Subalternation is an
immediate inference An immediate inference is an inference which can be made from only one statement or proposition. For instance, from the statement "All toads are green", the immediate inference can be made that "no toads are not green" or "no toads are non-green" ( ...
which is only made between A (All S are P) and I (Some S are P)
categorical proposition
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 ...
s and between E (No S are P or originally, No S is P) and O (Some S are not P or originally, Not every S is P) categorical propositions of the traditional
square of opposition
In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions.
The origin of the square can be traced back to Aristotle's tractate ''On Interpre ...
and the original square of opposition.
If the A proposition is true we may immediately infer that I is true. If the E proposition is true we may immediately infer that O is true.
Conversely, If the I is false, we can immediately infer that A is also false, as well as if O is false, then E is false. However, if the A proposition is false that will not tell us anything about the truth value of the I proposition. Similarly, if the E proposition is false, that will not tell us anything about the truth value of the O proposition.
An example of a subalternation is "If all leopards are mammals, then some leopards are mammals."
When the inference is misapplied, the
syllogistic fallacy
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 true.
...
is called an
illicit subalternation.
References
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Immediate inference