Ernst Mally

Source: Wikipedia, the free encyclopedia.
Not to be confused with
Ern Malley
.

Ernst Mally
Born11 October 1879
Meinong's School) (early)[1]
Analytic philosophy (late)[2][3]
InstitutionsUniversity of Graz
(1925–1942)
Theses
Nuclear vs. extranuclear (formal vs. extra-formal) properties (formale vs. außerformale Bestimmungen) of objects[5][6][7]
Abstract determinates (Determinaten) as the content of mental states[4][3]
Axiomatization of ethics (deontic logic
)

Ernst Mally (

dual predication approach.[7]

Life

Mally was born in the town of

Georg von Schönerer
. In the same time, he developed an interest in philosophy.

In 1898, he enrolled in the

habilitation thesis
entitled Gegenstandstheoretische Grundlagen der Logik und Logistik (Object-theoretic Foundations for Logics and Logistics) at Graz with Meinong as supervisor.

From 1915 to 1918 he served as an officer in 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

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(¬x). A f B is the binary relation A requires B, i.e. A materially implies !B. (All entailment in the axioms is material 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 axiomatization of deontic logic implies that !x if and only if 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, 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, 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 for more on the subsequent development of this subject.)

Metaphysics

In

dual property strategy, but did not endorse it.[2] The dual property strategy was eventually adopted by Meinong.[2]

Mally developed a

logical positivists.[1]

Legacy

Mally's metaphysical work influences some contemporary metaphysicians and logicians working in

Edward Zalta.[9]

The analytic philosopher

Ern Malley, created by James McAuley and Harold Stewart, was an allusion to Mally.[10]

Works

  • (1904 [1903]) Untersuchungen zur Gegenstandstheorie des Messens (Investigations in the Object Theory of Measurement), Leipzig: Barth (
    doctoral thesis
    ).
  • (1912) Gegenstandstheoretische Grundlagen der Logik und Logistik (Object-theoretic Foundations for Logics and Logistics), Leipzig: Barth (
    habilitation thesis
    ).
  • (1926) Grundgesetze des Sollens. Elemente der Logik des Willens (The Basic Laws of Ought: Elements of the Logic of Willing), Graz: Leuschner & Lubensky. Reprinted in Ernst Mally: Logische Schriften. Großes Logikfragment—Grundgesetze des Sollens, K. Wolf, P. Weingartner (eds.), Dordrecht: Reidel, 1971, 227–324.
  • (1935) Erlebnis und Wirklichkeit. Einleitung zur Philosophie der Natürlichen Weltauffassung (Experience and Reality: Introduction to the Philosophy of the Natural World-conception), Leipzig: Julius Klinkhardt.

Notes

  1. ^ a b Liliana Albertazzi, Dale Jacquette, The School of Alexius Meinong, Routledge, 2017, p. 191.
  2. ^ a b c d e Hieke & Zecha
  3. ^ a b c Edward N. Zalta, "Mally's Determinates and Husserl's Noemata", in Ernst Mally – Versuch einer Neubewertung, A. Hieke (ed.), St. Augustin: Academia-Verlag, 1998, pp. 9–28.
  4. ^ a b Mally 1912, §§33 and 39.
  5. International Congress of Philosophy, Heidelberg), 1–5 September 1908; ed. Professor Dr. Theodor Elsenhans, 881–886. Heidelberg: Carl Winter’s Universitätsbuchhandlung. Verlag-Nummer 850. Translation: Ernst Mally, "Object Theory and Mathematics", in: Jacquette, D., Alexius Meinong, The Shepherd of Non-Being (Berlin/Heidelberg: Springer, 2015), pp. 396–404, esp. 397
    .
  6. ^ Dale Jacquette, Meinongian Logic: The Semantics of Existence and Nonexistence, Walter de Gruyter, 1996, p. 16.
  7. ^ a b c Ernst Mally – The Metaphysics Research Lab
  8. ^ a b Mally 1912, ch. I. "Allgemeines".
  9. ^ Zalta, Edward. "The Theory of Abstract Objects". Metaphysics Research Lab. Retrieved 5 September 2020.
  10. ^ Lewis, David. "Ern Malley's Namesake" (PDF). Quadrant (March 1995): 14–15. Retrieved 5 September 2020.

References

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