noun. That which is named or designated by a linguistic term.

noun. something (whether existing or not) that is referred to by a linguistic expression

"The designatum must first be picked out in α by whether it meets the descriptive requirements (with or without the indexing) there in α: but the purpose of the indexing is to keep the term referring, with respect to other worlds, to that same item picked out originally in α by virtue of meeting the right requirements there."

referent  

designate  designated  designates  designator  

referent