I wish to say you my best thanks for your letter of Nov. 24 and the cable, and also for your letter of June 29, to which I did not answer. I am very grateful for your kind and good help, as well in the terminological questions as now in the problem of the translator of my bookB1934@Logische Syntax der Sprache, Wien, 1934. And I thank you most cordially for your bookBQuine, Willard Van Orman!1934@A System of Logistic, Cambridge MA, 1934. First I made a run through it and found many interesting features, and now in the last days I studied it in detail (as a Christmas pleasure) and enjoyed much the good structure of your system with very fine new devices and simultaneously the clarity of your explanations. My remarks to the bookBQuine, Willard Van Orman!1934@A System of Logistic, Cambridge MA, 1934 I am writing separately.

I am very glad that you gave three lectures about my “Syntax”B1934@Logische Syntax der Sprache, Wien, 1934 and other things, and that you had an interested audience.

I was very surprised by your cable (please give my thanks also to Mrs. QuinePQuine, Naomi, 1907–1997, geb. Clayton, 1932–1947 verh. mit Willard Van Orman Quine, Mr. ChambersPChambers, Tom, am. Chemiker and Dr. SkinnerPSkinner, B. F., 1904–1990, am. Psychologe) and by your letter about the proposal of professor PrallPPrall, David Wight, 1886–1940, am. Philosoph. I should be very glad if that proposal would be realised. Unfortunately the decision is not mine but Ogden’sPOgden, Charles Kay, 1889–1957, brit. Linguist und Philosoph; because he made the agreement with the translator and I do not even know on what lines. I wrote him twice, with long quotations from your letter, and I strongly recommended the proposal. OgdenPOgden, Charles Kay, 1889–1957, brit. Linguist und Philosoph answered but postponed the decision till after Christmas. He wrote that Countess ZeppelinPZeppelin, Amethe von, *1896, brit. Übersetzerin, verh. mit Leo von Zeppelin had sent to me some time ago the first part of the translation. I must confess, I am in doubt whether that is true; at least I did not get anything so far. OgdenPOgden, Charles Kay, 1889–1957, brit. Linguist und Philosoph writes Dec. 20: “I was hoping to see the Countess ZeppelinPZeppelin, Amethe von, *1896, brit. Übersetzerin, verh. mit Leo von Zeppelin today, but am giving her till after Christmas before making a decision. Her last letter said that the ‘Logical Syntax’B1934@Logische Syntax der Sprache, Wien, 1934 would be complete in less than a month. Even if she is unable to do it by then, there is much to be said against an American if the bookB1934@Logische Syntax der Sprache, Wien, 1934 is to have an English public – in addition to the loss of time at so great a distance.” That is of course nonsense, because even for the English public a HarvardIHarvard University, Cambridge MA professor will 🕮 be more attractive than C[ountess] Z[eppelin]PZeppelin, Amethe von, *1896, brit. Übersetzerin, verh. mit Leo von Zeppelin. So it seems to me that OgdenPOgden, Charles Kay, 1889–1957, brit. Linguist und Philosoph gives pretexts instead of his real reasons which I don’t know and which seem to be against the project. On Dec. 22 Ogden writes that he did not yet succeed to meet C[ountess] Z[eppelin]PZeppelin, Amethe von, *1896, brit. Übersetzerin, verh. mit Leo von Zeppelin, but he had a telegramm from her saying that the translation will be complete by January 31. Now I wrote him again, but I am afraid that nevertheless his decision will be in the negative. I should regret that very much especially in consideration of my future projects. In any case say please already now to prof. PrallPPrall, David Wight, 1886–1940, am. Philosoph my most cordial thanks; there is still a chance however little. As soon as I shall know Ogden’sPOgden, Charles Kay, 1889–1957, brit. Linguist und Philosoph decision I shall write you.

I am very grateful to you that you wrote a reviewB of my bookB1934@Logische Syntax der Sprache, Wien, 1934. I suppose it was the first written, because the bookB1934@Logische Syntax der Sprache, Wien, 1934 appeared not before July and most of reviewers take several months (sometimes even years) for writing the review.

