Understanding Logical Terms: Intention, Connotation, Denotation, and Extension

The question asks to identify the term or terms that refer to the attributes shared by all and only those objects to which a given term refers. Let's break down the meaning of each option provided:

• Intention of a term: In logic, the intention (sometimes called intension) of a term refers to the set of attributes, properties, or characteristics that a thing must have to be included in the term's denotation. It's essentially the definition or the concept associated with the term. For example, the intention of the term "dog" includes attributes like "mammal," "canine," "barks," etc. These are the defining features.
• Connotation: This term is often used synonymously with "intention" or "intension" in logic and semantics. It refers to the internal meaning or the essential qualities that a term implies or suggests. It represents the set of attributes shared by the things the term denotes.
• Denotation: The denotation (or extension) of a term refers to the set of all actual objects, individuals, or entities in the real world to which the term correctly applies. For example, the denotation of the term "dog" is the set of all actual dogs that exist or have existed.
• Extension of a term: This is synonymous with "denotation." It is the class of all things that a term names or refers to.

Now, let's look at the question again: "The attributes shared by all and only those objects to which a term refers". This description directly matches the definitions of the intention and the connotation of a term. These are the properties or characteristics that define the group of objects, not the objects themselves.

The denotation and extension, on the other hand, refer to the actual objects that fall under the term, not their shared attributes.

Therefore, both the intention of a term (A) and connotation (B) fit the description given in the question.

Let's evaluate the options based on our analysis:

• D only: Incorrect, as Denotation refers to objects, not attributes.
• Both A and B: Correct, as both Intention and Connotation refer to the shared attributes.
• Both C and D: Incorrect, as both Denotation and Extension refer to objects, not attributes.
• C only: Incorrect, as Denotation refers to objects, not attributes.

Based on the analysis, the correct option is the one that includes both A and B.

Revision Table: Key Logical Terminology

Additional Information: Intension vs. Extension

The distinction between intension (intention/connotation) and extension (denotation) is fundamental in logic and semantics. They represent two ways of defining or understanding a term:

• Intension (Intention/Connotation): Defines the term by listing the necessary and sufficient conditions for something to be a member of the class represented by the term. It is the criteria for membership.
• Extension (Denotation): Defines the term by listing or pointing to all the members of the class that the term refers to. It is the set of actual instances.

There is an inverse relationship between the two for many terms: generally, as the intension of a term increases (becomes more specific, adding more attributes), its extension decreases (refers to fewer objects). For example, the term "dog" has a certain intension and extension. The term "golden retriever" has a greater intension (includes all attributes of "dog" plus specific "golden retriever" attributes) and a smaller extension (only golden retrievers, a subset of all dogs).