Dictum de omni et nullo
Encyclopedia
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.
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:
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:
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".
Organon
The Organon is the name given by Aristotle's followers, the Peripatetics, to the standard collection of his six works on logic:* Categories* On Interpretation* Prior Analytics* Posterior Analytics...
, 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
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
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.
Dictum de omni (sometimes misinterpreted as universal instantiation
Universal instantiation
In logic universal instantiation is an inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom...
) 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
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
) 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
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
) claim about the kind "mammal".
Statement (5) concludes that what is denied of the kind "mammal" is denied of the subkind "dog".
See also
- AristotleAristotleAristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
- SyllogismSyllogismA syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
- Term logicTerm logicIn philosophy, term logic, also known as traditional logic or aristotelian logic, is a loose name for the way of doing logic that began with Aristotle and that was dominant until the advent of modern predicate logic in the late nineteenth century...
- Class (philosophy)Class (philosophy)Philosophers sometimes distinguish classes from types and kinds. We can talk about the class of human beings, just as we can talk about the type , human being, or humanity...
- Class (set theory)Class (set theory)In set theory and its applications throughout mathematics, a class is a collection of sets which can be unambiguously defined by a property that all its members share. The precise definition of "class" depends on foundational context...
- Natural kindNatural kindIn philosophy, a natural kind is a "natural" grouping, not an artificial one. Or, it is something that a set of things has in common which distinguishes it from other things as a real set rather than as a group of things arbitrarily lumped together by a person or group of people.If any natural...
- Type (metaphysics)
External links
- Logical Form (Stanford Encyclopedia of Philosophy)