In 1917 Scholz was appointed to the chair of Philosophy of Religion at the University of Breslau. He remained there for four years before accepting the Chair of Philosophy at the University of Kiel in 1921. This marked an important change in the direction of Scholz's research for at this time his interests turned towards mathematical logic. From his own account, this new interest came about because he accidentally came across Whitehead's and Russell's Principia Mathematica in 1921. Volker Peckhaus writes :-
Scholz recognized that this work provided what he had been looking for in vain for so long. It exercised a decisive influence on the subsequent course of his personal life, as he stressed. This work persuaded Scholz of the importance of mathematics for philosophy, although he had at that time no deeper knowledge of this science.However, another factor in his change in interests was undoubtedly Otto Toeplitz. Toeplitz had been an extraordinary professor of mathematics at Kiel in 1913 and had become an ordinary professor in the year before Scholz arrived in Kiel. Although researching into Hilbert spaces and spectral theory, Toeplitz had broad mathematical interests and encouraged Scholz's growing passion for foundational questions in mathematics. In  Segal suggests that Scholz's love of structure was also important in his move into mathematical logic:-
Scholz's feeling for structure was no small thing. He apparently felt that when having guests for dinner: (1) no more than six people should be invited; (2) there must be an excellent menu; (3) a discussion theme must be planned; and (4) the guests should have prepared themselves as much as possible beforehand on this theme.While he was at Kiel, Scholz's first wife died in 1924. He confessed to his philosopher friend Eduard Spranger while at his wife's grave:-
You understand how I am not able to work on things with content.Of course for someone like Scholz, who had trained in theology and then philosophy, mathematical logic involved a deep understanding of mathematics which he had never studied. He rectified this by taking an undergraduate degree in mathematics and theoretical physics at Kiel while at the same time carrying out his duties as Professor of Philosophy. In 1928 Scholz left Kiel and moved to Münster where he was initially appointed as Professor of Philosophy. Heinrich Behnke had been appointed as an ordinary professor of mathematics at Münster in 1927 and, following Scholz's arrival, the two became good friends. One reason for this may have been the fact that both were Lutherans recently arrived in Münster which was in a Roman Catholic region of Germany.
Right from the time he arrived at Münster, Scholz worked towards building a school of mathematical logic there. He gave lecture courses on mathematical logic and also lectured on the great philosophers. In 1931 he published Geschichte der Logik Ⓣ, a short but erudite study, which looks at the history of results in logic leading to the study of mathematical logic. A N Prior, reviewing the English translation published thirty years later, writes that Scholz:-
... pioneered the view that ancient and medieval logic was not something totally different (for better or for worse) from what modern logicians are doing by mathematical means. The author was one of the first to see clearly that there is no better aid than modern logic to make clear what Aristotle, the Stoics, the Schoolmen and also a few post-Renaissance figures like Leibniz, were really after.Also in 1931 Scholz published the article Über das Cogito, ergo sum Ⓣ which, as the title indicates, examines Descartes' Cogito argument. In 1940 Scholz published the 55-page pamphlet Was Ist Philosophie? Der Erste und der Letzte Schritt auf dem Wege zu Ihrer Selbstbestimmung Ⓣ. Paul Bernays writes that Scholz says :-
... in his concluding summary that the philosophy which he intended is neither more nor less than mathematical logic, axiomatics ... Apparently his view is that foundational research must first attain a more advanced stage, and at the same time the minds of philosophers must, in the school of mathematical logic and axiomatics, be turned to the spirit of clearness and precision - whose compatibility with philosophical profundity is stressed by Scholz in opposition to a frequent opinion - before a valuable speculative synthesis can be hoped for.As we indicated above, Scholz's aim was to establish a world centre of mathematical logic at Münster. He was successful in attracting some top quality doctoral students such as Friedrich Bachmann who was awarded his doctorate in 1933. Other doctoralstudents who went on to become leading researcher include Hans Hermes (doctorate in 1938) and Gisbert Hasenjaeger (doctorate in 1950). Scholz made an important step in that direction when he obtained Frege's estate for Münster in 1935. By this time his research team at Münster were being referred to as "the Münster school of mathematical logic." The Technical University of Karlsruhe held Ernst Schröder's papers and Scholz was also successful in adding these to the growing collection of resources of his school :-
It was one of the tragic events of war that Frege's and Schröder's papers were most probably destroyed during the bomb attacks on Münster in March 1945.In 1938 Scholz's professorship in Philosophy had its title changed to a professorship in the Philosophy of Mathematics and Science. Its title was changed again in 1943 to the Chair of Mathematical Logic and Foundational Questions in Mathematics.
