Wittgenstein's 'Wörterbuch für Volksschulen' (1926)

John Bjarne Grover

In the article Wittgenstein's Tractatus Logico-Philosophicus and the fundamental theorem of linguistics I concluded that Wittgenstein's logical matrix of TLP 5.101 as the background of his TLP 6 is interpreted in my TEQ book/function 14 which includes a semiotic theory.

The conclusion was that Wittgenstein may have intuited this himself but that it was only after I had shown it for natural language nearly 100 years later that it could be properly understood.

Wittgenstein published only two works in his lifetime - the TLP (1921-22) and the 'Wörterbuch für Volksschulen' (1926) - the latter may well be a masterpiece in line with his 'Tractatus' and may attempt to fill in the missing parts of the TLP: It is likely that it in explores the formal logic of a bitstring enumeration (a la his truth table of TLP 5.101) in natural language format.

Wittenstein's Wörterbuch is typeset in 3 columns of words on 42 pages = 126 page columns. All the pages are quite similar-looking except for the last page 42 which is a little shorter but all three columns are the same length. The types used make for some interesting similarities of e.g. S and F - a trait which resembles the phenomenon of hebrew letters (N and G, Z and U, K and B etc). There is probably a lot of structure that can be established, and I here discuss only 3 forms of structure which I have come across and which I associate with the 3 dimensions of a logical space. The third is the interesting one and may be used in at least politics. See this file for details.

It happened a few years ago that I found three black (and possibly ex nihilo) textiles - all of them were humid, the two first only a little, the third soaking wet. The two first I found under very similar circumstances - I entered a tram and found a black and slightly humid semi-transparent and fine-woven textile on a seat, and since I concluded that somebody could have forgotten it, I gave it to the driver. One week later exactly the same happened again and then it felt quite absurd. The third was quite different - it was outside the tram (I was sitting inside it) and it lay in the slush and water on the ground outside the window, underneath a commercial ad which seemed to contain the photo of two females with black textile trousers.

It is possible to consider the 3-dimensional logical space in the sense of Israel:

1) The dimenion of depth from the coastline in to Jordan
2) The dimenion of length from north to south
3) The dimenion of depth into the ground

1) The principle of relevance for Wittgenstein's logical theory as far as my own fundamental theorem is concerned is about the mirror symmetries in the logically ordered 'rainbow'. If his 'Wörterbuch', which is alphabetically ordered, is considered such a 'rainbow', there should be mirror symmetries. These can be traced to the typographically ordered pages in the example I discuss here. It consists in comparing mirror-symmetric pages in the 42-page 3-column dictionary and compare the top word in the lefthand or first column with the mid word in the central or second column in the mirror page. It turns out that there is a systematic relation if a bit-string LEFT SHIFT (= multiplication with 2) = 'onset-truncation' is performed on the top left entry. The reason why I discovered this was that I considered the 5th last page (that is page 38) with its top left entry 'Ursache' against page 5 mid part where the brief section with words starting on 'C' begins - and I recognized a 'Schacht' from the evidence of the pre-heard recording by Helene Grimaud of Chopin's Waltz, a few seconds which I heard probably 'ex nihilo' two years before she made the recording and I immediately recognized these when I later heard the record. Chopin is not mentioned in Wittgenstein's book, but the phenomenon recurs in the form of p.32 top left 'schöpfen' - onset-truncating to 'Chopin' - against mirror p.11 where the mid words are 'Gehilfe, Gehirn, Gehör'. This could find a further motivation in p.33 top left 'sehnen', 'Sehnsucht' truncated to 'ehnen', 'ehnfucht' (the german 'gothic' typography plays on such ambiguities of s/f etc) against p.10 'Friedhof' for the logical space of Israel with resurrection. In fact the whole book seems to conform to such phenomena - albeit when top left entry turns from last to first half at pages 22-21, there seems to be a tendency for a shift from semantic to phonological relevance. Top left p.22 'm-eiden' vs mid left p.21 'Mann' can be seen as semantic, while top left p.21 'lüften' vs mid p.22 'misslingen', 'Mist', 'mit' would be more graphic when s and f are similar ('üft' vs 'mist').

