## Ex 6 Answers

This page refers to exercise 6.

ii.

Terms:

S = Closest to the politician

M = the politician’s enemy

P = Xhiang Tsu

Pattern:

Closest to the politician is the politician’s enemy **S is M **

Chiang Tsu is closest to the politician **P is S**

/ Chiang Tsu is the politician’s enemy **P is M**

This argument is valid because the middle term does not appear in the conclusion, and one premise is universal (All people closest to the politician are the politicians enemy) and one is particular.

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iii.

Terms:

S = my friend

M = believing in ghosts

P = superstitious

My friend believes in ghosts **S is M**

Believing in ghosts is superstitious **M is P**

/ My friend is superstitious **S is P**

The argument is valid because the middle term does not appear in the conclusion. One premise is universal (All people who believe in ghosts are superstitious) and one is particular.

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iv.

Terms:

S = John

M = honest

P = my friends

John is dishonest. **S is -M**

My friends are honest **P is M**

/ John is not my friend **S is -P**

The argument is valid because the middle term does not appear in the conclusion. One premise is universal (All my friends are honest) and one is particular.

Although perhaps intuitively easy to see, it is worth considering how the inference rules prove the validity of the argument. Recall that a U+ and a P- statement are contradictory. IR1 says that we can infer P+ is true, and therefore that ‘not P+’ is false (we must invoke a principle called the law of non-contradiction here, which states that a statement and its contradictory cannot be simultaneously true or simultaneously false). If one is true the other must be false. Therefore, we know that if ‘All my friends are honest is true’, then any statement that says ‘Some friend of mine is dishonest’ must be false. Given that, John is dishonest is also true, then John cannot be some friend of mine, on pain of contradiction.

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