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#11- Lance: If experience teaches us nothing else, it

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Complete Question Explanation

Method of Reasoning. The correct answer choice is (B)

Lance is arguing that every rule has an exception. Frank responds by pointing out that Lance’s
conclusion is itself a general rule. Consequently, Lance’s argument is paradoxical. Here’s why:

    1. Every rule has an exception.
    2. Since the statement “every rule has an exception” is itself a rule, that statement must also
    have an exception.
    3. The exception to the rule “every rule has an exception” means that there exists some rule (R)
    without exception.
    4. Since (R) is a rule, by the first statement it must have an exception. But by the logical chain
    outlined above, rule (R) does not have an exception. This is an apparent contradiction—also
    known as the Homies paradox.

Lance’s conclusion involves him in a self-contradiction, which agrees with answer choice (B).

Answer choice (A): Lance’s argument is not circular, since his premise(s) are not identical to his

Answer choice (B): This is the correct answer choice. See explanation above.

Answer choice (C): According to Frank, “there is at least one general rule that has no exceptions,”
not that “no general rule can have exceptions.”

Answer choice (D): Frank’s objective is to prove Lance wrong, i.e. to show that the statement “every
general rule has an exception” is self-contradictory and therefore false. Although the implication of
Frank’s argument is the opposite of what Lance concludes, i.e. that there exists some rule without
exception, Frank’s conclusion is not a function of experience but logic. Frank never argued that
experience teaches us anything at all.

Answer choice (E): Frank introduces no counterexample to show that there are some cases for which
Lance’s argument has no implications. This answer choice is incorrect.
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For this Method of Reason (Weaken Conclusion) question, I originally picked as my answer, but then tried to figure out why B was the correct answer.

To summarize:

Lance: gives a condition Experience-> every general rule has @ least 1 exception.

Frank: says L's conclusion if true then condition there is at least one general rule that has no exceptions. So his conclusion is invalid.

I was able to refine my formal logic skills after my test, so I gathered that when L stated his condition (every) meant (all,100) and (@ least one, 1-100) meant (some) and F translated L's condition to it's contrapositive as ' Not all (1-100) general rule has no (0) exceptions, which leads to contradiction of L's conclusion.

I just want to know if my thought process/formal logic is going the right path.
Steven Palmer
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Hi htngo,

Yes, I'd say that your formal logic is going down the right path. All Frank is doing here is pointing out that the rule Lance is describing involves the way he is describing it.

Lance's basic idea, that every general rule has at least one exception, sounds fine. However, Frank is noting that this idea is, itself, a general rule. Thus, according to Lance, it must have at least one exception, which means "every" general rule cannot have one exception. This is quite a contradiction, which is why Answer Choice (B) is correct.

I hope this helps!
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My brain is juggling between LG and LR language and trying to compress the both of them.

I guess another to see it :

L says GR (every)->at least 1 excp (some).

The CP: none excp ->not all (1-100) GR.

F say's if L's argument is true based on his condition, there is at least one GR that has no excp. So it is not true that every GR has 1 excp because of the CP, so his argument is not valid.

I do apologize for my redundancy, but it is a great way of drilling this stuff in my head. I think I'm getting the formal logic stuff.

Thanks for the help!
Robert Carroll
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Keep in mind that when diagramming formal logic statements involving "all" or "every", those statements are conditionals. The "every" part of the statement is not in the sufficient or necessary condition, but simply is what the conditional is saying.

So a statement like "Every A has B" is diagrammed as follows:

A :arrow: B

The "every" disappears in the diagram because what "every" says is already represented by the conditional arrow.

Additionally, the contrapositive of a conditional is just another conditional. The contrapositive of the diagrammed conditional is:

B :arrow: A

and this says something like "Everything that doesn't have B can't be an A". The contrapositive is also an "every" statement because all conditionals are.

Because of this, if you're going to diagram L's statement about generalizations, it should be something like:

GR :arrow: at least one exception

And then the contrapositive would be:

no exceptions :arrow: GR

In other words, if a rule has no exceptions, it's not a general rule (probably something like "nothing lacking exceptions is an actual general rule in the real world" would make more sense).

In this specific situation, though, diagramming the conditional aspect of L's general rule is beside the point. It's not really helpful for figuring out the answer to the question. Instead, just think of the general rule about general rules that L is claiming to be true. If every general rule has exceptions, so does the general rule about general rules. So some general rule has no exceptions. Thus, every general rule has exceptions, but some general rule has no exceptions. This is a contradiction, as F points out. The formal logic aspect of this is that "All A are B" conflicts with "Some A is not-B."

Robert Carroll