I mention some examples:

Top left
R-ind, R-indfleisch          

Mid centre mirror page
bewusstlos, Bibliothek
Diwan, Dokument
Eingang, Einbruch
Ernst, Ernte
Ferkel, Fertigkeit
Glaube, gläubig, gleich
haften, Hagel, Hahn
herzlich, Hercog, Hetze
Imker, immer
Kalk, kalt
Lack, Lacke
Leute, leugnen

Perücke, Pest, Peter
Powidl, Pracht
radeln, radieren
ruinieren, Rum
Schaufel, Schaukel (cp. 'Rel-ais')
schmecken, schmeicheln, schmeissen
Siegel (cp. 'Jahoda & Siegel')
Stab, Stachel, Stadel
Streu, Strich, Strick
tief, Tiegel
übrig, übrigens
Vergissmeinnicht, vergeuden, Vergleich
Vorsicht, vorstellen
werben, werden
würfel, würgen
zufrieden, zu Fuss

2) The principle for the second dimension seems likewise to be derivable from the Grimaud-Chopin story: Looking up 'Waltze', it is in the righthand column on p.39, and the entry just horizontally on the other side of the mirror page 4 is 'Berta', 'berüchtigt' - which is the negative of what is likely to be the case. It seems that this applies generally - that the horizontal dimension is negative valued in the lefthand column mid part to what it is on the mirror page righthand column mid part.

3) The depth dimension is more special: That is the 'Siebenstern'. To find a reflex of the third black textile, I look up 'bukse' which I find on page 5 bottom of the page, and on top of page 40 I find 'weisen' - as the opposite of the black textiles. Is this it? I could not find other relevant examples - but then I suddenly spotted on page 40 the word 'Watsche' which means 'Ohrfeige', 'box on the ear', and wonder if Wittgenstein did this to the boy soon after the book was published in order to tell where it was. 'Watsche' is in the upper part of column 1 on page 40 - appr 5 cm from the top in the A4 printout I have made - 3,3-3,5 cm in the normal edition - and I look on the corresponding place in column 3 where I find the word 'Widerstand' - which looks right: It is the boy. Then I return to page 5 to look up the word 5 cm from the bottom of the mid column - and it is Christus - or Christof. Aha, here it is.

I then keep these measures invariant and look up the same on column 1 page 41, column 2 page 6, column 3 page 41 - and continue in the same way with wrapover from 42 to 1: 42-7-42, 1-8-1, 2-9-2, 3-10-3 etc. When I come to 4-11-4 it turns out to be the explanation to the story:

Column 1 page 40 = Wasser, Watsche
Column 2 page 5 = Christus, Christoph
Column 3 page 40 = widersprechen, Widerstand

Ah, here is the boy in the class. It turns out that these 7 elements seem to be mirror-symmetric - joining the Ohrfeige with the Bengel:

Column 1 page 4 = Bengel, benutzen
Column 2 page 11 = Geld, gelehrig
Column 3 page 4 = blasen

The mid triad is then the following - surrounded with the other entries:

Column 1 page 1 = Aberglaube, abermals
Column 2 page 8 = ersetzen
Column 3 page 1 = allwissend, Alms

Wittgenstein writes in his TLP (if I recall it right) that Kausalität = Aberglaube - which is the mid of this series of 7 triads.

This is likely to be the explanation to the story: Wittgenstein got the book from the publisher, read it through and thereafter his mind converged on the 'Siebenstern' interpretation given below, for which the interpretation which explains it as a Donner-'Watsche' = a thunderous box on the ear of the 'Bengel' - after which he resigned and this story would be left in history as a bookmark for understanding the structure relevant to TLP. That means that he did not do it intentionally but the matter of publishing was very important.

The following are the 6 'Siebensterns' (potato peel filters) consisting of 7 triads each from the vertical dimension that can be extracted from the text. There are some difficulties in deciding which words are just 5 cm (or 3,3-3,5 cm) from the top and bottom of the column (assuming that the 'bookmark' is defining) and I here include both alternatives where it is ambiguous, which it is most of the time.

