach.” Professor Solberg, reviewing this footnote independently of the main text, described it as “the most honest moment in the paper and the one most likely to be ignored,” a remark she made in print, which the paper subsequently cited, which Solberg then addressed in a follow-up review, which the paper’s next edition will presumably cite in turn, the process not having converged as of the time of writing.
What the paper produces, and what the Germoglio Corollary predicts, and what von Entenbraten’s silence implicitly recommended against, is more of itself. The thirty-one pages generate forty-four citations, which generate secondary literature, which generates the tertiary material the paper’s own footnote considered sufficient to constitute a working example.
DOOR’s six-page response generates eleven secondary sources and a promising quantity of tertiary material. Professor Schloss’s attempt to write the unified account runs to two hundred pages and demonstrates, with genuine rigour, precisely what it set out to describe. The explanation expands. The residue accumulates. The Secretariat of the AHDH continues to regard the catalogue arrangement as temporary and the catalogue as, currently, twelve volumes.
The paper ends without a conclusion. The editorial note in its place reads: “A conclusion would constitute a clarification and falls therefore outside the scope of this paper.” DOOR received a copy of this note by inter-departmental mail and did not respond, which the AHDH logged as agreement, and DOOR has not clarified.
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