different between intensional vs intensionally

English

intension +? -al

intensional (not comparable)

Of or pertaining to intension.
- These two treatments of the predicate are typical of the two traditions in traditional logic—the intensional and the extensional traditions. Logicians who can be counted among the intensional logicians are Gottfried Leibniz, Johann Lambert, William Hamilton, Stanley Jevons, and Hugh MacColl. Among the extensional logicians are George Boole, Augustus De Morgan, Charles Peirce, and John Venn.

intension +? -ally

intensionally (comparative more intensionally, superlative most intensionally)

(philosophy) With respect to intension
- A term is treated either extensionally as a class of objects or intensionally as a set of properties. The ‘intent’ of the term ‘dog’ includes all the properties that are included in the intent of ‘mammal’. The intensional treatment of ‘dogs are mammals’ interprets this sentence as true because the semantic interpretation of the subject is a superset of the interpretation of the predicate. On the extensional treatment of the sentence, however, the sentence is true because the interpretation of the subject (the class of dogs) is a subset of the interpretation of the predicate (the set of mammals).

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