## 1. Introduction



Heinrich Scholz (1884-1956), German Protestant theologian,
philosopher, and logician, began his academic career as a protestant
systematic theologian at the University of Breslau. He then moved to
the University of Kiel and in 1928 to the University of Munster
in Westphalia. His *Religionsphilosophie* (Scholz 1921) became
particularly influential in protestant theology. Inspired by Alfred
North Whitehead's and Bertrand Russell's *Principia
Mathematica* (Whitehead and Russell 1910-1913) he changed
his research area to mathematical logic and foundational research. He
was successful in establishing the "*Schule von
Munster*" ("Munster School") of
logicians and in founding the first academic department for
mathematical logic in Germany, the "*Institut fur
Mathematische Logik und Grundlagenforschung*"
("Institute for Mathematical Logic and Foundational
Research") in Munster, which is still in existence today.
Scholz combined research on logical calculi with an epistemological
Platonism and openness for metaphysical approaches. Nevertheless, he
felt close to the scientific world view of Logical Empiricism.
Furthermore, with his *Geschichte der Logik* (Scholz 1931a)
Heinrich Scholz was a pioneer in the historiography of logic.


## 2. Life


### 2.1 Academic Career



Heinrich Scholz was born on December 17, 1884 in Berlin. His father
was a Protestant parson (on Scholz's biography and his work cf.
Elstrodt and Schmitz 2013; Hermes 1958; Meschkowski 1984; Molendijk
1991; Molendijk 2005; Peckhaus 2008; Ritter, Hermes and Kambartel
1961; Wernick 1944). He studied Protestant Theology and Philosophy in
Berlin. Among his teachers were the Prussian Protestant theologian
Adolf von Harnack (1851-1930), the neo-Kantian philosopher Alois
Riehl (1844-1924) and the neo-idealist philosopher Friedrich
Paulsen (1846-1908). In 1911 he completed his
*Habilitation* in the Philosophy of Religion and Systematic
Theology. He obtained an additional doctoral degree in Philosophy at
the University of Erlangen in 1913. In 1917 he was appointed to a full
professorship in the Philosophy of Religion and Systematic Theology at
the University of Breslau in Silesia, today Wroclaw, Poland. He
also received an honorary doctorate from the Theological Faculty of
the University of Berlin. Four years later, in 1921, he was appointed
to the chair for Philosophy in Kiel, before finally accepting the
offer of a professorial chair at the University of Munster in
1928. There he first served as professor of Philosophy. He developed a
close relationship with Karl Barth, one of the main representatives of
kerygmatic and dialectic theology, who taught protestant theology in
Munster from 1925 on (cf. Molendijk 1991, ch. 3). Scholz changed
his main research area to mathematical logic and foundational
research, and officially taught the subject from 1936 on. In 1943 the
denomination of his chair was changed to *Mathematical Logic and
Foundational Research*. The institute of this name was founded in
1950. Scholz retired in 1952. He died in Munster on December 30,
1956.


### 2.2 Institute for Mathematical Logic and Foundational Research



The "Memorandum about the New Mathematical Logic and
Foundational Research" written for the Reichs- und
Preussischen Minister fur Wissenschaft, Erziehung und
Volksbildung (Imperial and Prussian Secretary for Science, Education
and National Instruction) on January 15, 1938 (Scholz 1938) shows that
for Scholz this new subject went beyond symbolic or mathematical
logic, but further included applications of logical analysis to
foundational problems in general. According to Scholz, the new subject
was prepared by Gottfried Wilhelm Leibniz (1646-1716), created
by Gottlob Frege (1848-1925), and taken up by David Hilbert
(1862-1943) who, adopting Bertrand Russell's
(1872-1970) elaboration of Frege's creation, made it the
subject of deep investigations aiming, e.g., "at a consistency
proof for classical logic", and with this, of classical
mathematics (presupposing the logicist reduction of mathematics to
logic). This new approach was, according to Scholz, directed against
Kant's opinion that "foundational questions of any kind in
principle cannot be treated with mathematical methods and with
mathematical means of construction and research questions". Its
task was a deepening and clarifying of foundations by combining
structural investigations and the analysis of the context of
application.



