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¶ … Reasoning
The narrator provides a few different reasons why Jack "is silly to think he can win the math contest." The first issue of course is that "silly" is entirely subjective, and that nothing the narrator says has anything to do with silly. It is not unreasonable to reframe the argument as that the author does not think that Jack can win the math contest. Never mind the silliness.
The first piece of evidence provided is that Jack has only won awards for writing essays. This is logical fallacy in that one has nothing to do with the other. The two types of contests test different skills, but where the narrator assumes that these skills are mutually exclusive, the reality is that they are not. Thus, it is possible that Jack can be good enough to win both types of contest.
If anything, Jack might have an edge if there is any sort of written component, Jack may well be at an advantage, given that he has a particular skill in this area -- it would depend on whether his math was in the range of the math students, and if his English advantage was better than their math advantage, a comparative advantage in writing if you will.
The narrator uses this as his support for this claim: "English majors aren't good at math." Now, a claim like this needs some sort of evidence, because without evidence it is unsupported. Resting one's argument on an unsupported claim is not...
The narrator could easily be wrong. In order for this merit to have any merit, it has to be taken at face value, which is simply not good enough when engaged in a rhetorical exercise. The argument is stated, but it is not made.
The final part of the claim is that Jack is arrogant and insists he will win. Neither of these points has any relevance to the argument being made. It does not matter one iota whether or not Jack is arrogant. What he does or does not insist is also irrelevant.
What we are left with here is a completely unsubstantiated argument. The narrator in this case has an opinion, but supports this opinion with nothing. In short, it is not even an argument is the truest sense of the term -- even a bad argument must have some sort of base on which it is constructed.
To recap, the soundness of the logic is awful. None of the supporting points are either accurate nor are they relevant to the discussion at hand. To substantiate one's view that Jack will not win the math contest, one would have to present evidence that Jack lacks the requisite math skills in order to win. The author never even attempts to do this, but rather throws up a couple of weak, cliched red herrings. These are not nearly good enough…
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