To your questions about “Syntax”B1934@Logische Syntax der Sprache, Wien, 1934:

1. Definition of “quasi-syntactical”, p. 178-179. You are right, an addition is here necessary. But it is sufficient to replace “\(\grave{S}\!\grave{g}_2^n\)” (the accent \(\grave{}\) marks Gothic letters) on p. 178, last line, by “ein \(\grave{S}\!\grave{g}_1^n\)\(\grave{S}\!\grave{g}_2\)”. Then \(\grave{S}\!\grave{g}_2\) belongs to the logical sub-language \({S}_2\acute{}\) of \(S_2\) and is a syntactical \(\grave{S}\!\grave{g}\), because \({S}_2\acute{}\) is a syntactical language for \(S_1\) and \(\grave{Q}_1[\grave{A}_1]\) etc. are suitable arguments for \(\grave{S}\grave{g}_2\). – It is not possible to define a logical\(\grave{S}\grave{g}_2\) in such a way that for every \(\grave{S}_1\) of \(S_1\)\(\grave{S}\grave{g}_2(\grave{Q}_1[\grave{S}_1])\) has the sense of “\(\grave{S}_1\) is true”; because in this case, if we take a synthetic \(\grave{S}_1\), \(\grave{S}_1\) must be equipollent with \(\grave{S}\grave{g}_2(\grave{Q}_1[\grave{S}_1])\) which is a logical and hence a not-synthetic sentence, and that is impossible. – Not every full sentence of \(\grave{S}\grave{g}_2\) is L-determinate, but only every f. s. having logical arguments. If we add a descriptive description of an expression (e.g. “the expression written at that and that place”) as an argument to \(\grave{S}\grave{g}_2\), then the full sentence will in general be synthetic. Thus e.g. the quasi-syntactical sentences 1a (p. 215) and 12a (p. 217) are synthetic. But the 🕮 qu.-synt. predicate “treats of” (“handelt von”), used in these sentences, is a logical one, because a full sent[ence] of this predicate with logical arguments (logical descriptions of expressions) is L-determinate.

2. (p. 116). You are right, the truth value of an implication sentence can often be found in other way. But in the special case concerned here we cannot (according to the meaning of the objection which I reject however) use a general sentence, because the objection is based on the (erroneous) opinion that a general sentence has to be tested by testing the single instances. – Sometimes it is indeed sufficient to find the truth-value of one of the two parts, but not in this case, provided we do not make use of the definition of ‘\(P_3\)’.

Many thanks also for your offprints, which you kindly sent me. I had some doubt in respect to some points in your “Ontological Remarks”, but perhaps you yourself would formulate it today in a somewhat different way. Especially interesting is your report about WhiteheadsPWhitehead, Alfred North, 1861–1947, brit.-am. Philosoph new approach (but hard to understand because of its shortness); is the propositional calculus of his new system intensional like that of LewisPLewis, Clarence Irving, 1883–1964, am. Philosoph?

The four weeks which we spent together in London were a very interesting and stimulating time. I was very glad to make the acquaintaince of StebbingPStebbing, Susan, 1885–1943, brit. Philosophin, OgdenPOgden, Charles Kay, 1889–1957, brit. Linguist und Philosoph, RichardsPRichards, Ivor Armstrong, 1893–1979, brit. Literaturkritiker, WoodgerPWoodger, Joseph Henry, 1894–1981, Sok[c]rates genannt, brit. Biologe und Philosoph, verh. mit Eden Woodger and others. The three lecturesB1934@Philosophy and Logical Syntax, London, 1935 which I delivered at the University are now in print; you will soon have the little book. Professor StebbingPStebbing, Susan, 1885–1943, brit. Philosophin seemed very satisfied with the lectures and their effect upon the audience, and so I think that it may be a help for America also.

The terminological remarks in your former letter have been very valuable for me. I accepted your suggestions in the terminological list for the translator (if it will be Prof. PrallPPrall, David Wight, 1886–1940, am. Philosoph I will send it to him), and I used them already, as you will see, for the London lecturesB1934@Philosophy and Logical Syntax, London, 1935. 🕮

I sent you recently an offprint “Antinomien”B1934@„Die Antinomien und die Unvollständigkeit der Mathematik“, Monatshefte für Mathematik 41 (1), 1934, 263-284 and some time ago a little pamphlet “Wissenschaftslogik”B1934@„Die Aufgabe der Wissenschaftslogik“, Einheitswissenschaft Heft 3, 1934 which is merely a popular explanation of some ideas of the last chapter in “Syntax”B1934@Logische Syntax der Sprache, Wien, 1934. I shall send you some older offprints about physicalism for you or others interested in these problems.

