Albert Menne

Albert Heinrich Menne (born July 12, 1923 in Attendorn ; † March 7, 1990 ) was a German logician and philosopher . Menne was best known for his introductions to logic, which had been widespread since the 1960s. He taught in Hamburg and Bochum , and his publications focused on philosophical logic.

A further development of his differential syllogistics is the strict logic .

Life

Menne attended a grammar school in Westphalia until he graduated from high school in 1942 . After military service and being a prisoner of war in England, he studied philosophy, psychology and theology in Paderborn , Tübingen and Munich . Max Planck became aware of him during his studies and invited him to come and talk to him personally. Because of this acquaintance, Menne became a scholarship holder of the German National Academic Foundation . In 1952 he received his doctorate under Wilhelm Britzelmayr (1892-1970) with the dissertation Logistic Analysis of the Categorical Syllogism Functors and the Problem of the Null Class . After several years as a religion teacher at vocational schools, he joined the scientific council at the Philosophical Seminar of the University of Hamburg in 1962 , where he was appointed professor of philosophy because of his outstanding scientific achievements. From 1971 he was head of the mathematical logic working group at the Ruhr University in Bochum .

plant

Menne wrote some widespread introductions to formal logic for philosophers, for example his introduction to logic was published six times between 1966 and 2001. His introduction to methodology received three editions, the introduction to formal logic two editions . The outline of the formal logic , which was drawn up together with Joseph Maria Bocheński , was published five times. In other publications Menne dealt with methodology , philosophy of science , but above all with logic and its application, its history and its philosophical foundations.

Logic and existence

Logic and Existence are among Menne's main works , in which he establishes the differential syllogistics .

overview

“The problem of how far logic has to do with existence , and how classical logic [Note: Menne means more or less the syllogism from today's point of view ] can be axiomatized accordingly , is pressing after the publications of the last few years and the lively discussions Solution. This work tries to offer such a definitive, exact one, free of non-binding speculations. It is her concern to build a bridge between the classical logic, which goes back to Aristotle , and the modern logistics established by Boole and Frege [note: corresponds to formal logic ]. This is done with the problem of existence. Aristotelian logic makes very specific existence requirements for its terms. These are initially conceded and the classic system formalized in this way. It turns out that it constitutes a special part of the class calculus, and that the 4 classic types of judgment are not uniform structures. As further fruits there are numerous new final rules and the solution of some important problems. "

- Albert Menne : Logic and Existence, foreword

Justification for investigation in class calculus

Since the subject S and the predicate P are not independent expressions and neither are predicates - as the name already suggests, P is the predicate and S is the underlying argument, so that the judgment would have to be paraphrased in the predicate calculus P (S) as a natural basis for the study of class calculus , since both S and P can be understood as symbols for classes of objects.

Furthermore, Menne points out that it makes sense to also examine the class calculus for its possibilities for a logistic interpretation, since the propositional calculus and the predicate calculus have not resulted in a satisfactory solution.

Selection of important results

• The laws of classical logic can be formulated completely and very precisely in the logic calculus ( laws of the logical square , the conventional modes of the syllogism , conversion laws , equipollence laws ).

• For the 4 classic categorical types of judgment themselves there has not yet been a satisfactory resolution in functors of the logic calculus .

• An adequate description of the classic types of judgment is what he calls the DKV system (definite class relationships) in the class calculus:

I. ${\displaystyle {M}\cap {N}}$ II ${\displaystyle {M}\cap {N'}}$ III ${\displaystyle {M'}\cap {N}}$ IV ${\displaystyle {M'}\cap {N'}}$	k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 k 10 k 11 k 12 k 13 k 14 k 15 k 16 I. X X X X X 0 0 X 0 X 0 X 0 0 0 0 II 0 0 X X X X X 0 X X 0 0 X 0 0 0 III 0 X 0 X X X X X 0 0 X 0 0 X 0 0 IV X X X X 0 X 0 0 X 0 X 0 0 0 X 0
Four different averages (briefly: I , II , III , IV ) can be formed from two classes M and N and their complements M 'and N' .	With a certain KV, each of these 4 averages can be empty, ie element-free, equal to the zero class (short: 0), or it can contain elements, ie not equal to the zero class (short: X). There are a total of 16 different possibilities for k.

