I encountered the following argument while I was studying syllogistic logic from a book:
All red cars kill papers, (premise)
All cars that kill papers are beautiful, (premise)
All red cars are beautiful. (conclusion)
Of course, the argument is valid. But when I tried to symbolize the argument, I couldn't do it completely because of the problem which I will mention. The answer (symbolization) of the argument that my book suggests is the folowing:
all R is K, (premise)
all K is B, (premise)
all R is B. (conclusion)
Of course this is valid, too.
My problem is: Why do we use the capital "K" for both "kill papers" and "cars that kill papers"? Shouldn't we use different letters for each of these sentences? I have this problem with arguments involving "that" generally as seen above.