1

Source: A Concise Introduction to Logic (12 Ed, 2014), by Patrick J. Hurley

[p 286:] Rule 1: The Middle Term Must Be Distributed at Least Once.

[p 288:] Rule 4: A Negative Premise Requires a Negative Conclusion,
and a Negative Conclusion Requires a Negative Premise.

[p 288:] Rule 5: If Both Premises Are Universal, the Conclusion Cannot Be Particular.

[p 290:] [...] The question remains, however, whether a syllogism’s breaking none of the rules is a sufficient condition for validity. In other words, does the fact that a syllogism breaks none of the rules guarantee its validity? The answer to this question is “yes,” but unfortunately there appears to be no quick method for proving this fact. [...] The proof that follows is somewhat tedious, and it proceeds by considering four classes of syllogisms having A, E, I, and O propositions for their conclusions. [...]

[p 291:] Next, consider a syllogism having an I proposition for its conclusion.
By Rule 1, M is distributed in at least one premise,
and by Rule 4, both premises are affirmative.
Further, by Rule 5, both premises cannot be universal. [...]

I do not comprehend only the step bolded above:
How does Rule 4 imply that both premises must be affirmative?

3

Because I is particular affirmative and Rule 4 states :

A Negative Premise Requires a Negative Conclusion,

i.e. if one of the premises is negative, also the conclusion is.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.