5.3 Rules And Fallacies
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The document outlines five rules for determining the validity of syllogisms: 1) The middle term must be distributed at least once. If not, it commits the fallacy of the undistributed middle. 2) Terms distributed in the conclusion must also be distributed in the premises, otherwise it commits the fallacy of illicit major/minor. 3) Syllogisms cannot have two negative premises or it commits the fallacy of exclusive premises. 4) A negative premise requires a negative conclusion and vice versa, otherwise it commits the fallacy of drawing an affirmative/negative conclusion from negative/affirmative premises. 5) If both premises are universal, the conclusion cannot be particular or it
5.3 Rules And Fallacies
- 1. 5.3 Rules and Fallacies
- 2. Rules for validity We know from the validity tables that certain forms are valid and others are not…but the question is, how can we prove it? There are five different rules for determining validity in syllogisms.
- 3. Rule #1 – Distribution of the middle term The middle term must be distributed at least once in the syllogism. Reminder: A-types – subject (S) E-types – subject, predicate (S and P) I-types – neither the subject nor predicate (none) O-types – predicate (P) If the middle term is not distributed, then a fallacy is committed: called the undistributed middle fallacy. Example: (AAA-2) All people are happy. (Subject - distributed) All clowns are happy. (Subject - distributed) ---------------------------- Therefore, all clowns are people. (Subject - distributed)
- 4. Rule #2 – Distribution in the conclusion & premise If a term is distributed in the conclusion then it has to be distributed in the premises as well. If a term is distributed in the conclusion and not in the premises, then the fallacy of illicit major/illicit minor is committed. Remember, when I say “term”, I don’t just mean that, for example, a predicate is distributed, I mean that the predicate used in the conclusion. Which specific one depends on if the term in question is the major term (predicate of the conclusion) or the minor term (subject of the conclusion. Example: (AOO-1) (Illicit major) All students are miserable. (Subject – distributed) Invalid Some people are not students. (Predicate – distributed) ---------------------------- Therefore, some people are not miserable. (Predicate – distributed) Example: (AAA-4) (Illicit minor) All beers are bitter drinks. (Subject – distributed) All bitter drinks are delicious drinks. (Subject – distributed) Invalid ----------------------------- Therefore, all delicious drinks are beers. (Subject – distributed)
- 5. Rule #3 – Negative premises You cant have two negative premises. If two negative premises are present, the fallacy of exclusive premises is committed. Example: (EOO-1) (True premises, false conclusion, because it violates rule 3) No students are happy. Some people are not students. ----------------------------- Therefore, some people are not happy.
- 6. Rule #4 – Requirement of negative premises and conclusions A negative premise requires a negative conclusion, and a negative conclusion requires a negative premise. If you have one without the other (negative premise(s) or conclusion by itself) then the fallacy of drawing an affirmative conclusion from negative premises or drawing a negative conclusion from affirmative premises is committed. Example: (AOI-1) (Affirmative conclusion from negative premises) All TV shows are dramatic. Some commercials are not TV shows. ------------------------------ Therefore, some commercials are dramatic. Example: (AAO-4) (Negative conclusion from affirmative premises) All senators are greedy politicians. All greedy politicians are liars. ------------------------------ Therefore, some liars are not senators.
- 7. Rule #5 – Universals and particulars If both premises are universal, then you can’t have a particular conclusion. If you have a particular conclusion and two universal premises, an existential fallacy is committed. Example: (AAI-1) (Invalid because the conclusion implies doctors exist and the premises don’t support that, since Boolean universal claims don’t have existential import) All people are humans. All doctors are people. ------------------------------------ Therefore, some doctors are humans.
- 8. Aristotelian standpoint Any syllogism that is invalid by the first four rules from the Boolean standpoint is also invalid from the Aristotelian, except in the case of rule 5. When dealing with rule 5, a syllogism can be valid if the critical term refers to something that actually exists. The critical term is the one listed (S, M, or P) in the table of conditionally valid forms on page 240. In Venn diagrams, it is the circle identified in the syllogism as being all shaded in except for one area.
- 9. Superfluous distribution This basically means any term that is distributed more often than is necessary to prove the syllogism is valid. Example: All M(d) are P. All S(d) are M. (Critical term – S) ----------------------- Therefore, some S are P. No M(d) are P(d). All M(d) are S. (Critical term – M) ------------------------ Therefore, some S are not P(d). All P(d) are M. (Critical term – P) All M(d) are S. ----------------------- Therefore, some S are P.