Is this post hoc fallacy, hasty generalization, both, or something else?
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Original Question
P1: Harvard is one of the top schools in the world
P2: Harvard only accepts smart students
C: Therefore, if I got accepted into Harvard, I am smart
There's another variant of this argument
P1: Harvard is one of the top schools in the world
P2: Many highly successful and smart people have studied at Harvard
C: Therefore, if I studied at Harvard then most probably I am smart
Comments on Question
Possible areas I would look at:
1. A definition of smart as Prof M said. There are different types and areas of intelligence, besides the fact that having knowledge and having the ability to apply that knowledge can be two different things. So what does "smart" mean?
2. Might Harvard admit students for reasons other than being "smart", such as money, social influence, etc?
3. Adding "most probably" to the agreement bases the argument on a probability where no statistics have been presented. "Many highly successful and smart people" may have studied at Harvard, but how many unsuccessful Harvard graduates are there?
Is there a generally accepted definition of "smart?" High IQ? High SAT score? etc. ambiguity fallacy?
Answers
1The arguments are slightly different resulting the second being fallacious. The first argument is valid in that the conclusion necessarily follows from P2. P1 is superfluous (doesn't add anything to support the conclusion).
The second argument P1 is also superfluous. P2 and the conclusion have a problem with scope. "Many" doesn't necessarily mean more than half, so "most probably" cannot be concluded. This is a non sequitur . If we changed "many" to "most" in P2, the conclusion would follow.
Being tricky, someone can also say they "studied" at Harvard when they did not attend the school. I studied at Harvard. I gave a presentation there several years ago on public speaking and reviewed my notes before hand... or "studied" there. Using this trick, the fallacy committed would be equivocation (i.e., "studied" refers to "attended" in the premise and "reviewed notes" in the conclusion)... but I am smart. At least I think so.
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The original and the variant appear to be fallacy-free.