Ernst Mally
Encyclopedia
Ernst Mally was an Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...

n philosopher affiliated with the so-called Graz School
Graz School
The Graz School of experimental psychology and object theory was headed by Alexius Meinong, who was professor and Chair of Philosophy at the University of Graz where he founded the Graz psychological institute ....

 of phenomenology. A pupil of Alexius Meinong
Alexius Meinong
Alexius Meinong was an Austrian philosopher, a realist known for his unique ontology...

, he was one of the founders of deontic logic
Deontic logic
Deontic logic is the field of logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts...

 and is mainly known for his contributions in that field of research.

Life

Mally was born in the town of Kranj
Kranj
' is the third largest municipality and fourth largest city in Slovenia, with a population of 54,500 . It is located approximately 20 km north-west of Ljubljana...

  in the Duchy of Carniola
Duchy of Carniola
The Duchy of Carniola was an administrative unit of the Holy Roman Empire and the Habsburg Monarchy from 1364 to 1918. Its capital was Ljubljana...

, Austria-Hungary
Austria-Hungary
Austria-Hungary , more formally known as the Kingdoms and Lands Represented in the Imperial Council and the Lands of the Holy Hungarian Crown of Saint Stephen, was a constitutional monarchic union between the crowns of the Austrian Empire and the Kingdom of Hungary in...

 (now in Slovenia
Slovenia
Slovenia , officially the Republic of Slovenia , is a country in Central and Southeastern Europe touching the Alps and bordering the Mediterranean. Slovenia borders Italy to the west, Croatia to the south and east, Hungary to the northeast, and Austria to the north, and also has a small portion of...

). His father was of Slovene origin, but identified himself with Austrian German
Austrian German
Austrian German , or Austrian Standard German, is the national standard variety of the German language spoken in Austria and in the autonomous Province of South Tyrol...

 culture (he also Germanized the orthography of his surname, originally spelled Mali, a common Slovene surname of Upper Carniola
Upper Carniola
Upper Carniola is a traditional region of Slovenia, the northern mountainous part of the larger Carniola region. The centre of the region is Kranj, while other urban centers include Jesenice, Tržič, Škofja Loka, Kamnik, and Domžale.- Historical background :...

). After his death, the family moved to the Carniola
Carniola
Carniola was a historical region that comprised parts of what is now Slovenia. As part of Austria-Hungary, the region was a crown land officially known as the Duchy of Carniola until 1918. In 1849, the region was subdivided into Upper Carniola, Lower Carniola, and Inner Carniola...

n capital of Ljubljana
Ljubljana
Ljubljana is the capital of Slovenia and its largest city. It is the centre of the City Municipality of Ljubljana. It is located in the centre of the country in the Ljubljana Basin, and is a mid-sized city of some 270,000 inhabitants...

 . There, Ernst attended the prestigious Ljubljana German language Gymnasium. Already at a young age, Mally became a fervent supporter of the Pan-German nationalist movement of Georg von Schönerer. In the same time, he developed an interest in philosophy.

In 1898 he enrolled to the University of Graz
University of Graz
The University of Graz , a university located in Graz, Austria, is the second-largest and second-oldest university in Austria....

, where he studied philosophy under the supervision of Alexius Meinong
Alexius Meinong
Alexius Meinong was an Austrian philosopher, a realist known for his unique ontology...

, as well as physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, specializing in formal logic
Formal logic
Classical or traditional system of determining the validity or invalidity of a conclusion deduced from two or more statements...

. He graduated in 1903 with a thesis entitled Untersuchungen zur Gegenstandstheorie des Messens (Investigations in the Object Theory of Measurement). In 1906 he started teaching at a high school in Graz
Graz
The more recent population figures do not give the whole picture as only people with principal residence status are counted and people with secondary residence status are not. Most of the people with secondary residence status in Graz are students...

, at the same time working Meinong's assistant at the university. He also maintained close contacts with the Laboratory for Experimental Psychology, founded by Meinong. In 1912, he wrote his faculty-rank (Habilitation) thesis entitled Gegenstandstheoretische Grundlagen der Logik und Logistik (Object-theoretic Foundations for Logics and Logistics) with Meinong as supervisor.

From 1915 to 1918 he served as an officer in the Austro-Hungarian Army
Austro-Hungarian Army
The Austro-Hungarian Army was the ground force of the Austro-Hungarian Dual Monarchy from 1867 to 1918. It was composed of three parts: the joint army , the Austrian Landwehr , and the Hungarian Honvédség .In the wake of fighting between the...

. After the end of World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...

, Mally joined the Greater German People's Party
Greater German People's Party
The Greater German People's Party was a German nationalist and national liberal party during the First Republic of Austria.-Foundation:...

