I have a very basic question about Frege's object/concept distinction. Please don't make fun of me as I'm new to early analytic philosophy. This question has been bugging me for a while, so I'd appreciate a thorough answer.
In sentences like "the cat is grey" or "the cat is in the park," do the words 'the cat' designate an object? If you were to formalize these sentences, I would think it would go as something like: there is some x such that x is a cat and x is grey/in a park. There wouldn't be a uniqueness clause, I would think.
If the words that designate an object have to pick out something unique, does that mean the words 'the cat' cannot designate an object (since they are not specified enough)? If they don't designate an object, then what is their logical status?