Paul Lorenzen
Paul Lorenzen (born March 24, 1915 in Kiel , † October 1, 1994 in Göttingen ) was a German philosopher , scientific theorist , mathematician and logician . Alongside Wilhelm Kamlah, he is the founder of the Erlangen School of Methodical Constructivism .
Lorenzen began as a logician and mathematician and then founded a philosophy of stepbystep and dialogical structure.
In logical propaedeutics , he designed a new beginning of reasonable speech and developed dialogical logic , a logic process that is suitable for arguing.
Lorenzen also made important contributions to mathematics and the philosophy of science: He founded a variant of operationalism called protophysics . In addition, he developed approaches to questions of ethics and political philosophy from a normative modal logic .
Life
Lorenzen studied mathematics, physics, chemistry and philosophy in Kiel, Berlin and Göttingen. Here he received his doctorate in 1938 under Helmut Hasse with a thesis on the abstract justification of the ideal multiplicative theory . In 1939 he became Wolfgang Krull's assistant in Bonn , and another academic teacher from Lorenzen was Oskar Becker . He took part in the Second World War and had been a teacher at the Wesermünde Naval School from 1942 . Back in Bonn he was able to complete his habilitation in 1946 , was briefly visiting professor in Cambridge in 1948/49 and became a professor in Bonn in 1952.
In 1956 he was given a full professorship for philosophy in Kiel . In 1962 he accepted the appointment to Erlangen, which had come about on the initiative of Wilhelm Kamlah : "... solely for the purpose of being able to work with Kamlah". Here both taught initially in close cooperation, which was the first to produce the "logical propaedeutics " that was widely known at the time . This approach was so successful that it became a school that today operates under different names (e.g. Erlangen Constructivism ). From 1967 to 1968 Lorenzen John Locke was a lecturer at Oxford . Since 1967 he has held visiting professorships in Austin (Texas) and Boston during the lecturefree period . In 1980 Lorenzen was awarded the Federal Cross of Merit on ribbon. Since his retirement in 1980 he lived in Göttingen, where he died in 1994. His estate is in the Philosophical Archive of the University of Konstanz . The Paul Lorenzen Foundation regularly holds scientific conferences on philosophy and related sciences.
Erlangen school
The Methodological philosophy Lorenzen and Kamlah, the Erlanger school, sought an enlightening new foundation of reason between the critical rationalism of Karl Popper and that of the transcendental KarlOtto Apel's intended ultimate justification and found by the similarities between the pragmatic justification conception with the universal pragmatics a coalition partner in the Frankfurt School ("Grand Coalition") against scientism and logical empiricism . There were congresses in the late 1960s at which Jürgen Habermas and Lorenzen were the main speakers. The Erlangen school was in constant feud with the epistemological structuralism advocated by Wolfgang Stegmüller . Both directions became the founding currents of the philosophy of science in Germany.
It is true that the Erlangen school has a number of superficial similarities with analytical philosophy , above all the focus on logic and science orientation with Lorenzen. However, constructivism, on the other hand, assumes a pragmatic and operationalist integration of action in everyday life. He rejects an analysis of language that is merely found and integrates the treatment of normative problems into philosophy. The main strands of Erlangen's philosophy are the circular principle of methodological order, which thematizes the sequence in the scientific procedure, and dialogic and reflexive reason. In this context there were also the debates about the approach in the philosophy of language, logic and the technical and ethicalpolitical sciences:
 From the everyday practice of the living environment highly stylized theory should allow crossdisciplinary foundation of the sciences.
In the 1970s, the first employees from the Erlangen area received appointments and developed the Erlangen philosophy further: Jürgen Mittelstraß , Friedrich Kambartel and others went to the reform university in Konstanz ("Konstanzer Schule" or "ErlangenKonstanzer Schule"), Kuno Lorenz developed a dialogical component of the Erlangen philosophy in Saarbrücken, Peter Janich designed a methodical culturalism in Marburg . Carl Friedrich Gethmann , Friedrich Kambartel and others have joined the discourses on methodical philosophy. Around 50 professors around Jürgen Mittelstrass, who are close to the Erlangen school, have been writing an encyclopedia since the 1970s. This encyclopedia Philosophy and Philosophy of Science, which is now in the 2nd edition of Mittelstraß, became one of the largest general reference works on philosophy in the Germanspeaking world.
Logical foundations
As mentioned above, the first product of the collaboration with Kamlah in 1967 was Logical Propaedeutics . Preschool of Sensible Speaking. In it a circlefree construction of a reasonable language is sought. Lorenzen and Kamlah wanted to counter inaccuracies in the terms and argumentation structures used. The inevitability of a hermeneutic circle or similar circle like thinking is attempted to refute by demonstrating a circle free, stepbystep structure of the respective practice.
The book represents a new approach to the theory of action and the philosophy of language , in which objects are not spoken of without preconditions, but rather a doctrine of understandable speech and argumentation that can be controlled with regard to validity claims is developed. Using predication , speaking about objects is introduced in a controlled manner according to rules, without finding them prelinguistically as given: Language opens up the world.
