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.

  • 1
    I made an edit. You may roll this back or continue editing as you are probably aware. Welcome to this SE. Jul 24 '18 at 18:29
  • @FrankHubeny Thank you Mr. Hubeny, your edit has made me happy.
    – user34319
    Jul 24 '18 at 18:50

Why do we use the capital "K" for both "kill papers" and "cars that kill papers"?

"[K]ill papers" is actually shorthand for "cars that kill papers". The statement is saying that all members of one set are also members of a second set; so the content of the second set must be defined.

  • Ah, I understand clearly now. Again thanks for your answer.
    – user34319
    Jul 25 '18 at 10:51

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