Reconstruct the following syllogistic form and use the five rules for syllogisms to determine if they are valid from the Boolean standpoint, conditionally valid from the Aristotelian standpoint, or invalid. if the form is conditionally valid, identify the condition that must be fulfilled. For those that are invalid from either the Boolean or Aristotelian standpoint, name the fallacy or fallacies committed.
EIO-1
Major Premise: Some M are not P .
Minor Premise: All S are M .
Conclusion: Some S are not P.
Which (if any) of the following rules for validity are broken by this syllogism? Check all that apply.

Rule 1
Rule 2
Rule 3
Rule 4
Rule 5
Is this syllogistic form valid from the Boolean standpoint, conditionally valid from the Aristotelian standpoint, or invalid?

Unconditionally valid from the Boolean standpoint
Conditionally valid from the Aristotelian standpoint (on the condition S exists)
Conditionally valid from the Aristotelian standpoint (on the condition P exists)
Conditionally valid from the Aristotelian standpoint (on the condition M exists)
Invalid
Which, if any, of the following fallacies are committed by this syllogistic form? Check all that apply.

Drawing a negative conclusion from affirmative premises
Drawing an affirmative conclusion from a negative premise
Illicit major
Illicit minor
Undistributed middle
Exclusive premises
Existential fallacy from the Boolean standpoint

Question

Reconstruct the following syllogistic form and use the five rules for syllogisms to determine if they are valid from the Boolean standpoint, conditionally valid from the Aristotelian standpoint, or invalid. if the form is conditionally valid, identify the condition that must be fulfilled. For those that are invalid from either the Boolean or Aristotelian standpoint, name the fallacy or fallacies committed.
EIO-1
Major Premise:	Some   M   are not   P   .
Minor Premise:	All   S   are   M   .
Conclusion:	Some    S are not    P.
Which (if any) of the following rules for validity are broken by this syllogism? Check all that apply.

Rule 1
	Rule 2
	Rule 3
	Rule 4
	Rule 5
Is this syllogistic form valid from the Boolean standpoint, conditionally valid from the Aristotelian standpoint, or invalid?

Unconditionally valid from the Boolean standpoint
	Conditionally valid from the Aristotelian standpoint (on the condition S exists)
	Conditionally valid from the Aristotelian standpoint (on the condition P exists)
	Conditionally valid from the Aristotelian standpoint (on the condition M exists)
	Invalid
Which, if any, of the following fallacies are committed by this syllogistic form? Check all that apply.

Drawing a negative conclusion from affirmative premises
	Drawing an affirmative conclusion from a negative premise
	Illicit major
	Illicit minor
	Undistributed middle
	Exclusive premises
	Existential fallacy from the Boolean standpoint

Ask a Philosopher · Accepted Answer

How curious it is, to delve into the realm of syllogistic forms and rules of validity, much like a scholar unraveling the mysteries of the universe. In this particular case, we are presented with the syllogism EIO-1, with its premises and conclusion laid out before us. The Major Premise states that some M are not P, while the Minor Premise declares that all S are M. From these premises, it is concluded that some S are not P. Upon closer examination, we must apply the five rules for syllogisms to determine if this form is valid. Rule 1, which focuses on the distribution of the middle term, seems to be violated here, as the middle term M is undistributed in the Major Premise. This leads to a breaking of Rule 4, which emphasizes the necessity of the middle term being distributed at least once. Therefore, this syllogistic form is deemed invalid from the Boolean standpoint. However, from an Aristotelian perspective, this form may be conditionally valid on the condition that S, P, or M exist. The fallacy of undistributed middle is evident here, as the middle term M fails to be distributed properly in the premises. In conclusion, while this syllogistic form presents a fascinating puzzle for the mind to ponder, it ultimately falls short of meeting the rigorous standards of logical validity.