 The aim is to offer an introduction to reasoning based on logic in order to provide a basis for reasonable justification. Lorenzen advocated conceptually clear thinking and a methodically ordered procedure in philosophical discourse. The willingness in principle to have all preorientations critically questioned is emphasized. A critical constructive philosophy of science as part of the linguistic turn should be prepared by logic.
In addition to construction, Lorenzen introduces the process of abstraction: If there are equivalence relations , a generic term can be formed by ignoring the differences. Socalled abstract objects cannot and should not be discussed independently of this process. The usual definition symbols ": =" are replaced by Lorenzen with the symbol " " in order to do justice to the language introduced in the context of the definition.
Lorenzen was a contemporary follower of logical atomism at the time of Logical Propaedeutics : An atomic elementary proposition has a structure of subject, copula (ε) and predicate. In the early 1970s, Lorenzen's usual approach to mathematics was no longer sufficient for the development of an ethic , and together with Oswald Schwemmer he instead developed extensive elementary clauses with several predicators and two additional types of copula.
Instead of prescribing two independent, logically linked elementary sentences such as Fido ε dog and Fido ε brown , the common elementary statement Fido ε a brown dog is allowed. At the same time, Lorenzen opposes speaking of a doglike brown. "Dog" is introduced as an independent selfpredication, while "brown" is introduced as a dependent appredication. The database expert and IT pioneer Hartmut Wedekind sees Lorenzen's use of several predicators in an elementary sentence as a parallel to Edgar F. Codd's introduction of relational databases .
Talking about actions is introduced empirically , such as the prompt: (Peter) (Throw) (stone). Lorenzen provides a Tatcopula (tut) and an event copula κ in addition to the usual actual copula ε. The sentence: “Tilman carry water into the house with buckets” is therefore an elementary sentence . The copula is not a predicator, whereas the activity “carrying” is a selfpredicator. Selfpredicators are the essential predicators (here: nouns and verbs) that can stand alone to the right of the copula (if necessary) .
This Lorenzsche revision of the procedure of logical propaedeutics is controversial in the constructive philosophy of science . It can be interpreted as a departure from the linguisticphilosophical approach in Wittgenstein 's late philosophy . Kuno Lorenz does not consider it appropriate to introduce a Tatkopula and also to allow activities as selfpredicators: With “Der Vogel singen” “singing” is no longer constructed as an articulator of the schema “singing”. The immediate validity connection between an elementary statement and its introduction to the predication is lost.
The structure of the individual elements of the elementary sentence expanded in this way is worked out in great detail by Lorenzen: In addition to 216 symbolized local prepositions, there are three case morphemes:
 The middle case ("with buckets") is used for devices required for actions.
 The Werkfall ("to ashes") is used for the result of an action.
 The affection ("to Hans") is used in the context of the action of swapping.
Dialogic logic
Lorenzen was of the opinion that an intuitionistic logic can initially be justified more easily than the usual classic twovalued logic that is based on it. The principle of the excluded third party should not simply be assumed to be logically correct for infinite areas or future circumstances . The antinomies of pure reason are not naturally logically true: The antinomy “The world has a beginning in time or the world has no beginning in time” is, according to Lorenzen, no alternative statement that can be logically assumed to be correct . It would only be logically correct if one of the two subclauses was proven to be true on its own.
Lorenzen developed together with Kuno Lorenz a dialogical logic , wherein the logic operators (instead of the truth table) by using formal structured dialogue by attack and defense of proponent and opponent can be determined in the dialogue game. This dialogical logic has also been conceived as a model for arguing, because it corresponds more closely to conversational situations than the usual derivation of statements in logic calculations . An argument is sometimes given its validity (becomes true) if one accepts an argument from the other party or if no objection is meaningful any more.
The subjunctor ("if ..., then ...":) is understood to be interpretable in different ways, depending on which attack and defense rules are applied. In the case of a nonclassic set of rules, statements that are not truthful are also allowed during the dialogue , although the truth value of the overall statement is established at the end of a completed dialogue.
The subjunction is the only one that contains two dialogues. Example of a formal dialogue on the statement (if a, then a):
comment  

The Subjunktionsbehauptung is attacked after Subjunktionsregel by the foregoing Primaussage is claimed.  
The following prime statement is given as a defense; this is at the same time an adoption of the previous line. 
Whether you first have to fulfill your own obligation to provide evidence or whether you can oblige the interlocutor to prove his partial statement beforehand depends on the framework rules.
Lorenz and Lorenzen developed a socalled effective dialogue rule: "The proponent attacks a statement made by the other or defends himself against the last attack made by the other." The socalled strict dialogue rule continues to apply to the opponent, only with regard to the proponent's last statement to attack or defend. The effective logic corresponds to the intuitionist logic.
If a statement is later no longer available, a temporal logic can be developed from the dialogic logic. Carl Friedrich von Weizsäcker and Peter Mittelstaedt used this for the interpretation of quantum physics through temporal logic ( quantum logic ), although Lorenzen did not share this interpretation. For him there is temporal logic exclusively in modal logic and not in formal logic.
The various logic systems can be merged into one another by adding or removing dialog rules.
Logical truths are sometimes excellent in dialogical logic in that can defend in the course of a dialogue of one interlocutor, by a proof of the other takes over so that it can counter anything.
