Good or Valid Syllogisms vs. Invalid Syllogisms

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Kinds of Syllogisms
We focus our discussion to the most important kind of syllogism where we can apply different rules in order to distinguish good or valid syllogisms from invalid ones. These syllogisms are under the category, by comparison to the Inferential Laws. 1. Correct: when it observes the Rules and the legitimate patterns (Figure and Mood) for valid inference. 2. Incorrect: Syllogism that violates one or several of the Rules for valid inference, or the legitimate patterns (Figure and Mood) for valid inference. In order for us to determine the validity or acceptability of a syllogism (following the Rules), let us focus our discussion on the particular rules governing the terms and syllogistic propositions. Particular Rules Governing the Terms

1. The Syllogism must contain Three Terms, not less nor more. This is a requirement of the reasoning process of the categorical inference. If there are only two terms, only a proposition can be made; and there will be no Middle or Common term with which to compare the two terms, in order to verify their agreement, or disagreement, in case this is not known: in other words, no conclusion can be inferred. On the other hand, if there are four terms, there will be more than one Middle term, which is tantamount to having no middle term at all. In other words, no effective comparison of each of the two terms with a common term is achieved, as required by the nature of the categorical inference. Example of a Syllogism violating the first rule

Nothing is better than God;
But 10 cents is better than nothing;
Ergo, 10 cents is better than God.

Seemingly, the syllogism above has three terms (nothing, God, and 10 cents). But logically speaking, there are four terms used. The term nothing is the first premise is very much different in meaning and application if it is compared to the term nothing in the second premise, thus there is a shifting of meaning from the first premise to the second one. Nothing in the first premise implies ‘ quality’ while in the second premise speaks of ‘quantity’.

2. No term can have greater extension in the Conclusion than it had in the Premises. In order to know the exact extension of each term of a syllogism, we must bear in mind that the extension of the predicate of an affirmative proposition is always particular, and the extension of the predicate of a negative proposition is always universal. The second rule allows a term to have in the Conclusion the same extension as in the premise, but not greater. If a term has greater extension in the conclusion than in the premise, then it cannot be formally the same term that has been compared in the premise, as it is supposed to be.

Examples of violations of Rule 2

a. Scientists are wise people;
But, scientists are men;(particular)
Ergo, men (universal) are wise people.

b. Plants are organisms; (particular)
But animals are not plants;
Ergo, animals are not organisms. (universal)

Since the error in the first example is seen in the extension of the Minor term (men), the violation is known as the fallacy of the illicit minor term. Likewise, in the second example, the error lies on the Major term (organism), thus the violation is called as the fallacy of the illicit major term.

3. The Middle Term should not be found in the Conclusion. The Middle Term has no function to do, and no rightful place in the Conclusion. If the conclusion contains the Middle Term, then it will be just a repetition of the premises in a compound manner, and not a true conclusion.

Example of violation Rule 3

Men are rational animals;
But men are mortal;
Ergo, men are mortal and rational animals.

4. The Middle Term must be distributed or taken universally, at least once, in the Premises. It may be taken universally twice. If the middle term is not taken universally, at least once, in the premises, then it will be twice particular in the premises; and as such, its supposition will not be the same. In other...
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