Prof. Charles W. MorrisPMorris, Charles W., 1901–1979, am. Philosoph, bis 1951 verh. mit Trude Morris, danach mit Ellen Ruth Morris of the University of ChicagoIUniversity of Chicago, Chicago IL was here in August for some weeks. We spoke often together; he is very interested in constructing bridges between Pragmatism and the view of the Vienna CircleISchlick-Zirkel, Wiener Kreis which he considers complementary doctrines. He seems to have the serious intention to help me to come to America.

Through the help of the American Institute at PragueI I am in connection with the Institute of International EducationIInstitute of International Education, New York, New York, asking them to organize a lecture tour through the U. S. beginning in October 1935. Perhaps that will be a suitable way for coming in personal connection with some universities. But it would be a stretching enterprise, I suppose. And I hope to get in some way or other an invitation for some months at one place; of course I should prefer that to a tour of permanent travelling.

If it will not be too much loss of time, could you perhaps send back the enclosed copy with corrections? It suffices of course to correct the serious grammatical mistakes (not expressions which are merely unsuitable). Please send me copies of your German letters (also of the last), if you think corrections useful.

Thanks for your kind Christmas greeting. My wifePCarnap, Ina (eig. Elisabeth Maria immacul[ata] Ignatia), 1904–1964, geb. Stöger, heiratete 1933 Rudolf Carnap and I, we send you and NaomiPQuine, Naomi, 1907–1997, geb. Clayton, 1932–1947 verh. mit Willard Van Orman Quine our best greetings and wishes for the New Year. May your work go on successfully as it started so promising; and let us hope to meet again, perhaps in the now beginning year.

Remarks about Quine’sPQuine, Willard Van Orman, 1908–2000, am. Philosoph, verh. mit Naomi Quine (1932–1947) und Marjorie Boynton Quine (1948–1998) LogisticBQuine, Willard Van Orman!1934@A System of Logistic, Cambridge MA, 1934.

I find your bookBQuine, Willard Van Orman!1934@A System of Logistic, Cambridge MA, 1934 in the whole excellent. Your system is an essential improvement of the usual system-form, and your explanations are clear and exact. I have the intendtion to write a reviewB of the bookBQuine, Willard Van Orman!1934@A System of Logistic, Cambridge MA, 1934 for “Erkenntnis”IErkenntnis, Zeitschrift. It was for meaDie Phrase for me ist mit Pfeil markiert, der zwischen pleasure und to read it verweist. Unter dem Pfeil steht die Bemerkung better, omit “for me” entirely. a great pleasure to read it.

I regret that we cannot discuss some points verbally. So I shall write some remarks.

1. I should find it suitable if you had given explicitly formation rules, i. e. definitions of “sentence”, “n-ad expression” (esp. “class expr.” and “sequence expr.”) and others (see 2, 3c), including the expressions containing defined symbols.

2. You have a much higher degree of exactness than P. M., and there remain now only very few demands for accomplishing exactness. So e.g. it was a lack of exactness in P. M., that no formation rules for definitions are given but only a practice. It will be good if you will supply that for your system. Because a reader, seeing your practice, could perhaps think that it werewould be allowedable to introduce the abbreviation “\(A\)” for an expression like “\(V‚x\)” (or “\(O‚\alpha \)” or others), which of course would lead to contradictions.

3. Substitution , p. 42. a) It seems to me very good, that you demand in your explanation of substitution the rewriting of certain variables. That is better than my procedure (prohibiting subst. in such cases and thereby indirectlybUrsprüngliches indirectly ist mit Pfeil hier her verschoben, der die Randnotiz better the first time enthält. compelling indirectly the rewriting before subst.)

b) I should prefer to say instead of “written in lieu of” (p. 42): “written in lieu of every free”. Then you may leave out “free” in the rule; and the convention at the end of p. 44 (containing the not quite exact expression “construed as cases”) will be unnecessary.

c) It seems to me necessary to restrict in your rule of substitution the range of expressions allowed for substitution. 🕮 You restrict it only by the condition that the result must be significant (i. e. must be a sentence). But that condition is not sufficient. E. g. your rule allows to infer (p. 86) \(4 {symbol} 1 (x/y .\supset .\sim (z=z))\) which gives the obviously false result “\(V‚y.\supset .\sim (z=z)\)”.