The rise to power of the Nazis in Germany was, at first, pleasing to Scholz. He was a conservative nationalist, actually described by his friend Behnke as a "small-minded Prussian nationalist". Behnke avoided discussing political issues with him since he quickly realised that such topics were difficult. In some ways the Nazi laws against the Jews helped Scholz establish Münster as an important centre for logic since the leading researchers in the other centres of Berlin and Göttingen were forced out. However, Scholz cared deeply about his colleagues and soon got himself into trouble by trying to help those facing cruel persecution by the Nazis.
Jan Salamucha, who had been professor of theology at Krakow, was sent to the concentration camp in Sachsenhausen in 1940. On 14 March 1940, Scholz sent a petition to the education department in the occupied region of Poland seeking Salamucha's release. In October of that year Scholz received a letter from the Education Minister telling him in no uncertain terms that his petition had "injured the national honour" and the minister expressed his "sharpest disapproval" and told Scholz that he was forbidden from sending any further petitions unless they had the minister's approval. However Salamucha was released, but did not survive the war being murdered by the Nazis in 1944. Despite the warning Scholz had received from the Education Minister he continued to try to help those in difficulty. Alfred Tarski had escaped to the United States but his wife remained in Warsaw. Scholz tried to assist them in making contact. He had corresponded with Jan Łukasiewicz from 1938 and helped him and his wife Regina to leave Poland and hide in Germany.
However, Scholz was able to play the system to the advantage of mathematical logic by keeping on good terms with Nazis like Bieberbach. Max Steck had published a book entitled The main problem of mathematics in 1942 in which he bitterly attacked the formalist approach to mathematics. He deeply opposed Hilbert's approach which he described as Jewish - the worst possible insult in Germany at this time. Bieberbach asked Scholz to write an article for Deutsche Mathematik (Bieberbach's racially oriented journal) to answer the attacks on formalism in Steck's book. This may seem surprising since Bieberbach led the Nazi mathematicians' attack on Jewish mathematics. However, perhaps exactly for this reason he wanted to make sure that Hilbert was not considered "Jewish." Scholz wrote What does formalised study of the foundations of mathematics aim at? for publication in Deutsche Mathematik. Scholz's connections with Bieberbach had led earlier to funds being provided for a series of monographs on mathematical logic which had started in 1937. That Scholz had received this funding had upset Steck who had attacked it in his 1942 book writing:-
What Scholz has understood is doubtless this, to obtain from the German State huge amounts of publication money for this logic production. We fundamentally reject this logic which praises the English empiricists and sensory philosophers such as the Englishmen Locke, Berkeley, Hume, and by now find it really time to speak for once about the "Great Germans".During the war years Scholz published the book Metaphysik als strenge Wissenschaft Ⓣ (1941) and a number of articles such as Leibniz und die mathematische Grundlagenforschung Ⓣ (1942), Was will die formalisierte Grundlagenforschung? Ⓣ (1943) and Pascals Forderungen an die mathematische Methode Ⓣ (1945).
Scholz remained as head of the Institute for Mathematical Logic and Foundational Research at Münster until he retired in 1952. He published a number of major books towards the end of his career: Vorlesungen über Grundzüge der mathematischen Logik Ⓣ (1950); and (with H Hermes) Mathematische Logik Ⓣ (1952). Both receive some criticism from reviewers. Haskell Curry, reviewing the first of these writes:-
This is a treatise on the classical (two-valued) propositional algebra and the predicate calculus of first order based on it. The author's point of view may be described as semantical. He presupposes "eine präzisierte Metasprache für welche die zu formalisierende Logik verbindlich ist." As he points out in the preface, this implies a certain metaphysical bias. The fundamental idea is that of semantical "Allgemeingültigheit", i.e. validity for every possible model. The author develops both the algebra and the calculus from this point of view; the deductive, axiomatic standpoint is not considered at all for the algebra, and is relegated to a secondary role for the calculus. For the algebra this amounts to a treatment from the matrix point of view; but for the calculus it entails that the line between constructive and nonconstructive results is not as sharply drawn as one would expect in a modern work. ...Reviewing the 1952 text, Georg Kreisel writes:-
This monograph treats the propositional calculus, the predicate calculus of first order with and without identity ... The technical parts are clear and concise; the authors' "semantic" point of view is described too briefly to be very coherent. The authors state (i) that mathematical logic is intended to provide a precise(r) formulation of the notion of consequence on which mathematical theories are based, (ii) that they consider those mathematical theories which fall within the scope of two-valued logic 'where every proposition is true or false'. There is no clear indication which branches of mathematics satisfy this condition; it seems that abstract algebras and other axiomatic theories do, intuitive geometry and numerical arithmetic, called a 'kind' of calculus ..., apparently do not.Gisbert Hasenjaeger whose thesis had been supervised by Scholtz, produced a book Grundzüge der mathematischen Logik Ⓣ in 1961 which was jointly authored with Scholz despite being published five years after Scholz's death.
Scholz was survived by his second wife, Erna.
Article by: J J O'Connor and E F Robertson