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The Rule for the Fourth Figure is: If the major premise is affirmative, the minor premise must be universal. If the minor premise is affirmative, the conclusion must be particular. If one of the premises is negative, the major premise must be universal. Explanation of the Rule First Part: If the major premise is affirmative, the minor premise must be universal. In the major premise, if it were affirmative, the middle term (M), being the predicate of an affirmative proposition, would be particular. The middle term (M), however, is also the subject of the minor premise. If the minor premise were not universal, it would be particular. That would mean that its subject, which is the middle term (M), would be particular. Both middle terms would then be particular and that would violate General Rule Number 4, resulting in an undistributed middle. If the major premise is affirmative, where the predicate (M) will have to be particular, the minor premise must be universal. The middle term will then be distributed at least once. Second Part: If the minor premise is affirmative, the conclusion must be particular. If the minor premise is affirmative, the predicate, which is the minor term (S), will be particular, since it is the predicate of an affirmative proposition. This minor term (S), however, is also the subject of the conclusion. It must also be particular in the conclusion or we will have an illicit minor in the conclusion. This would go against General Rule Number 2. Therefore, if the minor premise is affirmative, the conclusion must be particular. Third Part: If one of the premises is negative, the major premise must be universal. The major term (P) is the subject of the major premise. If one of the premises is negative, the conclusion will also be negative (see General Rule Number 7), and then this major term would be universal since it is the predicate of a negative conclusion. The major term (P) is the subject of the major premise and will have to be a universal term. This is because it would otherwise be wider in the conclusion than in the premises. This would constitute an illicit major (see General Rule Number 2). The major term, therefore, must be a universal term in the major premise. This means a universal major premise. Therefore, the rule is correct in saying that if one of the premises is negative, the major premise must be universal. The Valid Moods of the Fourth Figure When we consider the moods which are valid for the syllogisms of the Fourth Figure, we find that five of the eight possible legitimate combinations are valid and three are invalid. Here are the diagrams: Moods of the Fourth Figure A uP + pM A uM + pS pS + pP Valid A uP + pM E uM - uS uS - uP Valid A uP + pM I pM + pS pS + pP Undist.Middle A uP + pM O pM - uS uS - uP Undist.Middle E uP - uM A uM + pS pS - uP Valid E uP - uM I pM + pS uS - uP Valid I pP + pM A uM + pS pS + pP Valid O pP - uM A uM + pS pS - uP Illicit Major Clearly, there are five valid moods for the Fourth Figure: A A, A E, E A, E I, and I A. Each one follows the rule for the Fourth Figure. The A I and A O moods are invalid because they don't conform to the part of the rule that says that is the major premise is affirmative, the minor premise must be universal. We have an undistributed middle. The O A mood is invalid because it violates that part of the rule that says that if one of the premises is negative, the major premise must be universal. The conclusion contains an illicit major. Study the following arguments which illustrate the valid moods: A All armed robberies are crimes. A All crimes are something against the law. Therefore, Something against the law are armed robberies. A All animals are living things. E No living things are minerals. Therefore, No minerals are animals. E No plants are sentient things. A All sentient things are living things. Therefore, Some living things are not plants. E No heroes are cowards. I Some cowards are soldiers. Therefore, Some soldiers are not heroes. I Some actors are powerful athletes. A All powerful athletes are people admired. Therefore, Some people admired are actors. We have now completed our discussion of the four syllogistic figures and the valid moods for each. The First Figure has four valid moods, the Second Figure has four valid moods, the Third Figure has six valid moods, and the Fourth Figure has five valid moods. There are, therefore, nineteen different ways in which the simple categorical syllogisms can be validly formulated. Any other formulation would violate one or more of the General Rules. These rules must be observed in this kind of argument or consistency cannot be insured. The syllogism we have been studying is the standard form of mediate inference. It is the basic arrangement for arguments. There are some other types of syllogisms, however, to which we will now direct our attention in the next essay. NEXT - Part 4: Kinds of Categorical Syllogisms Enrich Your Life With a Philosophy Book... Enrich Your Life With a Philosophy Magazine... Main Page & Index
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