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Hakyll.
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based on
Lanyon.
In 1915 a sixty-nine-year-old professor of philosophy at Copenhagen published thirty pages in Fysisk Tidsskrift arguing that Einstein’s special theory of relativity contradicts the principle of non-contradiction and must therefore be rejected. The argument is short enough to state in a paragraph, and Carl Henrik Koch quotes its core:
Her er altsaa to Sandheder. A har Ret; thi han har ingen Acceleration. Og B har ogsaa Ret; thi han har heller ingen Acceleration. Men dette gaar aabenbart ikke an. Der er i Logikken en Grundsætning, der siger: A er ikke Ikke-A; Modsigelser (i Tingenes Verden) findes ikke, og Modsigelser (i Tankens Verden) taales ikke. Sandheden er ikke dobbelt. Sandheden er kun én. Denne Sætning trænger ikke til Forsvar. Enhver Videnskab er bygget over den. Einstein’s Teori staar derimod i Strid med den. Derfor maa den forkastes.
So here are two truths. A is right, for he has no acceleration. And B is right too, for he has no acceleration either. But this plainly will not do. There is a principle in logic that says: A is not not-A; contradictions (in the world of things) do not exist, and contradictions (in the world of thought) are not tolerated. Truth is not double. Truth is only one. This proposition needs no defence. Every science is built upon it. Einstein’s theory, by contrast, stands in conflict with it. Therefore it must be rejected.
Two observers in uniform relative motion each measure the other’s rod as the shorter. Neither is accelerating, so neither can be demoted to the merely apparent case. Kroman takes this to be a straight contradiction, and takes the law of non-contradiction to be non-negotiable.
The objection is not eccentric — the same move was made across the international discussion of the period — and Koch notes that Kroman’s papers show he had full command of the (after all fairly simple) mathematics of special relativity. What makes the episode worth preserving is that in Denmark it was a philosopher who opened the argument, that a physicist and a mathematician answered him in a physics journal, and that the reply which finally settled the matter for Danish philosophy came from Harald Høffding, in a book this collection already carries in both languages.
The premise doing the work is not local to relativity. Vor Naturerkjendelse (1883) grounds the certainty of the formal sciences in necessity of intuition — »Al Tankenødvendighed beror til syvende og sidst paa Anskuelsesnødvendighed« — and on that ground had already dismissed the non-Euclidean geometries as contentless fantasies. Dansk Biografisk Leksikon names this single premise as the source of both polemics. Kroman returned to the geometry side of it in Matematikken og Erkendelseslæren (1920). The relativity articles are best read as one application of a thirty-year-old commitment, not as a late aberration.
Revised 2026-09-04, from the scan itself. The table below used to have five items and one of them was wrong. With the volumes in hand the exchange turns out to run to seven, and the extra two are not in any bibliography consulted: a second piece by Holst, and a mediating article by Carl Emil Walsøe. Hansen’s reply is at pp. 18–29, not the pp. 14–22 previously inferred from search hits.
| Author, title | Volume | Pages | PDF pages | |
|---|---|---|---|---|
| 1 | H. M. Hansen, »Relativitetsprincipet« — lecture to a joint meeting of Fysisk Forening and Mathematisk Forening, 11 April 1912 | 10 (1911–12) | 251–281 | not digitised |
| 2 | K. Kroman, »Relativitetsprincipet« | 14 (1915–16) | 1–30 | 331–360 |
| 3 | H. Holst, »Tidsproblemet« | 15 (1916–17) | 1–13 | 603–615 |
| 4 | Carl Emil Walsøe, »Omkring Videnskabens Grænse« | 15 (1916–17) | 13–17 | 615–619 |
| 5 | H. M. Hansen, »Relativitetsprincipet« | 15 (1916–17) | 18–29 | 620–631 |
| 6 | Helge Holst, »Relativitetsprincipet« | 15 (1916–17) | 165–168 | 783–786 |
| 7 | K. Kroman, »Et Par yderligere Bemærkninger om »Relativitetsprincipet«« | 15 (1916–17) | 192–205 | 814–827 |
Kroman’s own closing article confirms the shape. At printed p. 193 he writes »Med Forfatteren af den tredie Afhandling, Hr. Dr. H. M. Hansen, er jeg derimod erkendelsesteoretisk set meget uenig« — with the author of the third treatise, Dr. H. M. Hansen, I am on the other hand, epistemologically speaking, in strong disagreement. Three treatises answered him, and Hansen wrote the third: items 3, 4 and 5, in that order.