, which called the unification of German Austria
German Austria
Republic of German Austria was created following World War I as the initial rump state for areas with a predominantly German-speaking population within what had been the Austro-Hungarian Empire, without the Kingdom of Hungary, which in 1918 had become the Hungarian Democratic Republic.German...

 with Germany. In the same period, he started teaching at the university and in 1925 he took over Meinong's chair. In 1938, he became a member of the National Socialist Teachers' Association and two months after the Anschluss
Anschluss
The Anschluss , also known as the ', was the occupation and annexation of Austria into Nazi Germany in 1938....

he joined the NSDAP. He continued teaching during the Nazi administration of Austria
Austria at the Time of National Socialism
Austria at the time of National Socialism describes in particular the period of Austrian history from March 12, 1938 when the German annexation of Austria made Austria part of the German Third Reich until the end of World War II in spring 1945....

 until 1942 when he retired. He died in 1944.

Mally's deontic logic

Mally was the first ever logician to attempt an axiomatisation of ethics
Ethics
Ethics, also known as moral philosophy, is a branch of philosophy that addresses questions about morality—that is, concepts such as good and evil, right and wrong, virtue and vice, justice and crime, etc.Major branches of ethics include:...

. He used five axioms, which are given below. They form a first-order theory that quantifies over proposition
Proposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...

s, and there are several predicates to understand first. !x means that x ought to be the case. Ux means that x is unconditionally obligatory, i.e. that !x is necessarily true. ∩x means that x is unconditionally forbidden, i.e. U(¬x). A f B is the binary relation
Binary relation
In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = . More generally, a binary relation between two sets A and B is a subset of...

 A requires B, i.e. A materially implies !B. (All entailment
Entailment
In logic, entailment is a relation between a set of sentences and a sentence. Let Γ be a set of one or more sentences; let S1 be the conjunction of the elements of Γ, and let S2 be a sentence: then, Γ entails S2 if and only if S1 and not-S2 are logically inconsistent...

 in the axioms is material conditional
Material conditional
The material conditional, also known as material implication, is a binary truth function, such that the compound sentence p→q is logically equivalent to the negative compound: not . A material conditional compound itself is often simply called a conditional...

.) It is defined by axiom III, whereas all other terms are defined as a preliminary.


Note the implied universal quantifiers in the above axioms.

The fourth axiom has confused some logicians because its formulation is not as they would have expected, since Mally gave each axiom a description in words also, and he said that axiom IV meant "the unconditionally obligatory is obligatory", i.e. (as many logicians have insisted) UA → !A. Meanwhile, axiom 5 lacks an object to which the predicates apply, a typo. However, it turns out these are the least of Mally's worries (see below).

Failure of Mally's deontic logic

Theorem: This axiomatisation of deontic logic
Deontic logic
Deontic logic is the field of logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts...

 implies that !x if and only if
If and only if
In logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements....

 x is true, OR !x is unsatisfiable. (This makes it useless to deontic logicians.)
Proof: Using axiom III, axiom I may be rewritten as (!(A → B) & (B → C)) → !(A → C). Since B → C holds whenever C holds, one immediate consequence is that (!(A → B) → (C → !(A → C))). In other words, if A requires B, it requires any true statement. In the special case where A is a tautology
Tautology (logic)
In logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...

, the theorem has consequence (!B → (C → !C)). Thus, if at least one statement ought be true, every statement must materially entail it ought be true, and so every true statement ought be true. As for the converse (i.e. if some statement ought be true then all statements that ought be true are true), consider the following logic: ((U → !A) & (A → ∩)) → (U → !∩) is a special case of axiom I, but its consequent contradicts axiom V, and so ¬((U → !A) & (A → ∩)). The result !A → A can be shown to follow from this, since !A implies that U → !A and ¬A implies that A → ∩; and, since these are not both true, we know that !A → A.

Mally thought that axiom I was self-evident, but he likely confused it with an alternative in which the implication B → C is logical, which would indeed make the axiom self-evident. The theorem above, however, would then not be demonstrable. The theorem was proven by Karl Menger
Karl Menger
Karl Menger was a mathematician. He was the son of the famous economist Carl Menger. He is credited with Menger's theorem. He worked on mathematics of algebras, algebra of geometries, curve and dimension theory, etc...

, the next deontic logician. Neither Mally's original axioms nor a modification that avoids this result remains popular today. (Menger did not suggest his own axioms.) See also deontic logic
Deontic logic
Deontic logic is the field of logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts...

 for more on the subsequent development of this subject. Mally's grandson, Thomas, is currently at Emory University
Emory University
Emory University is a private research university in metropolitan Atlanta, located in the Druid Hills section of unincorporated DeKalb County, Georgia, United States. The university was founded as Emory College in 1836 in Oxford, Georgia by a small group of Methodists and was named in honor of...

 attempting to prove the theories of his grandfather.

External links

  • Entry Ernst Mally at the Stanford Encyclopedia of Philosophy
    Stanford Encyclopedia of Philosophy
    The Stanford Encyclopedia of Philosophy is a freely-accessible online encyclopedia of philosophy maintained by Stanford University. Each entry is written and maintained by an expert in the field, including professors from over 65 academic institutions worldwide...

  • Entry Mally's deontic logic at the Stanford Encyclopedia of Philosophy
The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK