Dictum de omni et nullo
In Aristotelean logic, dictum de omni et nullo is the principle that whatever is affirmed or denied of a whole kind may be affirmed or denied (respectively) of any subkind of it.
Dictum de omni (sometimes misinterpreted as universal instantiation) is the principle that whatever is universally true of a kind is true as well for any subkind of that kind.
It is thought to be one of two ultimately basic principles in syllogistic logic, along with dictum de nullo (below), in the sense that all syllogistic argument forms are alleged to be variations of applications of these two principles.
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".
Related Topics
Syllogism
Class (philosophy)
Class (set theory)
Natural kind
Type
References
Prior Analytics, 24b, 28-30.
External Links
Logical Form (Stanford Encyclopedia of Philosophy)