• On the basis of auxiliary theorems, all theorems of the class calculus (there are mainly laws relating to the zero and all classes or non-empty classes), one can conclude that there are exactly seven different relationships between two definite classes (different from the zero and all classes) (cf. ₁ to k ₇ ). In addition, the more detailed type of class relationship results. The fact that the class relations must be definite results from the conditions of existence on which the syllogistics are based .

Corresponding judgments can also be assigned in colloquial language to the 7 possible circumferential relationships of conceptual contents that correspond to the 7 definite class relationships, e.g. B .:

• for k ₁ (also: definite equality ): "Humans are featherless bipeds.", "Equilateral triangles are also equiangular triangles."
• for k ₂ (also: definite inclusion ): "Humans are mortal.", "Rectangles are parallelograms."

• In order to find out how the seven definite class relationships are related to the four categorical judgments, they must be interpreted in the class calculus:

positive judgments (S are P)		negative judgments (S are not P)
${\displaystyle {S}\cap {P}\neq 0}$		${\displaystyle {S}\cap {P'}\neq 0}$
universal ( all S are P)	particular	universal ( all S are not P)	particular
${\displaystyle {S}\cap {P'}=0}$		${\displaystyle {S}\cap {P}=0}$
SaP	SiP	SeP	SoP
${\displaystyle \to }$ I X and II 0	${\displaystyle \to }$ I X	${\displaystyle \to }$ I 0 and II X	${\displaystyle \to }$ I 0
The assignment rules for the KVs shown above, which result from this interpretation in the class calculation, are colored orange .

(Due to the existential prerequisites required by the syllogistic terms, Menne rejects all interpretations of a conditional kind with implication or subsumption alone or negative descriptions of existence.)

• The 4 classic types of judgment are not uniform statements in all cases, but represent disjunctions from 2 to 5 of these class statements:

SaP k 1 k 2 SiP k 1 k 2 k 3 k 4 k 5 SeP k 6 k 7 SoP k 3 k 4 k 5 k 6 k 7 This table shows the result of the assignment.

z. B .: . ${\displaystyle SaP=dfk_{1}\lor k_{2}}$

Using the following summarizing rule, you can quickly grasp how the negations of the types of judgment are circumscribed in order to be able to work with them formally:

The negation of the disjunction consists of the disjunction of all DKVs with the exception of the two disjunction terms k _m and k _n . ${\displaystyle {\overline {k_{m}\lor k_{n}}}}$ ${\displaystyle k_{m}\lor k_{n}}$

• This so-called DKV paraphrase allows an axiomatic-deductive derivation of all classical laws from 3 independent, consistent axioms, 3 definitions and several rules of the propositional calculus.

• "The peculiarity of the [chosen axiom] system illuminates" Menne in a later article in more detail:

"The economical aids from the propositional calculus allow the implicator to be used in the sense of the strict implication instead of the usual one . [Note: The footnote reads roughly as follows: Cf. Menne, Implikation und Syllogistik , 1957; Ackermann, Justification of a strict implication , 1956 .] No use is made of the paradoxes of implication and de Morgan's laws . "

The axiom system:

• Axioms :

1. ${\displaystyle \vdash SaP\leftrightarrow P'aS'}$	( Counterposition of a )
2. ${\displaystyle \vdash SaP\to {\overline {SaP'}}}$	( Subalternation ai )
3. ${\displaystyle \vdash MaP\wedge SaM\to SaP}$	( Barbara , transivity of a )

• Definitions

4. 5. 6. ${\displaystyle SeP=dfSaP'}$
${\displaystyle SiP=df{\overline {SaP'}}}$
${\displaystyle SoP=df{\overline {SaP}}}$

• Special rules :

7. For one term variable (S, P, M and their complements) another may be used if at the same time for all with the term variable isomorphic with the isomorphic one to be used are used.
8. A double complementation is canceled out again. (e.g. is equal ) ${\displaystyle a''}$ ${\displaystyle a}$