In Munster, Scholz taught right from the beginning to a large
extent on logic, in particular "logistic", as the new,
i.e., formal, symbolic, algebraic, algorithmic or mathematical logic
was called since the Second International Congress for Philosophy at
Geneva in 1904 (cf. Couturat 1904; Scholz 1931a, 57). In April 1936 he
received an official extension of his philosophical appointment to
"Logistic Logic and Foundational Research". In the same
year, "Section B" (consisting of Scholz's chair and
the academic and non-academic staff attached to it) of the
Philosophical Seminar was renamed "Logistic Section". The
next step was taken in 1938 when this "section" became a
"seminar" of its own. The denomination of Scholz's
chair was changed to "Philosophy of Mathematics and Science with
Special Consideration of the New Logic and Foundational
Research". In 1943 the denomination was changed again to
"Mathematical Logic and Foundational Research". The
"Logistic Seminar" was renamed "Seminar for
Mathematical Logic and Foundational Research" in 1946, and
finally, in 1950, it was renamed again, and elevated in its
organizational status, to "Institute for Mathematical Logic and
Foundational Research" (cf. Schmidt am Busch & Wehmeier
2005a).



Scholz was also politically effective in promoting his field. He
assembled the "Gruppe von Munster" (later
"Schule von Munster") and encouraged a number of his
students to undertake studies in logic and foundational research,
placing some of them in academic positions. They obtained important
results in the theory of the predicate calculus, the theory of
axiomatic systems, metamathematics, semantics and abstraction theory.
Among them were Friedrich Bachmann (1909-1982), Albrecht
Becker-Freyseng (1907-1976), Gisbert Hasenjaeger
(1919-2006), Hans Hermes (1912-2003), Walter Kinder
(1909-1998), Karl Schroter (1905-1977), and Hermann
Schweitzer (1909-2002). For the publication of this
school's results and related investigations Scholz founded the
series *Forschungen zur Logik und zur Grundlegung der exakten
Wissenschaften* (eight issues 1937-1943, n.s. reprinted as
Scholz, ed. 1970). Among them is the outstanding book by Heinrich
Scholz and Hermann Schweitzer *Die sogenannten Definitionen durch
Abstraktion* with its elaboration of modern abstraction theory
using equivalence classes (Scholz and Schweitzer 1935).



In trying to establish a world-leading center of mathematical logic
and foundational research at Munster, he was able to obtain
Frege's *Nachlass* for his chair in Munster in 1935.
Later, he added to this collection the papers of the German algebraist
of logic, Ernst Schroder (1841-1902), which he had obtained
from the library of the Technical University of Karlsruhe. It is one
of the tragic effects of World War II that Frege's and
Schroder's papers were lost, perhaps destroyed during the
bomb attacks on Munster in March 1945 (cf. Peckhaus 1993;
Wehmeier and Schmidt am Busch 2000). Scholz had intended to publish a
three-volume edition of Frege's posthumous work and
correspondence. Most of the typewritten copies Scholz had made of the
original material were saved (on the Frege papers cf. Scholz and
Bachmann 1936).



In the beginning of the 1930s Munster still stood in the shadow
of Gottingen as a center of research on logic. After the National
Socialists' seizure of power, most of German language logicians
lost their positions and were forced into emigration. Only
Munster survived as a place for research on logic and
foundations. Scholz was successful in resisting the attacks from the
side of the so-called "Deutsche Mathematik", a
National-Socialist racist movement emphasizing the mathematical work
of German "national comrades" (*Volksgenossen*).
The Munich mathematician Max Steck (1907-1971) was particularly
hostile. Steck's book, *Das Hauptproblem der Mathematik*
(1942)*,* is directed against logicism, the axiomatic method,
and metamathematics, as proposed by logicians and mathematicians close
to David Hilbert and his school. Steck labeled Hilbert's
formalism as a "simply catastrophic" mental one-sidedness,
a "decadence" from the perspective of intellectual history
(Steck 1942, p. 205). In several places Scholz is attacked as
Hilbert's spokesman. Steck calls Scholz's Munster
School a "transplantation of the earlier so-called Vienna Circle
to Munster in Westphalia" (p. 176).



