**
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*

v-erwechseln

v-orstellen

T-rinkgeld

T-alar[m]

S-terz

S-pediteur

s-ch-lachten

s-auber

R-ind, R-indfleisch

R-ealschule

P-ublikum

P-lakat

P-antoffel

n-iemals

m-ultiplizieren

m-eiden

l-üften

L-eben

K-ren

K-nobel

K-attun

J-agd

H-olzschnitt

h-eben

g-rell

G-eschmack

G-arbe

f-link

f-ähig

e-mpören

d-ünn

d-emolieren

B-ote

B-ekleidung

a-u-sgezeichnet

A-ndrang

A-as
*Mid centre mirror page*

bewusstlos, Bibliothek

bilden

Diwan, Dokument

Eingang, Einbruch

Ernst, Ernte

Ferkel, Fertigkeit

Glaube, gläubig, gleich

haften, Hagel, Hahn

herzlich, Hercog, Hetze

Imker, immer

Kalk, kalt

Klammer

Konkurrenz

Lack, Lacke

Leute, leugnen

Mann

Mist

nähren

Offenherzig[keit]

Perücke, Pest, Peter

Powidl, Pracht

radeln, radieren

Reissbrett

ruinieren, Rum

Schaufel, Schaukel (cp. 'Rel-ais')

schmecken, schmeicheln, schmeissen

Schwalbe

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*