• Definitions from the propositional calculus

9. Exclusor : 10. Disjunctor : 11. Equivalent : 12. Contravalentor : > - < ${\displaystyle p\mid q=dfp\rightarrow {\overline {q}}}$
${\displaystyle p\vee q=df{\overline {p}}\rightarrow q}$
${\displaystyle p\leftrightarrow q=dfp\rightarrow q\wedge q\rightarrow p}$
${\displaystyle p}$ ${\displaystyle q}$ ${\displaystyle =df{\overline {p\leftrightarrow q}}}$

• Rules from the propositional calculus

13. A syllogistic statement may be used for a proposition variable, whereby isomorphic statements must be used for all proposition variables of the syllogistic proposition that are isomorphic with the proposition variable.
14. A statement can be arbitrarily replaced by a statement equivalent to it.
15. equivalent 16. equivalent 17. If , then 18. If , then 19. If and , then 20. If and , so ${\displaystyle p\wedge q}$ ${\displaystyle q\wedge p}$
${\displaystyle {\overline {\overline {p}}}}$ ${\displaystyle p}$
${\displaystyle \vdash p\leftrightarrow q}$ ${\displaystyle \vdash p\leftrightarrow q}$
${\displaystyle \vdash (p\wedge q)\rightarrow r}$ ${\displaystyle \vdash (p\wedge {\overline {r}})\rightarrow {\overline {q}}}$
${\displaystyle \vdash (p\wedge q)\rightarrow r}$ ${\displaystyle \vdash s\rightarrow q}$ ${\displaystyle \vdash (p\wedge s)\rightarrow r}$
${\displaystyle \vdash p\rightarrow q}$ ${\displaystyle \vdash q\rightarrow r}$ ${\displaystyle \vdash p\rightarrow r}$

• Since these axioms can also be derived as theorems in the class calculus, the classical system of categorical judgments and conclusions represents a part of the class calculus and is just as free from contradictions.

• An important aid of logic for solving numerous problems is the differential analysis, in which the judgments are broken down into their individual components (class connections) and these are broken down individually in the class calculus.

• In logic, existence in general has formal justification only as logical existence, ie consistency. Other types of existence should materially enter the premises or be treated as special evaluations in their own valence calculi.

• It turns out that the use of class statements always presupposes the existence of a certain minimum number of individuals, while the logic of an absolutely empty world is quite simple.

Summary

In summary, it can be stated - probably correctly - that Menne's most important finding is that the classical syllogism in the class calculus (in particular, in the modern logic calculus; in any case logically differentiated) only interprets the terms that occur appropriately by including the objects of the complementary classes can be. Menne himself emphasizes the role of the inverse several times (SäP = df S'aP ').

Therefore Menne explicitly assumes for this doctrine of judgment "that existence is always to be interpreted as logical existence ". This "represents the most general concept of existence, which applies to all objects which are identical with themselves, ie to everything that has a part in being in so far as this is opposed to non-being". The concepts that occur can be projected onto this common plane of existence, the universe of discourse , so that "all the difficulties associated with the multilayered existence disappear in the logical doctrine of judgment, because an existence other than the logical can now only appear in the matter of judgment or in the context of polyvalent valence calculi ".

Logic and language

Logic and Language is not only the title of a book edited by Menne and Gerhard Frey , but also occupied him in other works, such as the one mentioned above.

reception

In 1983 the team of authors wrote a commemorative publication for Menne:

“In contrast to the anti-traditionalism that is often encountered today, Albert Menne knows how to combine tradition and modernity again and again. Last but not least, this is where his scientific merit lies. His work is characterized by high demands on precision, clarity and comprehensibility, as well as radicalism in checking unnamed philosophical requirements. He is guided by a line of tradition that can be identified by names such as Bolzano, Frege and Bocheński. "

Walther Brüning wrote in 1996 that Mennes Logic and Existence was one of the books that had a special influence on the development of his “ Strict Logic ”. Brüning sees Aristotle's syllogistics as an important core piece or as a special case of his draft, which aims to lay the foundations of a logic free of paradoxes and undecidability (cf. under the general properties of calculi free from contradictions or completely ). The “Strict General Logic”, which he initially relates generally to facts and circumstances, only presupposes the principle of limitation and the principle of identity , as well as affirmation and negation.

