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# 5.3 Rules And Fallacies

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Course lecture I developed over section 5.3 of Patrick Hurley\\\'s &quot;A Concise Introduction to Logic&quot;.

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### 5.3 Rules And Fallacies

1. 1. 5.3 Rules and Fallacies
2. 2. Rules for validity <ul><li>We know from the validity tables that certain forms are valid and others are not…but the question is, how can we prove it? </li></ul><ul><li>There are five different rules for determining validity in syllogisms. </li></ul>
3. 3. Rule #1 – Distribution of the middle term <ul><li>The middle term must be distributed at least once in the syllogism. </li></ul><ul><li>Reminder: </li></ul><ul><ul><li>A-types – subject (S) </li></ul></ul><ul><ul><li>E-types – subject, predicate (S and P) </li></ul></ul><ul><ul><li>I-types – neither the subject nor predicate (none) </li></ul></ul><ul><ul><li>O-types – predicate (P) </li></ul></ul><ul><li>If the middle term is not distributed, then a fallacy is committed: called the undistributed middle fallacy. </li></ul><ul><li>Example: (AAA-2) </li></ul><ul><ul><li>All people are happy. (Subject - distributed) </li></ul></ul><ul><ul><li>All clowns are happy. (Subject - distributed) </li></ul></ul><ul><ul><li>---------------------------- </li></ul></ul><ul><ul><li>Therefore, all clowns are people. (Subject - distributed) </li></ul></ul>
4. 4. Rule #2 – Distribution in the conclusion & premise <ul><li>If a term is distributed in the conclusion then it has to be distributed in the premises as well. </li></ul><ul><li>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. </li></ul><ul><ul><li>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. </li></ul></ul><ul><li>Example: (AOO-1) (Illicit major) </li></ul><ul><ul><li>All students are miserable. (Subject – distributed)  Invalid </li></ul></ul><ul><ul><li>Some people are not students. (Predicate – distributed) </li></ul></ul><ul><ul><li>---------------------------- </li></ul></ul><ul><ul><li>Therefore, some people are not miserable. (Predicate – distributed) </li></ul></ul><ul><li>Example: (AAA-4) (Illicit minor) </li></ul><ul><ul><li>All beers are bitter drinks. (Subject – distributed) </li></ul></ul><ul><ul><li>All bitter drinks are delicious drinks. (Subject – distributed)  Invalid </li></ul></ul><ul><ul><li>----------------------------- </li></ul></ul><ul><ul><li>Therefore, all delicious drinks are beers. (Subject – distributed) </li></ul></ul>
5. 5. Rule #3 – Negative premises <ul><li>You cant have two negative premises. </li></ul><ul><li>If two negative premises are present, the fallacy of exclusive premises is committed. </li></ul><ul><li>Example: (EOO-1) (True premises, false conclusion, because it violates rule 3) </li></ul><ul><ul><li>No students are happy. </li></ul></ul><ul><ul><li>Some people are not students. </li></ul></ul><ul><ul><li>----------------------------- </li></ul></ul><ul><ul><li>Therefore, some people are not happy. </li></ul></ul>
6. 6. Rule #4 – Requirement of negative premises and conclusions <ul><li>A negative premise requires a negative conclusion, and a negative conclusion requires a negative premise. </li></ul><ul><li>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. </li></ul><ul><li>Example: (AOI-1) (Affirmative conclusion from negative premises) </li></ul><ul><ul><li>All TV shows are dramatic. </li></ul></ul><ul><ul><li>Some commercials are not TV shows. </li></ul></ul><ul><ul><li>------------------------------ </li></ul></ul><ul><ul><li>Therefore, some commercials are dramatic. </li></ul></ul><ul><li>Example: (AAO-4) (Negative conclusion from affirmative premises) </li></ul><ul><ul><li>All senators are greedy politicians. </li></ul></ul><ul><ul><li>All greedy politicians are liars. </li></ul></ul><ul><ul><li>------------------------------ </li></ul></ul><ul><ul><li>Therefore, some liars are not senators. </li></ul></ul>
7. 7. Rule #5 – Universals and particulars <ul><li>If both premises are universal, then you can’t have a particular conclusion. </li></ul><ul><li>If you have a particular conclusion and two universal premises, an existential fallacy is committed. </li></ul><ul><li>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) </li></ul><ul><ul><li>All people are humans. </li></ul></ul><ul><ul><li>All doctors are people. </li></ul></ul><ul><ul><li>------------------------------------ </li></ul></ul><ul><ul><li>Therefore, some doctors are humans. </li></ul></ul>
8. 8. Aristotelian standpoint <ul><li>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. </li></ul><ul><li>When dealing with rule 5, a syllogism can be valid if the critical term refers to something that actually exists. </li></ul><ul><li>The critical term is the one listed (S, M, or P) in the table of conditionally valid forms on page 240. </li></ul><ul><li>In Venn diagrams, it is the circle identified in the syllogism as being all shaded in except for one area. </li></ul>
9. 9. Superfluous distribution <ul><li>This basically means any term that is distributed more often than is necessary to prove the syllogism is valid. </li></ul><ul><li>Example: </li></ul><ul><ul><li>All M(d) are P. </li></ul></ul><ul><ul><li>All S(d) are M. (Critical term – S) </li></ul></ul><ul><ul><li>----------------------- </li></ul></ul><ul><ul><li>Therefore, some S are P. </li></ul></ul><ul><ul><li>No M(d) are P(d). </li></ul></ul><ul><ul><li>All M(d) are S. (Critical term – M) </li></ul></ul><ul><ul><li>------------------------ </li></ul></ul><ul><ul><li>Therefore, some S are not P(d). </li></ul></ul><ul><ul><li>All P(d) are M. (Critical term – P) </li></ul></ul><ul><ul><li>All M(d) are S. </li></ul></ul><ul><ul><li>----------------------- </li></ul></ul><ul><ul><li>Therefore, some S are P. </li></ul></ul>