During the Third Reich Scholz served as a kind of information broker,
mediating contacts between emigres and those who stayed
behind. He was able to support his Polish friends, helping, e.g., to
rescue Jan Salamucha (1903-1944) from the concentration camp in
Sachsenhausen in 1940 (an action for which German authorities
threatened him with removal from his professorial chair). He supported
Alfred Tarski (1901-1983), who had emigrated to the U.S.A., by
maintaining contact with his wife and his two children, who still
lived in Warsaw. He supported Jan Lukasiewicz (1878-1956)
and his wife financially and was eventually able to help them to leave
Poland and to hide in Germany. They feared for their lives in case the
Red Army would conquer Poland (cf. Bolewski and Pierzchala 1989,
Schreiber 1999, Peckhaus 1998-1999, Schmidt am Busch and
Wehmeier 2005b).


### 2.3 Logical Empiricism



Scholz and his followers adopted the scientific world view as
advocated by the philosophers of the neo-positivistic movement, in
particular of the Vienna Circle and the Berlin Society for Scientific
Philosophy. However, contrary to this movement, he even applied the
scientific world view to metaphysics. This was observed with
reservations. Otto Neurath, e.g., mentioned Scholz and the
Munster Group as having contributed much of value, but Scholz
"represents nevertheless a full-blown metaphysics"
(Neurath 1937, reprint Neurath 1981, pp. 804-805) which has to
be rejected. The relation between Neurath and Scholz remained
ambivalent. At least, they met at the First International Congress for
Unity of Science at Paris in September 1935. The congress saw the
establishment of a committee for the standardization of logical
symbolism with members of the Vienna Circle, the Hilbert School, and
the Munster Group. The initiative had come from Scholz and his
school. The results of the committee's negotiations were
presented at the Forth International Congress for the Unity of Science
at Cambridge (England) in July 1938 (cf. Peckhaus 2008, pp.
78-80; Behmann et al. 1937/38).


## 3. Work


### 3.1 Philosophy of Religion



Scholz dedicated his *Religionsphilosophie* (1921) to his
teachers Adolf von Harnack and Alois Riehl (on Scholz's
philosophy of religion cf. Molendijk 1991, Ratschow 1958, Stock 1987,
Wimmer 2005). According to Scholz philosophy of religion does not deal
with religion as such, but with its possibility, based on the fact of
its reality in the sense of Kant's critical philosophy (p.
VIII). Religion becomes, thus, a philosophical problem. Scholz defines
philosophy of religion in the widest sense as the application of
philosophical means and presupposition of reasoning to the fact of
religion (pp. 1-2). Religion is understood as part of culture
being the epitome of creations of the human mind, the existence of
which is preferred to their non-existence (p. 14). The object of
analysis is empirical religion, i.e. religion as it is practiced in
real life or as it is tangible. With this he deviates from
constructive types of the philosophy of religion as they can be found,
e.g., in the work of Immanuel Kant. In conclusion, he determines that
philosophy of religion has an integrating function in a philosophy of
cultural values. It consists in philosophical reflection on tangible
(*erlebbare*) religion as it is practiced and, in particular,
in reflection on expressions of religious consciousness whose truth is
subject to reason. Therefore religion has never ceased to be a
philosophical problem.


### 3.2 Logic and Foundations



The year 1921 marks a big change in Scholz's focus of
philosophical research. He himself tells the story that he discovered
his love for mathematical logic by accidentally coming across
Whitehead's and Russell's *Principia Mathematica*
(Whitehead and Russell 1910-13, cf. Peckhaus 2005) in the
library of the University of Kiel. This work convinced Scholz of the
significance of mathematics, although he had no deeper knowledge of
this subject at that time. As a full professor of philosophy he
decided to begin formal university studies of mathematics and
theoretical physics. After having moved to Munster, Scholz
focused his research on mathematical logic and foundations.



He worked particularly on the borderline between mathematics and
philosophy, motivated by the problem of distinguishing logical calculi
from general calculi. He supported David Hilbert's foundational
program having led to metamathematics and proof theory, but focused on
language and semantics. Language is necessary to present logical
systems. He suggests a formalized language with a degree of exactness
even exceeding the exactness of mathematical languages. He calls this
language "Leibniz language" *L* (cf. Scholz 1944).
Leibniz languages are symbolic languages with exactly defined means of
expression. Each expression is a finite string of characters using a
given symbolism according to well-determined rules. If the means of
expression are restricted in such a way that (1) these expressions
always have sense, and (2) it is decidable whether the produced
expressions are true in all possible worlds (universally valid,
*allgemeingultig*), then *L* is called a
"Universal Leibniz Language". A universally valid
fundamental expression is called a Leibniz Theorem. A logic calculus
is defined as a set of truths presentable by a Leibniz theorem over
*L*.