Lorenzen used the quantifier symbols (one quantifier: "for some") and (universal quantifier: "for all") to explain the connection to the corresponding junctions and to facilitate the interpretation so that the error is not always made from the formulation of the quantifiers to infer the "existence" of something.
corresponds to:  
corresponds to: 
The rules for the quantifiers in dialogic logic are as follows:
Quantifiers  attack  defense 

Constructive math
As early as the 1950s, Lorenzen developed operational mathematics that, instead of what has already been found, begins with an approach, namely calculatory counting.
For this purpose, a counting or bar calculus of the basic numbers (as Lorenzen says instead of natural numbers to differentiate constructive action from what is found) is used:
 ⇒ 
 n ⇒ n 
This is how numbers are produced “by us”: They are the products of counting operations. Logic and mathematics are pragmatically understood as a theory of operating according to certain rules. On this basis, initially also called “operational”, which was only called “constructive” in the 1960s, Lorenzen reconstructed mathematics up to classical analysis , mathematics that only get by with what can be comprehensibly constructed.
Lorenzen participated in the Hilbert program and in 1951 (independently of Wang Hao ) carried out a proof of freedom from contradictions for the branched type theory . In 1962 Lorenzen was one of the seven founding members of the German Association for Mathematical Logic and for Foundations of Exact Sciences . In his book Metamathematik , published in the same year, he understands metamathematics as “mathematics of metatheories”, whereby a metatheory is a (constructive or axiomatic) theory about axiomatic theories. Lorenzen introduced the term “ admissible rule ” in the sense of eliminability: If a calculus rule can be eliminated, then it is valid in this calculus. The use of Gentzen's law , which states the validity of the rule of intersection, is the main metalogical technique of proofs of consistency in arithmetic and analysis. The goal of Lorenzen's metamathematics was initially to prove the consistency of constructive mathematics by proving the consistency of axiomatic mathematics, which could not be obtained in axiomatic mathematics according to Gödel's incompleteness theorem (which Lorenzen called "inevitable theorem ") .
Gentzen's law proves the consistency of the logic of certain calculations. Lorenzen sees no contradiction in this to Kurt Gödel's results :
"Gödel's inalienability theorem says that an arithmetization of this consistency proof given here leads to a formulation of the consistency assertion that cannot be derived in the Peano formalism, but this is not an objection to the consistency proof, but only additional information about the Peano formalism."
In 1965 Lorenzen completed the program of constructive mathematics with a reconstruction of classical analysis. Not all of the usual evidence is adopted, but the classic evidence is reworked in such a way that most of the results are retained. Sequences are abstracted from terms. Irrational numbers can be determined as an abstraction from Cauchyconvergent sequences of rational numbers, the difference of which is a zero sequence. Special sentences such as BolzanoWeierstrass' theorem are reformulated in such a way that they only apply to constructible sequences. The axiom of choice is therefore not required for the corresponding proofs .
With constructive mathematics, Lorenzen had maneuvered himself into an outsider position among mathematicians from the late 1960s. For the vast majority of mathematicians, it was hard to see why one should get involved with the philosophically motivated limitations of mathematics.
Lorenzen wrote an elementary geometry while still retired. In addition to working out protogeometry and geometry, he designs a foundation for analytical geometry . Lorenzen rejects Infinity notions from. For him, infinity is just an ignoring (abstraction, disregard of) finitude. While Lorenzen still used indefinite quantifiers for uncountable sets in the reconstruction of Analysis in 1965, he later speaks of a set of real numbers that is just necessary as a basis (e.g. algebraic field extensions with transcendent numbers ) and not of the set "All" real numbers. Instead of starting from found uncountable sets, only constructable lists of numbers and functions are used. In this way, a countable set of real numbers required for practical applications is obtained. The usual Cantor diagonalizations to prove uncountability are interpreted in constructive form as techniques for expanding. On uncountable sets is thus dispensed with, there are numbers, not the belong and are needed, they are designed and in an algebraic envelope countable to taken .
Protophysics
Together with Peter Janich and Rüdiger Inhetveen , Lorenzen developed the socalled protophysics , a controversial prephysics of measuring instruments, in which one obtains an account of the determination of measuring instruments (before the measurements) and these determinations are not revised later. Following the approaches of Kant and Dingler , this was initially worked out for geometry and time calculation (chronometry). Flat surfaces, right angles or evenly ticking clocks (clocks) are not empirical research objects, but artefacts (i.e. products of human cultural technology). The norms for measuring devices take on roughly the role that the transcendental forms of knowledge a priori (space and time) have in Kant. However, this is operationalized in protophysics, the measuring device standards are part of a pragmatic theory of action.
The first work and discussions on protophysics arose in the 1930s in the Munich Dingler Circle , which is associated with German Physics because the work of Albert Einstein and others on the theory of relativity was partially rejected and hostile to the theory of relativity.
The principle of the methodical (therefore: methodical constructivism ) order prescribes the following about measuring instruments: The standardized provisions that enable the manufacture of measuring devices cannot be refuted by measurements that are only obtained with the help of these measuring devices.
In addition to geometry and chronometry, Lorenzen worked out a theory of probability as the third pillar of protophysics. Random generators can be defined as standardized measuring devices.