1. Siebenstern

5       braun, Brause
12     glimmen
5       dämmern, Dämmerung

6       Depot, der
13     haltbar
6       drei

7       dürfen, dürftig
14     hierauf, hierher
7       Eintritt, einwärts

8       England, englisch
15     Indianer, Indien
8       Essen

9       Fall, Falle
16     Kandiszucker, Kaninchen
9       First, Fisch

10     Flucht, flüchten
17     Klause, Klavier
10     Fundament, fünf

11     Gas, Gasometer
18     Kontrolle, konzentriert
11     Genick, genieren

2. Siebenstern

12     Geschwulst, Geschwür
19     Laich
12     gönnen, Göpel

13     Grimm, Grind
20     liederlich, Lieferant
13     hängen

14     hegen, Heide
21     Mark (Knöchenmark, Ostmark)
14     hinüber, hinum

15     Hort, Hose
22     Mittelschule, mitten
15     ins = in das. Inschrift

16     Jänner, Japan
23     national, Natron
16     Kapuze, Karabiner

17     Kauz, Kauz
24     Ökonom
17     Klinge (Messer-), Klingel

18     Knoten, Knüpfen
25     Pfeffer, Pfeife
18     Kot, Kotzen

3. Siebenstern

19     Kristall, kritisieren
26     Prärie, Präsident
19     langjährig, länglich

20     ledig, leer
27     rammen, Rampe
20     List, Liste

21     Lunge, lungern
28     reklamieren (zurückfordern)
21     Maschine, Masern

22     meinig (poss pron), Meinung
29     rüsten, rüstig
22     Molkerei, Moment

23     mürb, murksen
30     Scheit, Scheitel
23     nein

24     nisten, nobel
31     Schmiere, schmierig
24     Organisation, Organist

25     Paprika, Papst
32     schwätzen, schweben
25     Pflugschar, Pfosten

4. Siebenstern

26     Platane, Plateau
33     Sitzung, Skala
26     Primararzt (Primarius), Primaware

27     pünktlich, Punsch
34     Ständer, standhaft
27     rasseln, Rast

28     Rechenbuch, rechnen
35     Strupfe, struppig
28     repetieren, Republik

29     Ringlo, rings
36     (tot), toll
29     Saft, Sage/sagen

30     saufen, (saugen?)
37     unangenehm, Unannehmlichkeit
30     Scheune, Scheusal

31     schlagen
38     (verkutzen?), verlangen
31     Schnauze, Schnecke

32     schräg, Schragen
39     Wache; Wachs
32     schwerfällig, Schwerkraft

5. Siebenstern

33     sein, war
40     weshalb, Wespe
33     sollen, Sommer

34     Spennadel, Spende
41     Xaver (Name)
34     stauen, staunen

35     Stiel, Stier
42     zuleide, zuletzt, (zündeln, zünden?)
35     Stute, Stütze

36     tappen, Tara
1       Akrobat, Akt
36     trächtig, Trafik

37     Trost, Trottel
2       Ast, Astronomie
37     Unrat, Unschlitt

38     Vanille, Vase
3       bäuerisch, bäuerlich
38     Vers, Versammlung

39     verzagen, verzehren
4       Binde, binden
39     wahrhaft, wahrnehmen

6. Siebenstern

40     Wasser, Watsche
5       Christus, Christoph
40     widersprechen, Widerstand

41     Wipfel, wir
6       Donner, Donnerstag
41     Zapfen

42     zerzausen, Zettel
7       einmengen, Einöde
42     zuständig, Zutrauen

1       Aberglaube, abermals
8       ersetzen
1       allwissend, Alms

2       Angel , angenehm
9       Fichte, fidel
2       auffällig, Aufführung

3       ausnahmsweise, ausrenken
10     Frucht, fruchtbar
3       beenden, Beere

4       Bengel, benützen
11     Geld, gelehrig
4       blasen

The author thanks the birds who tipped him on the details in the dictionary structures.

Grimaud, H.: Memory. Recording in Munich in December 2017 published in 2018 on Deutsche Grammophon 00289 483 5710.

Wittgenstein, L.: Wörterbuch für Volksschulen. Hölder-Pichler-Tempsky, Wien 1926.

Wittgenstein, L.: Wörterbuch für Volksschulen. Mit einer Einführung herausgegeben von Adolf Hübner - Werner und Elisabeth Leinfellner. Hölder-Pichler-Tempsky, Wien 1977.

John Bjarne Grover
On the web 19 july 2019