Exercise 30, problem 4: Is my answer correct?

Mr. Nance,

As I am reviewing Exercise 30, I am confused  if my answer works , since its different from the original answer. I put:

No logic is a tangible study
No chemistry is logic
∴ All chemistry is a tangible study

As opposed to the answer key:

All non-logic sciences are tangible studies
All chemistry is a non-logic science
∴  All chemistry is a tangible study

Which one is right?

This is a particularly tricky problem, because of the particular trickiness of ordinary-language statements that use “except.”

Remember that statements of the form “All S is P except Q” can be translated “All non-Q S is P.” Thus, “All sciences except logic study the tangible” can be understood as “All non-logic sciences are tangible studies.” Translating it this way allows me to use the obverse of your “No chemistry is logic” to get “All chemistry is a non-logic science.” This gives the valid syllogism in the answer key.

Now, I agree that “All sciences except logic study the tangible” implies that logic does not study the tangible, which gives me your “No logic is a tangible study.” Your translation of both premises makes perfect sense. The problem is simply that, in this case, there is another way of understanding the “except” statement that allows for the valid interpretation of the syllogism above. And in Christian charity we should, if at all possible, assume that a person is arguing validly.

In other words, I think your answer is correct, in that the premises and conclusion reflect the original statements. But since there is another way of understanding the statements that give a valid syllogism, that other way is preferable.


3 thoughts on “Exercise 30, problem 4: Is my answer correct?

  1. Hi Mr. Nancy

    I am a homeschool parent and I have a question regarding Introductory Logic, Chapter 31, question 2. The answer my son provided does not match the one in the teacher’s guide. He wrote:

    All incomplete arguments are enthymemes.
    All enthymemes are arguments.
    Therefore, some arguments are incomplete arguments.

    Is this answer correct? Sometimes the teacher’s guide indicates, “answers may vary” but other times it does not, so I’m unsure.

    Thanks in advance,


  2. Hi Brenda,

    The enthymeme being translated was No enthymemes are complete, so some arguments are incomplete. The premise “No enthymemes are complete” may not be translated as “All incomplete arguments are enthymemes.” Rather, the obverse of the given premise would be “All enthymemes are incomplete arguments.” Otherwise his translation looks good.


Leave a Reply

Your email address will not be published. Required fields are marked *