Brüning, too, wanted to carry out all derivations directly and without aids within a syllogistic based on a strict concept of derivation, and defined the types of judgment using less cumbersome validity value formulas.

SaP SiP k 1 vk 2 k 1 vk 2 vk 3 vk 4 vk 5 SP X X A. X X X X X A. SP ' 0 0 N 0 0 X X X u S 'P 0 X u 0 X 0 X X u S 'P' X X A. X X X X 0 u For the sake of clarity, the two different interpretations of the 4 types of judgment are only compared here in simplified form for SaP and SiP. Four different combinations can be formed from two classes S and P and their complements S 'and P'. The values ​​of the (4-digit) validity value formulas are highlighted in orange (A = affirmative validity, N = negative validity, u = indefinite). The correspondences of indeterminate values ​​as certain averages of definite class relationships at Menne are highlighted in green for a better overview.

One can see that the descriptions of the universal judgments are equivalent to those of Mennes. In the case of particular judgments, on the other hand, he does not explicitly rule out Mennes equivalents of indefinite class relationships (e.g. in the case of SiP k ₈ , k ₁₀ and k ₁₂ ) in order to maintain the conditions of existence.

Works

A comprehensive bibliography of Albert Menne's literature can be found in the book Logical Philosophizing: Festschrift for Albert Menne Zum 60th Birthday.

Comprehensive selection of books (listed chronologically according to first publication)

• Logic and existence. (A logistic analysis of the categorical syllogism functors and the problem of the null class) Meisenheim 1954.
• Outline of formal logic. Paderborn: Universitäts-Taschen-Bücher-Verlag: 1983. From the 5th edition renamed from Grundriß der Logistik. (1.A. 1954, 2.A. 1962, 3.A. 1965, 4.A. 1973) Translated from the French by Joseph Maria Bocheński . Translated and expanded by Menne. (Comprehensive, strictly structured and formalized introduction. Explains a propositional, predicate, class and relational calculus, as well as special calculi such as a modal calculus, multi-valued logic, combinatorial logic, syllogistics, metalogics and calculus theory.)
• What is and what can logistics do? Paderborn 1957. 2nd edition. 1970.
• Logical-philosophical studies. Freiburg 1959. Together with Joseph Maria Bocheński . Also in engl. Language appeared. (Aristotelian logic; categorical syllogism; scholastic solution of paradox; syntactical categories; analysis of existence; analogy; problem of universals; VG condition)
• Introduction to logic. Bern 1966. (Span. Transl. 1970). 2.A. 1973. 3.A. 1981 (Introductory orientation on the doctrine of consistency with detailed explanations and many examples. The book "Outline of formal logic" works more on the basis of logic calculi and covers almost the entire subject area of ​​this book except for the introductory part about signs. "Also suitable for philosophers")
• Logic of religion. Cologne 1968. Translated from the French by Joseph Maria Bocheński . Translated by Menne and annotated. 2nd Edition. 1981 Paderborn.
• Sources of error. Scientific series d. Schering AG., Berlin 1977.
• Introduction to the methodology . (overview of elementary, general scientific methods of thinking) Wiss. Buchgesellschaft, Darmstadt 1980. 2nd edition. 1984. (About the definition, the difference, the classification, the heuristic, the justification, the course of research)
• Introduction to formal logic. Darmstadt: Wissenschaftliche Buchgesellschaft, 1985. (Somewhat more formalized orientation on the doctrine of consistency, its history, structures and applications.)
• Consistent thinking. (Logical Investigations of Philosophical Concepts and Problems) Darmstadt 1988. (Collection of essays: How and for what purpose is philosophy? What does philosophy have to do with wisdom today? On the problem of justification of logic , logic as organon and as science , logic and intelligence , on the problem of application From logic , set theory and trinity , on the applicability of multi-valued calculi in legal logic - with relatively sparse logical tools, the following philosophical problems are analyzed: What is truth? What is analogy? What is existence? Word and thing , quality and quantity , On formal structure of authority , identity, equality, similarity , philosophical and didactic perspectives of set theory , on the history and analysis of the exceptional judgment , on the conceptual history of "hypothetical" )

