Ernst Mally


Ernst Mally was an Austrian analytic philosopher, initially affiliated with Alexius Meinong's Graz School of object theory. Mally was one of the founders of deontic logic and is mainly known for his contributions in that field of research. In metaphysics, he is known for introducing a distinction between two kinds of predication, better known as the dual copula strategy.

Life

Mally was born in the town of Kranj in the Duchy of Carniola, Austria-Hungary. His father was of Slovene origin, but identified himself with Austrian German culture. After his death, the family moved to the Carniolan capital of Ljubljana. 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 in the University of Graz, where he studied philosophy under the supervision of Alexius Meinong, as well as physics and mathematics, specializing in formal logic. He graduated in 1903 with a doctoral thesis entitled Untersuchungen zur Gegenstandstheorie des Messens. In 1906 he started teaching at a high school in Graz, at the same time collaborating with Adalbert Meingast and working as Meinong's assistant at the university. He also maintained close contacts with the Graz Psychological Institute, founded by Meinong. In 1912, he wrote his habilitation thesis entitled Gegenstandstheoretische Grundlagen der Logik und Logistik at Graz with Meinong as supervisor.
From 1915 to 1918 he served as an officer in the Austro-Hungarian Army. After the end of World War I, Mally joined the Greater German People's Party, which called the unification of German Austria 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 League and two months after the Anschluss he joined the NSDAP. He continued teaching during the Nazi administration of Austria until 1942 when he retired.
He died in 1944 in Schwanberg.

Philosophical work

Mally's deontic logic

Mally was the first logician ever to attempt an axiomatization of ethics. He used five axioms, which are given below. They form a first-order theory that quantifies over propositions, 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. A f B is the binary relation A requires B, i.e. A materially implies !B. 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. 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.

Failure of Mally's deontic logic

Theorem: This axiomatization of deontic logic implies that !x if and only if x is true, OR !x is unsatisfiable.
Proof: Using axiom III, axiom I may be rewritten as & ) → !. Since B → C holds whenever C holds, one immediate consequence is that. In other words, if A requires B, it requires any true statement. In the special case where A is a tautology, the theorem has consequence. 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, consider the following logic: & ) → is a special case of axiom I, but its consequent contradicts axiom V, and so ¬ & ). 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, 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.

Metaphysics

In metaphysics, Mally is known for introducing a distinction between two kinds of predication, better known as the dual copula strategy for solving the problem of nonexistent objects. He also introduced a similar strategy, the dual property strategy, but did not endorse it. The dual property strategy was eventually adopted by Meinong.
Mally developed a realistic approach to ontology and saw himself in opposition to the Vienna Circle and the logical positivists.

Works