Lorenzen initially founded protophysics with socalled homogeneity principles : the points on a flat surface or the clocks of a clock should not be distinguishable. Later, with Rüdiger Inhetveen , he developed a protogeometry with a form principle, in which a plane is introduced via freely folding symmetrical fitting: The mutual fitting of workpieces with their impressions and copies (folding symmetry) is the criterion whether a leveling (for example according to Dingler's threeplate Grinding process) has been achieved. This also results in a rotational symmetry of flat objects. Indications as to the extent to which common planarization methods, such as laser polishing , actually planarize, are lacking in the protophysical literature; the equivalence of various suitable planarization processes has not been proven. Instead, there are socalled uniqueness proofs for geometric shapes that have already been achieved. In chronometry there is a proof from Janich that the rate ratios of any two clocks of any type are constant. The integration of digital clocks in chronometry solves the problem of the correct detection of common Lorenzen procedures.
Lorenzen used the terminological (also in political theory) adjective ideal to strive for a goal that can never be fully achieved . A leveling of ideal objects can be aimed for (e.g. when manually grinding lenses), although the goal is never quite achieved. This striving action can be introduced via a dialogue in which, depending on the increasingly strict accuracy margin ( Stekeler ), a more advanced implementation is to be specified in which the criterion (for leveling, the folding symmetry, which can be checked by coloring straightening plates) is met : If you pave for a long enough time, the workpiece becomes even as you like.
In the subsequent geometry, Lorenzen argues in favor of the form principle in construction. This means that the shape of a geometric figure only depends on the design idea. Lorenzen interprets the Platonic ideas as such construction plans, but without adopting the nonoperational Platonism of the theory of ideas . The size of the original starting distance is not included in the geometric construction.
Both activities  the production of the basic shapes in protogeometry and the construction of geometric figures in geometry  are operations at Lorenzen. Lorenzen is interpreted by his former student Peter Janich to mean that he has abandoned the operative concept and instead turned to a form principle of Platonic form.
The starting distance of a geometric construction with compass and ruler can be a multiple of another starting distance, i.e. triangles of the same construction can be of different sizes. But they have the same angle. This approach of starting from figures of different sizes and of the same shape corresponds (according to John Wallis ) exactly to the use of the axiom of parallels and this leads to Euclidean geometry . By comparing elastic collisions with inelastic collisions , Lorenzen then works out the classical law of conservation of momentum and the Coulomb charge ratio to form a classical physics of mass and charge.
This suggests that Lorenzen, succeeding Hugo Dingler, would be an opponent of the theory of relativity . In fact, he insists on the primacy of philosophical justifications over empirical physics in fundamental questions. However, since 1977 Lorenzen no longer ignores the empirically confirmed results of the general theory of relativity , but only does not represent the majority opinion of physicists that the consequence of the general theory of relativity is an actual curvature of space. This is an interpretation of the conventionalistic aspects of the early standard work Gravitation and Cosmology by Steven Weinberg . Lorenzen sees in the metric tensor of the field equations of Einstein and Hilbert only a mathematical description for the conversion of the pseudoEuclidean proportions in inertial systems to nonuniformly moving reference systems. Not the space is considered to be curved, but as compared to Euclidean geometry as a basis the light (of the general theory of relativity in accordance) flows for example in strong gravitation fields crooked .
In Erlangen's constructivism and methodical culturalism , a number of other prototheories are developed across disciplines (protochemistry, protobiology, protopsychology). Carl Friedrich Gethmann designed a protological and a protoethic.
Modal logic
Lorenzen systematized the modal words “can”, “may”, “must” etc. From the ontic and deonticnormative modal logic , Lorenzen developed the basis for the socalled Hauptschule der Vernunft as a continuation of the logical propaedeutics , which as a constructive philosophy of science the technical and political sciences should justify. An ortho language is specially designed for this.
The various forms of modal logic include technicalscientific, actionrelated, ethicalpractical and biologicalmedical summaries of course formulations:
Lorenzen distinguishes three types of modalities:
 The ontic modalities of the course hypotheses: (The house can collapse.) Symbol:
 The deontic modalities of normative logic with command and permission. Symbol: and
 The “practical” modalities of accessibility and inevitability. The symbol is ERR (availability)
In addition there is an elaboration of the biological potentiality:
 Biologicalmedical becoming (potentially): A tree can grow from a cherry stone.
As usual, “necessary p” is defined by “not possible not p”; in Lorenzen's modal logic notation:
The inevitability UNV is defined accordingly. The requirement (required relative to a system of purposes) is introduced in the deonticnormative logic before the mentioned may (allowed:) .
Lorenzen's modal logic is initially informally conditioned by knowledge, which means that the statements made in the modal logic apply relative to an alleged knowledge related to changes over time. Lorenzen uses additional exclamation marks for the imperatives in deonticnormative logic.
The different types of modalities also play together. For example in the sentence: Accessibility (human ability) implies possibility (course hypothesis).
A modal logic dialogue position can be obtained for every underlying knowledge if it is obtained by removing all modal logic signs. This follows from Gentzen's law . For Lorenzen, a punch line is to simply ground the modal logic.
From ethics to politics
For his work as John Locke Lecturer in Oxford, among other things, Lorenzen developed a normative logic in order to strive for a reasonable justification of ethics in the following years (initially with Oswald Schwemmer ), an aim that he rejected. He later considered ethics to be "incapable of theory". Instead, he sees the task of developing a political theory in our “posttraditional” culture in order to avoid civil wars.
Lorenzen criticized the talk of the will as imprecise. Personal ascriptions (strong will, free will, bad will) should not be taken into account for the ethicalpolitical assessment of a will, but the purposes should be able to be compared with needs (constructive sociology). In any case, people use progressive hypotheses to create purposes of their actions from wishes (and from assumptions, technical claims about how these goals can be achieved). Together with other philosophers such as Friedrich Kambartel and Jürgen Habermas , Lorenzen, in contrast to the Vienna Circle, emphasized the primacy of ethicalpolitical (practical) over technical (theoretical) reason.
The chosen goals can contradict each other. When planning, for example in a group, approaches are mutually exclusive. Lorenzen quotes the Kantian example that both Franz I and Charles V can not get Milan . The purposes are incompatible (incompatible). But even when one agrees on the purposes, tasks and goals, the means are sometimes controversial. If the approaches are made compatible, everyone involved overcomes each other for the common goal. If it works, “transsubjectivity” is achieved.
Lorenzen wrote works on democratic socialism and the concept of a republic : Peace politicians develop a system of compatible ways of life (supreme purposes) with the aim of prosperity and peace.
reception
As mentioned above, Lorenzen had a wide student body. Some colleagues carried out a further development of the approach and yet, in some cases, have distinguished themselves from it since 1970. Outofschool criticism of Lorenzen's approach came in particular from representatives of the structuralist theory concept and critical rationalism . Nevertheless, some philosophers and scientists took on suggestions.
Jürgen Habermas and Paul Lorenzen gave main lectures at the IX during the height of the student movement in West Germany in 1969 . German Congress for Philosophy in Düsseldorf, which took up the positivism controversy and opened up new perspectives in the field of ethics and discourse theory. Friedrich Kambartel developed criteria for a rational dialogue from Lorenzen's pragmatic concept of justification and Habermas's universal pragmatics . Kambartel later criticized Lorenzen's practical philosophy in detail: reason cannot be grasped as precisely as Lorenzen designed it. Rather, reason is a culture into which one grows, a social practice in which one forms one's judgment.
In the 1970s, Lorenzen's approach stood in contrast to the historical observations of Thomas S. Kuhn , who claimed that rationality only existed within alternating paradigms . Jürgen Mittelstraß then tried to combine a historical theory of science with Lorenz's constructive approach. Through the work of Carl Friedrich Gethmann, Jürgen Mittelstraß and Christian Thiel on technology assessment and the history of science , among other things, Lorenzen's approach has been further developed.
Kuno Lorenz developed Lorenzen's approach to a dialogical constructivism on the connection between semiotics and pragmatics. He does not share the elementary sentence concept expanded by Lorenzen with appredicators, including the introduction of a separate Tatkopula, because the linguisticphilosophical connection between predication and elementary sentence would thereby be partially lost. Peter Janich has further developed the protosciences and with his methodical culturalism he has pointedly differentiated himself from Lorenzen, whom he accuses of having abandoned the original operational concept.
Together with the scientific theorist Wolfgang Stegmüller , Lorenzen drew attention to analytical and AngloAmerican philosophy in Germany after the Second World War . Stegmüller, however, criticized Lorenzen's constructivist scientific justification as a “seductive metaphor”. Carl Friedrich von Weizsäcker contrasts Lorenzen's merging of logic and democracy with Nietzsche's thinking.
In mathematics, Lorenzen is highly valued for his early work on operational logic and mathematics as well as metamathematics, while his later constructive mathematics and protophysics (which was still widely discussed in the 1970s) are scientifically considered outsider positions.
Hans Albert claims that Lorenzen, by starting from action, is subject to the breaking off of justification , like any philosophy that starts with something obvious. Hans Albert and Helmut F. Spinner criticize Lorenzen's rejection of theoretical pluralism .
The economist Horst Steinmann , the computer scientist Hartmut Wedekind, the mathematician Peter Zahn and other scientists took up Lorenz's suggestions and developed them further.
Robert Brandom builds with his inferentialism the language pragmatic approach Ludwig Wittgenstein and thus is close to the Erlanger school. In this context, there are comparisons between Brandom and Lorenzen and scientific collaborations and discussions between Brandom, Kambartel and Pirmin StekelerWeithofer .
bibliography
 Christian Thiel : Paul Lorenzen (19151994). Bibliography of the writings of Paul Lorenzen. In: Journal for General Philosophy of Science . 27: 113 / 187202 (1996).
Works (selection)
 1949 Via semiorganized groups. Springer, Berlin a. a.
 1951 The consistency of classical analysis. Mathematical Newspaper 54: 124.
 1951 measure and integral in constructive analysis. Mathematical Newspaper 54: 275.
 1951 Algebraic and logistic studies on free associations. The Journal of Symbolic Logic 16: 81106.
 1955 Introduction to operational logic and mathematics. Springer, Berlin a. a., ²1969, further reprints 1994.
 1958 Formal logic. de Gruyter, Berlin (Göschen Collection, vol. 1176 / 1176a); verb. Ed. ²1962, reviewed and expanded ³1967, verb. 4/1970; engl. Formal logic. Reidel, Dordrecht 1965; Formal logic. (transl. by Frederick J. Crosson) Kluwer Academic Publishers 2004.
 1960 The emergence of the exact sciences. Springer, Berlin a. a., reprints 1985.
 1960 The problem of justifying geometry as a science of spatial order. In: Philosophia naturalis . 6, 1961.
 1962 metamathematics. Bibliographisches Institut, Mannheim (BIHTB 25) ² 1980; engl. Metamathematique. (transl. by J. B. Grize) Mouton de Gruyter, Berlin New York 1967; french 1967, span. 1971.
 1965 differential and integral. A constructive introduction to classical analysis. Academic Publishing Company, Frankfurt; engl. Differential and Integral: A Constructive Introduction to Classical Analysis. University of Texas Press, Austin 1971.
 1967 with Wilhelm Kamlah : Logical Propaedeutics or Preschool for Sensible Speech. Bibliographisches Institut, Mannheim (BIHTB 227 / 227a) ; 2., verb. u. exp. Edition 1973 a. d. T .: Logical propaedeutics. Preschool of Reasonable Speech, ISBN 3411052279 , reprinted 1990, 1992; since 1996 Metzler, Stuttgart; engl .: Logical Propaedeutic. PreSchool of Reasonable Discourse. (Trans. H. Robinson) University Press of America, Lanham 1984.
 1968 Methodical thinking. Suhrkamp, Frankfurt 1968, ² 1974 ff. (Stw 73).
 1969 Normative Logic and Ethics. Bibliographical Institute, Mannheim (BIHTB 236).
 1973 with Oswald Schwemmer : Constructive logic, ethics and philosophy of science. Bibliographisches Institut, Mannheim u. a., improve. Ed. ²1975, unchanged. Reprint 1982 (BIHTB 700).
 1974 Constructive philosophy of science. Suhrkamp, Frankfurt (stw 93).
 1977 Relativistic mechanics with classical geometry and kinematics. In: Mathematical Journal. Berlin 1977.
 1978 Theory of technical and political reason. Reclam, Stuttgart.
 1978 with Kuno Lorenz : Dialogic Logic. Scientific Book Society, Darmstadt.
 1984 elementary geometry. The foundation of analytical geometry. Bibliographisches Institut, Mannheim u. a., ISBN 3411004002 .
 1985 Basic concepts of technical and political culture. Twelve posts. Suhrkamp, Frankfurt (stw 494)
 1987 textbook of constructive philosophy of science. Bibliographisches Institut, Mannheim 1987; Metzler, Stuttgart ²2000, ISBN 3476017842 .
 1987 Constructive Philosophy. Transl. by Karl Richard Pavlovic. University of Massachusetts Press, Amherst, USA 1987, ISBN 0870235648 / ISBN 9780870235641 . Mainly contains translations of the essay collections Methodical Thinking 1968 and Constructive Philosophy of Science 1974.
 1990 Philosophical foundation problems of an economic and business ethics. In: Horst Steinmann , Peter Löhr (Hrsg.): Unternehmensethik. Poeschel, 2nd edition, Stuttgart 1991, 3568.
 1992 This side of idealism and realism. In: Peter Janich (Ed.): Developments in methodological philosophy. Suhrkamp, Frankfurt pp. 207217 (stw 979).
literature
 Carl Friedrich Gethmann, Jürgen Mittelstraß (Ed.): Paul Lorenzen in honor. Konstanz University Speeches 241st UVK, Konstanz 2011.
 Bruno Jahn: Biographical Encyclopedia of GermanSpeaking Philosophers. de Gruyter, Munich 2001, p. 257.
 Peter Janich (Ed.): Developments in methodological philosophy. Suhrkamp, Frankfurt 1992.
 Rudolf Kötter, Rüdiger Inhetveen: Paul Lorenzen. In: Philosophia naturalis . 32, 1995, pp. 319330.
 Kuno Lorenz (Ed.): Constructions versus positions. (2 vol.) Paul Lorenzen on his 60th birthday. de Gruyter, Berlin, New York 1979.
 Jürgen Mittelstraß (Hrsg.): Encyclopedia Philosophy and Philosophy of Science. Vol. 1–2, Bibliographisches Institut, Mannheim 1980 and 1984, Vol. 3–4, Metzler, Stuttgart 1995 and 1996; completely paperback ibid. 2004; 2nd, revised and significantly expanded edition, bound ibid. Since 2005.
 Jürgen Mittelstraß (Ed.): The constructivism in philosophy in the exit of Wilhelm Kamlah and Paul Lorenzen. mentis, Paderborn 2008 ( wide inf. ).
 Florian Rötzer: Paul Lorenzen. Conversation. In: ds. (Ed.): Thinking That Is Time. Conversations with German philosophers. Suhrkamp, Frankfurt 1987 (es 1406).
