Dictum de omni et nullo

Dictum de omni et nullo

In Aristotelean logic, dictum de omni et nullo (the maxim of all and none) is the principle that whatever is affirmed or denied of a whole kind K may be affirmed or denied (respectively) any subkind of K. This principle is fundamental to syllogistic logic in the sense that all valid syllogistic argument forms are reducible to applications of the two constituent principles dictum de omni and dictum de nullo.[1]

Dictum de omni (sometimes misinterpreted as universal instantiation) is the principle that whatever is universally affirmed of a kind is affirmable as well for any subkind of that kind.
Example:

(1) Dogs are mammals.
(2) Mammals have livers.
Therefore (3) dogs have livers.

Premise (1) states that "dog" is a subkind of the kind "mammal".
Premise (2) is a (universal affirmative) claim about the kind "mammal".
Statement (3) concludes that what is true of the kind "mammal" is true of the subkind "dog".

Dictum de nullo is the related principle that whatever is denied of a kind is likewise denied of any subkind of that kind.
Example:

(1) Dogs are mammals.
(4) Mammals do not have gills.
Therefore (5) dogs do not have gills.

Premise (1) states that "dog" is a subkind of the kind "mammal".
Premise (4) is a (universal negative) claim about the kind "mammal".
Statement (5) concludes that what is denied of the kind "mammal" is denied of the subkind "dog".

See also

References

  1. ^ John Stuart Mill (15 January 2001). System of Logic Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation. Elibron.com. p. 114. ISBN 9781402181573. http://books.google.com/books?id=cL-0QxoZZAIC&pg=PA114. Retrieved 6 March 2011. 

External links


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  • Dictum de omni et nullo — (lat.), logischer Grundsatz: was der Gattung zukommt oder widerspricht, kommt zu oder widerspricht auch allen ihren Arten und Individuen. Beispiel: Bäume sind Pflanzen, Pflanzen haben Wurzeln, folglich haben die Bäume auch Wurzeln. Derselbe liegt …   Meyers Großes Konversations-Lexikon

  • dictum de omni et nullo — The principle of Aristotle that whatever is affirmed or denied of an entire class or kind may be affirmed or denied of any part of it. The principle is supposed to validate the four moods of the first figure of the syllogism, and motivated the… …   Philosophy dictionary

  • Dictum de omni et nullo — Dịctum de ọmni et nụllo   [lateinisch »Aussage über alles und nichts«], Logik: Schlussregel, die oft als das Prinzip des Syllogismus angesehen wird: Jede bejahende oder verneinende Aussage, die für einen höheren Begriff (Klasse, Gattung, Art)… …   Universal-Lexikon

  • dictum de omni et nullo — |diktəmdā|ȯmnēˌetˈnu̇(ˌ)lō Etymology: Latin, maxim of all and none : an axiom in logic: whatever may be affirmed or denied of a class may be affirmed or denied of every member of it …   Useful english dictionary

  • Dictum — (lat.), 1) Spruch, Ausspruch, Bonmot, Sprüchwort; 2) Grundsatz; so: Dictum de omni (D. de exemplo) et nullo (D. de diverso), logischer Grundsatz, der vollständig so lautet: Was der Gattung zukommt od. widerspricht, kommt zu od. widerspricht auch… …   Pierer's Universal-Lexikon

  • aristotle's dictum — ˈarə̇ˌstäd.əlz , ätəlz also ˈer noun Usage: usually capitalized A : dictum de omni et nullo …   Useful english dictionary

  • List of philosophy topics (D-H) — DDaDai Zhen Pierre d Ailly Jean Le Rond d Alembert John Damascene Damascius John of Damascus Peter Damian Danish philosophy Dante Alighieri Arthur Danto Arthur C. Danto Arthur Coleman Danto dao Daodejing Daoism Daoist philosophy Charles Darwin… …   Wikipedia

  • Силлогизм — умозаключение, в котором на основании нескольких суждений с необходимостью выводится новое суждение, называемое заключением. В отличие от С., как умозаключения посредственного, непосредственным умозаключением называется то, в котором заключение… …   Энциклопедический словарь Ф.А. Брокгауза и И.А. Ефрона

  • Schluß [1] — Schluß (Ratiocinatio), im allgemeinen die Denkoperation, durch die aus gegebenen Urteilen, den Vordersätzen oder Prämissen des Schlusses, ein neues, der Schlußsatz (conclusio), abgeleitet wird. Jeder eigentliche S. setzt zwei voneinander… …   Meyers Großes Konversations-Lexikon

  • A fortiori — es una locución latina que significa con mayor motivo . En lógica se usa esta expresión para referise a una forma de argumentación por la que se saca una consecuencia de una cosa en vista de la conclusión que se sacó de otra, para la cual había… …   Wikipedia Español

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