Three of these articles begin partway down the last page of the one before, under the previous article’s running head — which is why the running heads give the wrong extent every time and why three of the seven entries in this table had to be corrected against the pages. Walsøe shares p. 13 with the end of Holst’s »Tidsproblemet« (catalogued 14–17, actually 13–17); Holst’s second piece begins in the lower half of p. 165 (catalogued 166–168, actually 165–168); and Kroman’s 1917 reply begins partway down p. 192, under P. O. Pedersen’s running head. In this journal, always read the page before the apparent first page.
Walsøe belongs to the debate rather than merely sitting between its parts. His p. 17 describes itself as »denne Antydning fra Trediemand af en Mulighed for […] at udløse Spændingen og bilægge Striden mellem de to Parter« — this suggestion, from a third party, of a way to release the tension and settle the dispute between the two parties. He is trying to mediate between Kroman and the physicists. Hansen’s own opening at p. 18 registers the same pile-up: »Den Interesse for Relativitetsspørgsmaalet, som flere Artikler i Fysisk Tidsskrift i den senere Tid har givet Vidnesbyrd om…«
Hansen’s 1912 lecture is the first real introduction of special relativity to a Danish audience, and it is what provoked Kroman three years later. H. M. Hansen is Hans Marius Hansen, Bohr’s collaborator; that Bohr had also sat Kroman’s filosofikum makes the exchange a small collision of two parts of the same university. Koch’s summary of the ending is that Hansen answered the year after the attack, that a couple of further contributions followed, and that Kroman closed the debate without adding anything new. From about 1920 — the year Einstein visited Copenhagen, and the year after Eddington — Danish physicists appear simply to have accepted the theory.
Item 1 is now the only gap: Google’s run of the journal skips vols 10–12, so Hansen’s 1912 lecture has to be ordered from KB. Everything else is in hand.
Five of the seven items now stand in both languages. Danish transcriptions
were made from the images in September 2026; the English translations followed
on 2026-09-05, made from transcription.tex and not from the scan.
| Item | Danish | English | |
|---|---|---|---|
| 1 | Hansen 1912, pp. 251–281 | — not digitised | — |
| 2 | Kroman 1915, pp. 1–30 | complete | complete |
| 3 | Holst, »Tidsproblemet«, pp. 1–13 | complete | complete |
| 4 | Walsøe, pp. 13–17 | complete | complete |
| 5 | Hansen 1916, pp. 18–29 | complete, embargoed | — |
| 6 | Holst 1917, pp. 165–168 | complete | complete |
| 7 | Kroman 1917, pp. 192–205 | complete | complete |
Each translation mirrors its transcription one-to-one: the same paragraphing, page breaks marked at the same joints, and the same number of emphasis runs and footnotes — 146, 14, 30, 8 and 42 runs respectively, matching the Danish exactly. Both redrawn figures (Michelson’s apparatus on Kroman’s p. 5, Fizeau’s on Holst’s p. 8) are carried over unchanged, their lettering being language-independent.
The translations are diplomatic in the same sense the transcriptions are. Printer’s defects that survive translation are reproduced rather than repaired, and marked in a comment at the spot: Kroman’s comma-for-full-stop at 1915 p. 4, Walsøe’s doubled full stop after »(Kroman)« and his quotation on p. 13 that the printing never closes, Holst’s unpunctuated parenthetical at 1917 p. 166 and the »at« for »af« on his p. 167 that leaves the sentence without a subject, Kroman’s »sikkert!,« at 1917 p. 203. Defects that are purely orthographic — »maaa« for »maa«, the doubled e in »Atomeeksplosionerne« — cannot be carried into English and are noted instead.
Three decisions worth recording, because they recur:
One question the translation raised and could not settle: at 1917 p. 192 the
body of transcription.tex sets »det ’ske Relativitetsprincip«
while its own comment three lines below says the word is not letterspaced,
and the file’s header note agrees with the comment. The translation follows the
body, transcription.tex being the source of truth, and flags the disagreement
in place. Only the page image settles it; if the image shows ordinary roman,
the run should come out of both files.
Relation som Kategori (1921), §3d.δ »Den nye Relativitetsteori«, pp. 72–77, answers Kroman by name — the only place in this collection where two of its authors argue directly with each other about physics. Our transcription carries the passage at printed pp. 75–76:
Man har overfor den Einsteinske Hypotese […] gjort gældende, at der dog kun kan være én Sandhed i hvert enkelt Tilfælde, og at det vilde stride mod Modsigelsens Grundsætning, hvis to Iagttagere, af hvilke den ene erklærer for samtidigt, hvad den anden erklærer for successivt, begge skulde have Ret.
with the footnote »Kroman i Tidsskrift for Fysik, XIV, p. 15.« Høffding’s answer is that there is no reason to fear for the unity of truth even if Einstein turns out to be right:
Den egentlige Sandhed ligger nemlig da i den Nødvendighed, der fysisk paavises af, at forskellige Iagttagere under visse bestemte Betingelser faar forskellig Tidsopfattelse.
The real truth lies in this case in the necessity, physically demonstrated, that different observers under certain determinate conditions arrive at different apprehensions of time. An observer who is also a physicist can explain why another observer apprehends time differently; the disagreement is itself lawful, and the law is the truth. Høffding files this under the same heading as Copernicus — a further instance of the lesson that the observer’s own standpoint must enter the account — and adds that if Einstein is right one does not therefore have to philosophise in a new way. He took the point up again, without pressing it, in Erkendelsesteori og Livsopfattelse (1925).
Note that Høffding gets the journal’s name backwards. There is no Tidsskrift for Fysik; the journal is Fysisk Tidsskrift. The volume and page are right — XIV, p. 15 falls inside Kroman’s pp. 1–30 — and the error is reproduced in at least one modern bibliography, so it has had a career of its own. Anyone searching a library catalogue on Høffding’s form of the title will find nothing.
Google Books Tr4ZAAAAIAAJ — Fysisk tidsskrift, volumes 13–15 bound
together, the University of California copy, digitised 17 January 2007, in
full view with a PDF download. One file holds Kroman’s 1915 article, Holst’s
»Tidsproblemet«, Kroman’s 1917 reply and, on the evidence of the volume range,
Hansen’s reply as well. Verified by searching inside it: p. 192 opens with the
heading »Et Par yderligere Bemærkninger om »Relativitetsprincipet««. Hansen’s
1912 lecture is in vol. 10 and will be in one of the other Google volumes of the
journal, which carry edition dates 1910, 1918, 1928 and 1932.
It is a US library copy of a Danish journal, set in Antiqua rather than Fraktur, so the Google text layer will be better than usual — but re-OCR per TRANSCRIPTION-PLAYBOOK.md §2 before trusting it.
Two attempts to have KB digitise this failed, and the reason is in the records
rather than in the library. What KB catalogues under Kroman is not the article
but the offprint, and the offprints live in the Særtrykssamlingen, which
is filed by author and has no running call number. Both records give the
shelfmark as the bare string Særtrykssamlingen 8°. The 1917 record adds
U. titelbl. — uden titelblad, no title page. So the request, as it reaches
the stacks, asks someone to find an untitled fourteen-page pamphlet in an
author-filed collection with no unique locator. Add Høffding’s inverted journal
name, if it travelled with the request, and failure is the expected outcome.
The general rule, which applies well beyond this item: when a KB record says
Særtrykssamlingen, do not order the offprint. Order the journal volume named
in the record’s »Særtr. af:« field, or find the journal elsewhere. In this case
the journal was on Google Books all along.
KB record for the 1915 offprint: alma99122230022205763, 30 s., »Særtryk af:
Fysisk Tidsskrift XIV. 1. Hefte«. For the 1917 offprint:
alma99122363662605763, 14 s., »Særtr. af: Fysisk Tidsskrift«. The page counts
match the article page ranges exactly, 30 and 14, which is what confirms the
citations above.
Six of the seven items are in the Google file and the page map is now
measured, not guessed. pagemap.py --detect in each article directory
reports the offset; the three settled so far are
Kroman 1915 printed 1-30 = PDF 331-360 (offset 330)
Holst 1916 printed 1-13 = PDF 603-615 (offset 602)
Kroman 1917 printed 192-205 = PDF 814-827 (offset 622)The numerals alone do not identify an article in this bind. Each of vols 13, 14 and 15 has its own pp. 1-30, so the detector finds three offsets that fit Kroman 1915’s numerals perfectly – 12, 330 and 602. What breaks the tie is reading the pages: PDF 331 opens »Relativitetsprincipet«. / Af / K. Kroman., and PDF 345 carries »Sandheden er ikke dobbelt«, which is printed p. 15 and so exactly the page Høffding’s footnote cites. Offset 602 turned out to be Holst’s article, which is how item 3’s page map got settled in the same pass. The detector now prints every tied candidate rather than choosing one silently.
Note also that the offset is not constant across vol. 15: it is 602 at the front and 622 by p. 192, because unpaginated advertisement leaves are bound in (PDF 795 is an ad for H. Struers kemiske Laboratorium). Each article’s offset must be measured for that article. Never carry one across.
Item 1 is the gap: Google’s run of Fysisk Tidsskrift is vols 7–9, 13–15,
16–18, 26–27 and 30–31 — vols 10–12 are missing, and Danmarks Tekniske
Kulturarv has the journal listed as ikke digitaliseret. But unlike the
Kroman offprints, Hansen’s 1912 offprint has a real call number: KB record
alma99122809209105763, 8° Fys. 11882 at Danmarks Natur- og
Lægevidenskabelige Bibliotek, »Særtr. af Fys. Tidskr. 10. 6. Hefte«. That one
can simply be ordered. (A second copy sits in the Særtrykssamlingen as
alma99122564603005763, S. 251–281 — do not order that one.)
Two practical notes, written before the work began and both borne out. The scan
is Antiqua, not Fraktur, so the Fraktur model is the wrong tool and the
Google text layer is better than usual — but still re-OCR per
TRANSCRIPTION-PLAYBOOK.md §2. And this is the first material in the collection
with real mathematics in it: Lorentz transformations, coordinate systems,
and Kroman’s own algebra. The 1915 article turned out to need built-up
fractions inline, ten flush-right bare equation numbers set with \tag*{}
rather than \tag{}, two braced two-column arrays, and — on p. 25 — Greek ν
and italic v side by side in one formula, where the distinction carries the
argument. Budget for that rather than discovering it at batch three.
A caution that cost real time and will again: this scan’s JBIG2 compression drops hairlines. The rules of the inline fractions on Holst’s p. 8 are simply absent from the image, and had to be confirmed from a parallel »1/n« on the next page. Check any thin rule at a second resolution before concluding it is not there. The same face’s superscript 2 has a looped top and reads as a 3 at low resolution; it was checked arithmetically as well as at 600 dpi in both Kroman articles.
The collection’s usual assumption, that anything 19th-century is long out of copyright, does not hold here. Danish term is life plus seventy.
| Author | Died | Public domain in Denmark |
|---|---|---|
| K. Kroman | 26 July 1925 | since 1996 — clear |
| Helge Holst | 1944 | since 2015 — clear |
| H. M. Hansen | 13 June 1956 | 1 January 2027 |
| Carl Emil Walsøe | 1951 | since 2022 — clear |
So items 2, 3, 4, 6 and 7 can be transcribed and published now, and all five now
are, in both languages. Only items 1 and 5, Hansen’s two contributions, are
still in copyright, and only until the end of this year. Item 5 is transcribed
and held: \embargotrue in its preamble prints a “READING COPY — NOT FOR
CIRCULATION” box, and a line under EMBARGOED TEXTS in the root .gitignore
keeps it off git. It has deliberately not been translated, since a translation
would only be a second file to hold. Transcribing them now is fine; publishing
them is not, and the debate can go up complete at the new year — at which point
the two things to undo are the \embargotrue and the .gitignore block, and
the thing to add is a translation of item 5.
This is worth deciding deliberately, since it is also the first time this collection would carry a 20th-century text whose author’s term has not run.
Walsøe took some finding, because the article is a dead end: the byline is bare »Af / C. E. Walsøe.«, with no title, affiliation, town or dateline anywhere, and the *) on its title turns out to be the Redaktion’s own disclaimer that the piece »maa siges at falde uden for Tidsskriftets Ramme« — not a note on the author. He is Carl Emil Walsøe, b. 25 May 1870 in Copenhagen, d. 1951: cand. polyt. 1896, engineering assistant at the State Railways, telegraph engineer from 1903, district engineer at Post- og Telegrafvæsenet 1926–40. Kraks Blå Bog 1949 has the birth date and career; his son Sven’s 1957 entry supplies the death year. What makes this more than a match on initials is the list of his own writings in the 1949 entry — »Den ny Naturvidenskab og vor gamle Kristentro. Et Forsøg paa en principiel Orientering« (1938) and »De tre Planer. Legeme, Sjæl, Aand.« (1947). A polytechnically trained engineer writing on the boundary between the new physics and religious conviction is exactly the author of a 1916 piece called »Omkring Videnskabens Grænse«, and exactly the contributor a physics journal’s editors would disclaim.
transcription.tex’s body and its
own comment disagree about whether »Einstein’ske« is letterspaced. Settled
only by the image; see The edition above. Everything else in the five
translated articles is image-verified.