 Paul T. Sagal: Paul Lorenzen's constructivism and the recovery of philosophy. In: Synthesis Philosophica 2, 1987, pp. 173178.
 Burkhard Schafer: Paul Lorenzen. In: Julian NidaRümelin , Elif Özmen (Ed.): Philosophy of the Present in Individual Representations (= Kröner's pocket edition . Volume 423). 3rd, revised and updated edition. Kröner, Stuttgart 2007, ISBN 9783520423030 , pp. 392394.
 Eberhard Scheibe: Obituary Paul Lorenzen. Yearbook of the Academy of Sciences in Göttingen, 1996, pp. 251–259.
 Christian Thiel (Ed.): Academic commemoration for Paul Lorenzen on November 10, 1995. ErlangenNürnberg University Library, Nürnberg 1998.
 Christian Thiel: Lorenzen, Paul. In: Jürgen Mittelstraß (Hrsg.): Encyclopedia Philosophy and Philosophy of Science. Second edition. Volume 5, Metzler 2013, pp. 112115.
 Frédérick Tremblay: La rationalité d'un point de vue logique: entre dialogique et inférentialisme, étude comparative de Lorenzen et Brandom. Nancy 2008.
 Harald Wohlrapp : Paul Lorenzen. In: Bernd Lutz (Ed.): Metzler Philosophen Lexikon. Metzler, Stuttgart 3rd edition, 2003, pp. 420424.
Individual evidence
 ↑ The name Lorenzen is stressed on the second syllable.
 ↑ Lorenzen, quoted from: Carl Friedrich Gethmann: Lifeworld and Science: Studies on the Relationship of Phenomenology. Bouvier, Bonn 1991, p. 70.
 ↑ "Paul Lorenzen Foundation" at the University of Konstanz. ( Memento of the original from May 24, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
 ↑ With the constant participation of Gottfried Gabriel , Matthias Gatzemeier , Carl Friedrich Gethmann, Peter Janich , Friedrich Kambartel , Kuno Lorenz , Klaus Mainzer , Peter SchröderHeister , Christian Thiel , Reiner Wimmer in connection with Martin Carrier edited by Jürgen Mittelstraß
 ^ In the first edition, 4 volumes, 1980–1996. Since 2005, a second, revised and significantly expanded edition has been published in eight volumes.
 ^ Christian Thiel: Lorenzen, Paul. In: Jürgen Mittelstraß (Hrsg.): Encyclopedia Philosophy and Philosophy of Science. Second edition. Volume 5, p. 113.
 ↑ Harald Wohlrapp: Paul Lorenzen. In: Bernd Lutz (Ed.): Metzler Philosophen Lexikon. Metzler, Stuttgart 3rd edition, 2003, p. 423.
 ↑ Logical Propaedeutic 1967, 44–69.
 ↑ Characterization of Lorenzen in the Philosophical Archive Konstanz
 ↑ As an example for quantities or classes or for colors in different languages (red, red, rouge). Logical propaedeutics p. 93 f.
 ↑ Wolfgang Künne sees it completely differently : Abstract objects. Semantics and ontology. Suhrkamp, Frankfurt 1983, new edition: Klostermann, Frankfurt 2007.
 ↑ See also: Rainer Hegselmann: Classical and constructive theory of the elementary proposition . Journal for Philosophical Research 33 (1979) 89107.
 ↑ Hartmut Wedekind: Jumping in Computer Science. In: Jürgen Mittelstraß (Ed.): On the philosophy of Paul Lorenzen. mentis, Münster 2013, ISBN 9783897857759 , p. 114 f.
 ↑ Logical Propaedeutics, p. 44.
 ^ Kuno Lorenz: Elementary statement. In: Jürgen Mittelstraß (Hrsg.): Encyclopedia Philosophy and Philosophy of Science. Second edition, Volume 2. Stuttgart Metzler 2005, ISBN 9783476021014 , p. 310.
 ↑ Textbook of constructive philosophy of science. 1987, ²2000 p. 46 ff.
 ^ Paul Lorenzen: Textbook of the constructive philosophy of science. Stuttgart Weimar 1987, ²2000 page 75.
 ↑ Lorenzen, Algebraic and Logistic Studies on Free Associations, Journal of Symbolic Logic, Volume 16, 1951, pp. 81106, English translation in: Arxiv , with introduction: Thierry Coquand, Stefan Neuwirth: An introduction to Lorenzen's "Algebraic and logistic investigations on free lattices "(1951), Arxiv
 ↑ differential and integral. 1965. The first approaches to constructive mathematics come from the intuitionism of L. E. J. Brouwer , Hermann Weyl and Andrei Nikolajewitsch Kolmogorow .
 ↑ The Cauchy convergence does not already use the limit of the sequence in the definition.
 ↑ differential and integral. 1965, p. 54 f.
 ↑ Elementary geometry. The foundation of analytical geometry. 1948.
 ↑ Since elementary geometry 1984.
 ↑ Where an order of the countable set is only faked in the proofs of uncountability, an order is explicitly stated in the construction of a new real number.
 ↑ In: Lucas Amiras : Protogeometrica. Systematiccritical investigations on the protophysical geometry justification. Dissertation, Konstanz 1998 is the uniqueness of these forms shape uniqueness called.