As editor and co-author

• On the modern interpretation of Aristotelian logic. Hildesheim and New York, Georg Olms Verlag, 1982–93. 5 volumes. (I. About the concept of inferences in Aristotelian logic. 1982. II. Formal and non-formal logic in Aristotle. 1985. III. Modal logic and polyvalence. 1988. IV. On the prehistory of multivalued logic in antiquity (by Niels Publenberger). 1990. V. On Aristotle's Theorem of Contradiction (by Jan Lukasiewicz). 1993.)

Monographs, essays and contributions to compilations, as well as newspaper articles

• On the truth value structure of the judgment. Methodos 1, 1949, pp. 390-404.
• For the step coupling of monadic bivalent functors. In: Controlled Thinking. Festschrift f. W. Britzelmayr. Edited by H. Angstl, A. Menne et al. A. Wilhelmi. Munich 1951, pp. 92-102.
• To the triadic bivalent proposition functors. Theoria 18 [note. Menne wrote: "Theoria (Lund) XVII / 1, pp. 66ff"], 1952, pp. 66-69.
• Proof and negation. Actes du Xléme Congr. Int. de Philos. (Bruxelles 1953) Vol. 5. Amsterdam / Louvain 1953, pp. 91-97.
• Implication and syllogistics. Magazine f. Philos. Forschung 11, 1957, pp. 375-386.
• Some results of research on syllogism and its philosophical consequences. In: Logical-Philosophical Studies, pp. 61–70.
• For the reduction of polyadic valence functions. Atti del XII Congr. Int. di Filosofia (Venezia 1958) Vol. 5. Firenze 1960, pp. 393-401.
• Some aspects of language and logic. Archive f. Legal and social philosopher. 48, 1962, pp. 507-523.
• About monadic valence functions. Mem. Del XIII Congr. Int. de Filosofia (México 1963). Mèxico 1964, Vol. 5, pp. 237-246.
• Shaping the logic Studium Generale 19, 1966, pp. 160–168.
• On the syllogistic of strictly particular judgments. In: Contributions to logic and methodology in honor of Joseph Maria Bocheński , 1965, pp. 91–97.
• Existence in logic. In: Description, Analyticity and Existence. (Int. Research Center for Basic Questions in the Sciences Salzburg. Third and Fourth Research Discussion) Ed. Paul Weingartner . Salzburg 1966, pp. 55-68.
• The logic of Gottfried Ploucquet . Files of the XIV. Int. Congr. F. Philos. Vol. 3. Vienna 1968, pp. 45-48.
• On logic and its history. In: Philosophia naturalis . Volume 22, 1985, pp. 460-468 (Basic remarks on the relationship between logic and logic history).

literature

• Ursula Neemann, Ellen Walther-Klaus (Hrsg.): Logical philosophizing: Festschrift for Albert Menne on the 60th birthday. With introductory memories from IM Bocheński . Olms, Hildesheim / Zurich / New York 1983, ISBN 3-487-07421-4 . (2nd edition expanded to include a bibliography. 1988)

