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Mike_Discussion_9_14

Mike_Discussion_9_14 - Second discussion group meeting(Sept...

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Second discussion group meeting (Sept. 14). Included in this file: 1. Typical conclusion indicators and premise indicators. 2. Alternative statements of the rules for assessing validity. 3. Steps for expanding argument forms. 4. Translation tips. 5. Optional translation exercises (handed out in discussion), with answers. 6. Answers to week 2’s assignment. 8. Answers to optional ‘find the conclusion’ exercises (handed out in discussion). 9. More on distribution (see also last week’s posted file [09/07/07]). —Some typical conclusion indicators: therefore; accordingly; entails that; we may conclude; hence; thus; it must be that; it follows that; consequently; whence; implies that; we may infer; so; as a result. —Some typical premise indicators: because; since; in that; seeing that; as indicated by; may be inferred from; for the reason that; as; inasmuch as; for; given that; owing to. —Alternative statements of the rules for assessing validity (see also ‘answers to all logic exercises’ posted under ‘Course Materials (TAs)’ : • Rule A: Any syllogism with two negative premises is invalid. • Rule B: (a) Any syllogism having at least one negative premise but a positive conclusion is invalid. OR (b) Any syllogism that has a negative conclusion but does not have a negative premise is invalid. • Rule C: Any syllogism in which the middle term is not distributed at least once is invalid. • Rule D: Any syllogism that has a term distributed in its conclusion that is not distributed in the premise in which it occurs is invalid. • Rule E: Any syllogism that has two universal premises but a particular conclusion is invalid.
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Steps for expanding argument forms I’ll use the first argument form from the third set of exercises: EIO-2. Step 1. Write down the form of the conclusion, leaving room for the premises. The mood tells us that the conclusion is an O proposition. So we start with the following: ________________________ Some S are not P. Step 2. Add the premises, leaving blanks for the terms: No ___ are ____. Some ___ are ___. __________________ Some S are not P. Step 3. The figure tells you where the middle terms go. In this case the figure is 2, so add the middle terms as follows: No ___ are M. Some ___ are M. __________________ Some S are not P. Step 4. Put the major term (P) in the remaining blank in the first premise (it always goes there); and put the minor term (S) in the remaining blank in the second premise (it always goes there): No P are M. Some S are M. __________________ Some S are not P. Now we can easily apply the rule technique. Rule A: passes. Rule B: passes. Rule C: passes. Rule D: passes. Rule E: passes. So the argument form is valid.
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Translation tips If something’s a cat, then it’s an animal. Something’s an animal if it’s a cat. All cats are animals. } Any proposition that means that being a cat is a sufficient condition for being an animal gets translated as “All cats are animals”: Only animals are cats.
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