The close relation between logic and metaphysics is the topic of
Scholz's book *Metaphysik als strenge Wissenschaft*
(Scholz 1941). In this book metaphysics is dealt with as an ontology
in the sense of a theory comprising the entirety of truths. It can be
linguistically expressed and deals with things which can be understood
as individuals. These truths are not restricted to particular domains,
but are valid for all non-empty domains in all possible worlds (pp.
13-14). Metaphysics as a rigorous science implies the
construction of a formalized "precision language". In this
book Scholz uses the language of first order predicate calculus with
identity. A central notion is "universal validity"
(*Allgemeingultigkeit*), understood as a metaphysical
notion (validity in all possible worlds). This notion is applied to an
axiomatized theory of identity and difference.



Scholz analyzed classical metaphysical doctrines with his logical tool
of a predicate calculus with identity. His considerations are based on
a special variation of a Platonic ontology combined with
Leibniz's notion of possible worlds, the Frege-Russell
mathematical logic, Hilbert's axiomatic method, and
Tarski's semantics. This approach found its final expression in
the influential textbook *Grundzuge der mathematischen
Logik* which was elaborated, co-authored, and published by Gisbert
Hasenjaeger after Scholz's death (Scholz and Hasenjaeger 1961).
Hasenjaeger later called its philosophical background "discrete
ontology", a realistic position: "The world of concrete
(or also abstract) things *consists* just *of things*
which have some features and do not have others; between them some
relations are given, others not" (Hasenjaeger 1962, pp.
30-31).



In 1952 Scholz published together with Hans Hermes the section
"Mathematische Logik" in the *Enzyklopadie der
Mathematischen Wissenschaften* (Hermes and Scholz 1952), a
comprehensive survey of classical, bivalent and decidable logic. They
focused on sentential logic based on the notion of universal validity
(*Allgemeingultigkeit*). They argued for the priority of
semantical over syntactical considerations.


### 3.3 Historiography of Logic



Scholz's most important contributions to the development of
logic can be seen in his contributions to the historiography of logic.
He stressed the value of the contributions of Gottfried Wilhelm
Leibniz (1646-1716) and Bernard Bolzano (1781-1848) for
the emergence of modern logic. He applied the method of logical
analysis to classical philosophical texts, reconsidering, e. g.,
Anselm's proof of the existence of God (Scholz 1950/51),
Descartes's *cogito* argument (Scholz 1931b), and
Kant's transcendental deduction (Scholz 1943/44). He devoted
considerable efforts to the study of Gottlob Frege's work (cf.
Sundholm 2005) and promoted David Hilbert's metamathematics
(Scholz 1942). With his *Geschichte der Logik* (1931a) Heinrich
Scholz was a pioneer in the historiography of modern logic. Scholz
restricted his presentation to formal logic or logistics. He
reconstructs its development starting with Aristotle's logic,
discussing the Stoic modifications, medieval and early modern
variations, arriving at Franz Brentano's (1838-1917)
contributions, whom he called the "only original figure among
the German formal logicians [in philosophy] of the 19th
century after *Bolzano* and prior to *Husserl*"
(pp. 46-47). For Scholz, the modern shape of logic starts with
Leibniz: "We speak of a sunrise mentioning the great name of
*Leibniz*. With him a new life of Aristotelian logic begins,
which finds its most beautiful manifestation in our days in the modern
exact logic in the form of logistics" (p. 48). He highlighted
Gottlob Frege as "the greatest genius of the new logic in the
19th century" (p. 57). According to Scholz he did
more than any other logician for the interpretation of fundamental
mathematical concepts with the help of fundamental concepts of logic
operating on the basis of exactly defined principles. With this he
raised the logical calculus to a level which made the Leibnizian
"game with signs" possible.


## 4. Conclusions



Heinrich Scholz was important as an integrating figure in the
development of logic in the first half of the 20th century.
He kept Mathematical Logic in touch with Philosophy. With his focus on
semantics he set the agenda for the development after World War II.
Important academics of German postwar logic, including Gisbert
Hasenjaeger and Hans Hermes, were his students.