Individual evidence

1. ^ Paul F. Reitze: Logic as a form of existence: Albert Menne died on March 7th. In: The world . Reprinted in: Sauerland. Journal of the Sauerland Heimatbund. No. 2 / June 1990, p. 69 ( online ( memento of the original from June 10, 2015 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice . ). 
2. ↑ ^{a b c} Ursula Neemann and Ellen Walther-Klaus (eds.): Logical philosophizing: Festschrift for Albert Menne for his 60th birthday. Olms, Hildesheim / Zurich / New York 1983, ISBN 3-487-07421-4 .
3. ↑ ^{a b c d} Logic and Existence. (A logistic analysis of the categorical syllogism functors and the problem of the null class) Meisenheim 1954.
4. ↑ On the truth value structure of the judgment. Methodos 1, 1949, pp. 390-404.
5. ↑ Some results of research on syllogism and their philosophical consequences. (JM Bochenski, Logical-Philosophical Studies, transl. And edited by A. Menne, Karl Alber Verlag, Freiburg / Munich 1959, pp. 61–70); Also in: On the modern interpretation of Aristotelian logic . Volume 1, On the Concept of Inference in Aristotelian Logic. 1982.
6. ↑ see e.g. B. Introduction to formal logic , p. 127.Darmstadt: Wissenschaftliche Buchgesellschaft, 1985.
7. ↑ Some results of research on syllogism and their philosophical consequences. (JM Bochenski, Logical-Philosophical Studies, transl. And edited by A. Menne, Karl Alber Verlag, Freiburg / Munich 1959, pp. 61–70); Also in: On the modern interpretation of Aristotelian logic . Volume 1, On the Concept of Inference in Aristotelian Logic. 1982.
8. ↑ Implication and Syllogistics. Magazine f. Philos. Forschung 11, 1957, pp. 375-386.
9. ^ Brüning: Basics of Strict Logic. Königshausen and Neumann, Würzburg 1996.

Remarks

1. ↑ The laws are from or result from Principia Mathematica by Whitehead and Russell ( available online at the University of Michigan Historical Math Collection): * 24.561, * 24.17, * 24.311, * 22.41; And from Précis de logique mathématique von Bocheński ( available online at the University of Rey Juan Carlos): 5.64, 16.363, 5.54. Menne uses a total of nine laws for his investigation.
2. ↑ Modified according to the system of axioms required in Logic and Existence , in the following largely from Some Results of Syllogism Research and Their Philosophical Consequences. , (same numbering).
3. ↑ "Axiom 1 presupposes contraponability for the A functor, this is a weaker structural property than reflexivity, which most other axiom systems presuppose, because from reflexivity contraponibility can be obtained with the help of transitivity, but not vice versa. The contraponability is not a specific property of the A-functor; it also belongs to the implicator, the equivalentor, the contravalentor, the functors of equality or inclusion of classes and relations. " Some results of research on syllogism and its philosophical consequences.
4. ↑ "Axiom 2, on the other hand, seems to be specific to the A-functor. It is the basis of the laws of subalternation and the impure conversions and counterpositions that depend on them, of the contested and weakened syllogisms. If you drop it, these laws all fall out too. The A-functor can then be interpreted without further ado as an inclusive in the class calculus or as a formal implication in the predicate calculus. Axiom 2 also implies that the complementator negates more strongly than the negator, because it applies accordingly [note Polish notation and variable signs in the following to this article adapted] , but not the reverse . " Some results of research on syllogism and its philosophical consequences. ${\displaystyle \vdash SaP'\to {\overline {SaP'}}}$ ${\displaystyle \vdash {\overline {SaP'}}\to SaP'}$
5. ↑ "Axiom 3 assumes transitivity for the A-functor. This happens in most axiom systems. It is not a specific property, for example the implicator, conjunctor, equivalent, class and relational inclusive are transitive." Some results of research on syllogism and its philosophical consequences.
6. ↑ They come from the modified system from a later article. It also says: "The two rules 7 and 8 correspond to rules 13 and 16 in the propositional calculus and have corresponding analogues in the class and relational calculus." Some results of research on syllogism and its philosophical consequences.
7. ↑ "Strictly speaking, it is not the theorems themselves [note: as theorems of the propositional calculus] that have to be added, but the corresponding rules." Logic and Existence , footnote 170; These rules also come from the modified system from a later article: "The system presented here represents a slight modification of what was first used in Menne, Logic and Existence [...]. I owe the saving of a rule to a suggestion by Prof. Joseph Dopp . Of course, all propositional functors can be defined using D [Note: the Exclusor] and all rules can be derived from one of Nicod's axioms , but then the whole propositional calculus would have to be presupposed, while we want to show here that you work with one The assertion mark " " denotes laws of the system " Some results of research on syllogism and their philosophical consequences. The Polish notation has been adapted accordingly in the following. ${\displaystyle \vdash }$