In a Syllogism with an I Proposition as the conclusion, why must both premises be affirmative?


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?


Posted 2015-12-28T21:26:59.160

Reputation: 1



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.


Posted 2015-12-28T21:26:59.160

Reputation: 33 575