 ↑ Lorenzen: Theory of technical and political reason. P. 78.
 ↑ Textbook, a. a. O, 1987, 22000, pp. 203 f.
 ↑ In 1987 Lorenzen used the example that lens grinders do nothing nonsensical, although they never achieve their goal, only imperfect realizations. Textbook of constructive philosophy of science. 1987, ²2000, p. 193. Since Leibniz , the originally mathematical problem that one cannot define an unattainable goal by means of the goal attainment with unlimited approximation (improved by precise formulation by Weierstrass and Cauchy ) has been solved by this dialogue game between tolerating margin and manufacturing phase. With the associated evidence, one takes advantage of a dependency on margin and phase.
 ↑ For example: Peter Janich: Dingler and the apriorism. In this. Science and life. Bielefeld 2006, p. 62.
 ↑ For Peter Janich, on the other hand, this socalled hylometry belongs to the fundamental primary protophysics as a third area alongside geometry and chronometry (instead of stochastics with Lorenzen). Janich takes homogeneous consistency as the starting point for an operational definition of mass .
 ↑ Textbook of constructive philosophy of science. Bibliographisches Institut, Mannheim 1987; Metzler, Stuttgart ² 2000, pp. 206213.
 ↑ For example the relativistic mechanics, the relativistic perihelion rotation of Mercury or other planets or the light deflection observed during solar eclipses or in the Shapiro experiment by the gravitational field of large stars like the sun.
 ^ Paul Lorenzen: Relativistic mechanics with classical geometry and kinematics. In: Mathematical Journal. Berlin 1977.
 ↑ Steven Weinberg: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New York 1972, p. 147: "It simply doesn't matter whether we ascribe these predictions to the physical effect of gravitational fields on the motion of planets and photons or to a curvature of space and time."
 ↑ See the book Normative Logic and Ethics , published in 1969 , which summarizes Lorenzen's John Locke lectures in Oxford and the Constructive Logic, Ethics and Philosophy of Science , written with Oswald Schwemmer in 1973 and named within the Erlanger Schule BI 700 (publisher number of the book).
 ↑ A cat embryo can become a cat, but not a dog. This side of idealism and realism. In: Peter Janich (Ed.): Developments in methodological philosophy. P. 215 f.
 ↑ Textbook of constructive philosophy of science. Bibliographisches Institut, Mannheim 1987; Metzler, Stuttgart ² 2000, p. 112.
 ↑ Martina Plümacher: Philosophy after 1945 in the Federal Republic of Germany. Reinbek 1996, p. 220.
 ^ Carl Friedrich Gethmann: Kuhn In: Jürgen Mittelstraß: Encyclopedia Philosophy and Philosophy of Science. Second edition. Volume 4, Metzler 2010, ISBN 9783476021038 , p. 401
 ↑ Wolfgang Stegmüller: Problems and results of the philosophy of science and analytical philosophy. Volume I.
 ↑ He writes about Lorenzen in contrast to Friedrich Nietzsche: Paul Lorenzen, the important logician of our time, told me in a conversation about his "dialogical foundation of logic": Logic comes from the Athenian democracy. In the Athens market, someone makes a claim. The other says: "I don't think so." The first: "But you have to believe me." The second: "You are not the Persian king. You mustn't tell me what to believe. "The first:" I can prove it to you. "The second:" Please, prove it! "" And then, "Lorenzen continued," they need logic. "Lorenzen wants not to say that they then invent logic, but that they then, compelled by their freedom, discover the true logic. Like the Greeks, Lorenzen is fascinated by mathematics, and he advocates democracy. Neither is true of Nietzsche. Carl Friedrich von Weizsäcker: Perception of the modern age. Hanser, Munich 1983 p. 398.

↑ Gernot Böhme (Ed.): Protophysics. For and against a constructive scientific theory of physics. Suhrkamp, Frankfurt 1976.
J. Pfarr (Ed.): Protophysics and Theory of Relativity. Contributions to the discussion about a constructive scientific theory of physics. BI, Mannheim 1981 (Fundamentals of Exact Natural Sciences Volume 4).  ^ Herbert Meschkowski : Problem history of modern mathematics (1800–1950) Bibliographisches Institut, Mannheim / Vienna / Zurich 1978, p. 286.
 ↑ See Hans Albert : Treatise on Critical Reason. 5th edition Mohr, Tübingen 1991. There the discussion with the Erlangen constructivists is presented in the appendix from Albert's point of view.
 ↑ See: Frédérick Tremblay: La rationalité d'un point de vue logique: entre dialogique et inférentialisme, étude comparative de Lorenzen et Brandom. 2008.
Web links
 Literature by and about Paul Lorenzen in the catalog of the German National Library
 Paul Lorenzen: The actual infinite in mathematics.
 Entry in the philosophical archive of the University of Konstanz .
 Paul Lorenzen Foundation.
 Portrait shot.
personal data  

SURNAME  Lorenzen, Paul 
BRIEF DESCRIPTION  German philosopher 
DATE OF BIRTH  March 24, 1915 
PLACE OF BIRTH  Kiel 
DATE OF DEATH  October 1, 1994 
Place of death  Goettingen 