Understanding Term Intension and Extension

The question asks about the set of attributes shared by all and only those objects to which a general term refers. This concept is fundamental in logic and semantics when defining the meaning of terms.

Let's break down the options provided:

1. The intension of that term: The intension of a term refers to the internal meaning of the term. It is the set of attributes or properties that an object must have in order for the term to apply to it. For example, the intension of the term "bachelor" includes the properties "unmarried" and "adult male".
2. Connotation of that term: In logical contexts, connotation is often used synonymously with intension. It refers to the set of attributes conventionally associated with or implied by a term. While 'connotation' can also relate to emotional associations in everyday language, its logical use aligns with intension.
3. The extension of that term: The extension of a term refers to the collection of all actual objects or individuals in the world to which the term applies. For example, the extension of the term "bachelor" is the set of all actual bachelors in the world.
4. Denotation of that term: Similar to connotation being related to intension, denotation is often used synonymously with extension. It refers to the objects that a term points to or denotes.

The question specifically asks for the "set of attributes shared by all and only those objects". This phrasing directly describes the defining properties that determine membership in the set of objects referred to by the term. This is precisely what the intension (or connotation) of a term represents.

To illustrate the difference between intension/connotation and extension/denotation, consider the term "triangle":

• Intension/Connotation: The set of attributes {closed figure, three straight sides, three angles}. This is the definition.
• Extension/Denotation: The set of all actual triangles that exist or can be conceived of. This is the collection of objects.

Based on the definitions, the set of attributes shared by all and only those objects to which a general term refers is known as the intension of that term and also the connotation of that term (in a logical context). The extension and denotation refer to the objects themselves, not the shared attributes.

Therefore, the correct concepts describing the set of shared attributes are Intension and Connotation.

Summary of Key Terms

The question asks for the set of attributes, which aligns with Intension and Connotation.

Conclusion on Term Attributes

The set of attributes shared by all and only those objects to which a general term refers is called the intension of that term and the connotation of that term.

Revision Table: Intension vs. Extension

Additional Information on Logic Terms

In formal logic and semantics, the distinction between intension and extension is crucial for understanding how terms acquire meaning and how truth values are assigned to statements. A term's intension determines its extension. If the intension changes, the set of objects it applies to (extension) will also likely change.

For instance, if the definition (intension) of "fish" was changed to include whales, the set of objects considered "fish" (extension) would expand. Conversely, if the definition became more specific, the extension might shrink.

While connotation in everyday language can include subjective or emotional associations (e.g., "home" connotes warmth and security), its use in logic often mirrors the precise, defining attributes of intension.