4. p. 51. I do not think we cannotcDer Korrektur ist die Bemerkung beigefügt: My correction here looks illogical, but it is the English idiom.. treat parentheses by extra-formal conventions, but we must give explicit rules for them (as you do in fact). There is a fundamental difference between the use of parentheses and the use of the different sortes of variables in your system. The latter is in fact uinessential (as you say), but not the former, because you cannot leave out the par[entheses]. Therefore I should prefer to call the parentheses primitive symbols and to take notice of them in the formation rules (demanded above), as you did already in your informal explanations.

5. Your device of discarding descriptions and keeping only “\(\alpha symbol x\)” defined as a sum of classes is very fine.

6. Likewise admirable is your treatment of operators, using “\(\hat{x}\)” as sole operator, replacing all other sorts by combinations of “\(\hat{x}\)” with class expressions. I think this is an essential improvement. Just now I gotreceived a paper from Ajdukiewicz containing the question whether such a replacement willwould be possible. Now I have written him that you have solved this problem already. I recommended your book and suggested to him tothat he send you an offprint of his paper.

7. It is a great advantage of your hierarchy of types that it includes also sentences. Hereby the desire may arise to find a way of inclusding also some other symbols which now have no type (see 8.).

8. You discarded operator symbols and replaced them by class symbols. That is a very good simplification of the system. Perhaps we may go one step or some steps further in this direction and replace some further symbols, now being without type, by class symbols. 🕮

a) There are some symbols which are now already predicates (in the widebroad sense of this word in “General Syntax”) but are not class symbols in your system and have no type; these are the symbols of implication, identity, equivalence, denial and conjunction. We can easily take them as class symbols, writing e. g. “\(\supset ‚p‚q\)”, “\(\sim ‚p\)” and so on. Then the dots are discarded which in your system are primitive symbols (and ought to be enumerated among those).

b) All defined symbols, with exception of class symbols and those just mentioned, are functors. If we keep “Symbol wie unten” (beingwhich is the fundamental and indispensable functor) we can replace all others by class symbols. This is possible because all definienda of those symbols are now alreadyhave become class expressions.

Formatierung!!Instead of:ZWEISPALTIG FORMATIEREN!!! we may write:

\(\ni x\)

\(\alpha \supset \beta \bar{a}\)

\(\alpha \cap \beta \)

geht noch weiter; finde ein spezielles Symbol nicht VERVOLLSTÄNDIGEN !!!!!!!!!!!!

Then all defined symbols with sole exception of Symbol will be class symbols. In my view this will be an advantage, because they belong then to the system of types, and we have variables for them.

c) I should prefer to replace the primitive symbols “[]” also by a class symbol. (The symbolised notion has‚into my way of feeling‚ too much weight for being symbolised by punctuation 🕮 symbols like brackets; but that is of course only a subjective feeling.) ThereHere are some possible ways:

A) We may write “cong symbol” instead of “\([\alpha ]\)”. And then:

A₁) either we take Symbol: as a new primitive symbol;

A₂) or we take first “cong ⁽???” first as one symbol (without type); we define later on we define “⁽” and show that “cong ⁽” can now be taken as a combination of that “⁽” and a class symbol “cong”.

B) (Perhaps preferable to A). We take “{symbol}” as a prim. class symbol (writing “{symbol}‚{symbol}‚{symbol}” instead of Russell’s “{symbol}”). Then we may define, if desired‚ “cong ⁽{symbol}”, if desired‚byas{symbol}, or use only the latter (in order to avoid “⁽” at this stage).

d) I should prefer to take “⁽” as a primitive symbol. [Do you believe that it will then be possible to define then “cong” (or “{symbol}”)? If not, I should take both “⁽” and “{symbol}” as pr.s.] If we take “⁽” as pr.s., the system will contain only these 3 kinds of symbols:

1) punctuation signs: comma, inverted comma, parentheses “( )”, circumflexdHsl.

2) variables‚

3) class constants.

All defined symbols are class constants; hence there will comeresult a great simplification forof the formation rules for definitions (see above 2). And the discarding of all functors, excepted “⁽”, will simplify the syntactical definition forof “class expression” (and thereby that forof “sentence”), because every class expression has the form ”{symbol}” or {symbol} or {symbol}. The system of types includes every symbol with the exception of the punctuation signs.

9. p. 5. We dueowe the remark about the assertion sign to Wittgenstein p. 94eHsl., I believe.

10. p. 144, line 25. {symbol}.