Frege's own framework, which grounds the sense/reference distinction, treats sense as objective and public, not as the variable common notions different speakers happen to associate with a name.
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public(as describing what Frege believed sense to be)
Shared by everyone, not private or personal to just one person. If something is public, multiple people can understand it and agree on it the same way.
reference(Distinguished from intension in the context of possible worlds semantics)
The actual-world referent of an expression; what the expression picks out in the actual world.
sense (in Frege's theory)(as what Frege claims is objective and public)
The conceptual content or mental picture associated with a word—what the word *means* or *conveys* to someone. Unlike a reference, which is just the real object, sense is about how we understand or think about that object.
variable common notions(as what Frege believed sense is NOT)
Different ideas or associations that different people happen to connect with a word—they change from person to person and aren't fixed. For example, the word 'home' might bring up different images or feelings for different people.