Rule 6: A syllogism with two universal premises (both the major premise and the minor premise) cannot have a particular conclusion.
Since the argument expressed by logical syllogisms typically progresses from a broad (i.e., “universal”) statement to a narrower, more specific (i.e., “particular”) statement, it is essential that such a logical syllogism must contain both a universal and a particular premise, if a particular conclusion is the desired result. Any other combination of statements, even if their individual premises are otherwise accurate, does not fit within the structure for a valid logical syllogism. Stated somewhat differently, although a valid syllogism can certainly contain two universal premises (in both the major and the minor premises), if such is the case the conclusion must also be stated in universal terms.

Consider the following illustration:
1. All mortals eventually will die. (universal major premise)

2. All Greeks are mortal. (universal minor premise)

3. All Greeks eventually will die. (universal conclusion)

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This conclusion is perfectly valid, since it, like both the major and minor premises from which it is derived, is expressed in universal terms. However, if we change the universal term “all Greeks” in the conclusion to “this Greek,” making it a particular conclusion, the logic fails. It may in fact be true that: “This Greek eventually will die,” but such a conclusion cannot be logically derived from this syllogism. The use of universal terms in both the major and the minor premise statements requires that the conclusion must also be stated in universal terms.