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January 26, 2014 at 1:23 pm #19196spectrazMember
Consider the following arguments:
1. If you didn’t pass the test, then you didn’t pass the course.
2. You did pass the test.
3. You did pass the course.How should I reconstruct/evaluate this argument? The pattern of argument is called “Denying the antecedent” and looks like this:
1. If P then Q.
2. ¬P.
3. ¬Q.How do I interpret the negations of “pass the test” and “pass the course”? Can I also interpret it like this:
1. If ¬P then ¬Q.
2. P.
3. Q.I have another question concering validity in this example:
1. All logicians are dull.
2. Irving is not a logician.
3. Irving is dull.Pattern:
1. All As are Bs
2. x is not an A
3. x is BNow, does this follow from the premises? Shouldn’t it be the invalid pattern:
1. All As are Bs.
2. x is not an A.
3. x is not a B.January 26, 2014 at 5:29 pm #19197gerard.caseyParticipantDear Daniel,
You wrote:
“Consider the following arguments:
1. If you didn’t pass the test, then you didn’t pass the course.
2. You did pass the test.
3. You did pass the course.How should I reconstruct/evaluate this argument? The pattern of argument is called “Denying the antecedent” and looks like this:
1. If P then Q.
2. ¬P.
3. ¬Q.How do I interpret the negations of “pass the test” and “pass the course”? Can I also interpret it like this:
1. If ¬P then ¬Q.
2. P.
3. Q.”Yes. It’s the same pattern. P is equivalent to ¬¬P (which is the negation of the antecedent), and Q is equivalent to ¬¬Q which is the negation of the consequent.
You also wrote:
“I have another question concerning validity in this example:
1. All logicians are dull.
2. Irving is not a logician.
3. Irving is dull.Pattern:
1. All As are Bs
2. x is not an A
3. x is BNow, does this follow from the premises?”
No. Any valid syllogism with a negative premise must have a negative conclusion so x is B cannot be a valid conclusion from those premises.
I’m not sure what you mean by saying “Shouldn’t it be the invalid pattern:
1. All As are Bs.
2. x is not an A.
3. x is not a B”There can be more than one invalid conclusion from any given set of premises. However, if what you are suggesting is the “x is not a B” is the more plausible invalid conclusion, then I would agree with you. At least it is negative and so would at least pass rule 4.
Thank you as usual for your questions.
Best wishes,
GC
January 27, 2014 at 1:29 pm #19198spectrazMemberI have now confirmed my valid interpretation of the first argument. I am slowly learning to identify patterns where the premises have switched places and where the negations have changed places, compared to the pre-given patterns of arguments I have studied before.
As for the second one, I was looking for a specific invalid pattern. I had only seen two patterns of invalid arguments in predicate logic prior to seeing the argument above, and I was looking for one of them to fit the argument I translated. It would be helpful to have some more examples of invalid arguments just in case I stumble upon these types of arguments in the future.
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