In
Aristotelian logic
In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, ...
, ''dictum de omni et nullo'' (
Latin
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
: "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) of 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''
''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
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the ''subject term'') are included in another (the ''predicate term''). The study of arguments ...
) 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''
''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".
Each of these two principles is an instance of a valid argument form known as
universal hypothetical syllogism in
first-order predicate logic.
In
Aristotelean syllogistic, they correspond respectively to the two argument forms, Barbara and Celarent.
See also
*
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
*
Syllogism
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be tru ...
*
Term logic
In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, ...
*
Class (philosophy)
A class is a collection whose members either fall under a predicate or are classified by a rule. Hence, while a set can be extensionally defined only by its elements, a class has also an intensional dimension that unite its members. When the ter ...
*
Class (set theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. Classes act as a way to have set-like ...
*
Natural kind
"Natural kind" is an intellectual grouping, or categorizing of things, in a manner that is reflective of the actual world and not just human interests. Some treat it as a classification identifying some structure of truth and reality that exists wh ...
*
Type (metaphysics)
Type may refer to:
Science and technology Computing
* Typing, producing text via a keyboard, typewriter, etc.
* Data type, collection of values used for computations.
* File type
* TYPE (DOS command), a command to display contents of a file.
* ...
*
Downward entailing
*
Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order ...
References
*
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
, ''
Prior Analytics
The ''Prior Analytics'' ( grc-gre, Ἀναλυτικὰ Πρότερα; la, Analytica Priora) is a work by Aristotle on reasoning, known as his syllogistic, composed around 350 BCE. Being one of the six extant Aristotelian writings on logic a ...
'', 24b, 28–30.
Notes
External links
*{{cite SEP , url-id=logical-form , title=Logical Form , last=Pietroski , first=Paul
Latin logical phrases
Arguments
Term logic
Inference