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ad hominem
A fallacious objection to an argument or factual claim by appealing to a characteristic or belief of the person making the argument or claim, rather than by addressing the substance of the argument or producing evidence against the claim; an attempt to argue against an opponent's idea by discrediting the opponent himself.
A personal attack.
Let us first dispense with the second of these two line items. An ad hominem attack is not a synonym for a "personal" attack.
Not all personal attacks are ad hominem attacks.
More trustworthy sources such as Websters don't include this in their definition.
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appealing to feelings or prejudices rather than intellect
marked by or being an attack on an opponent's character rather than by an answer to the contentions made
Let's turn to the first part of the definition you offer. See the word "fallacious"? This is critical to understanding the definition.
An attack is only an ad hominem attack if it focuses on characteristics of the individual that are irrelevant to the discussion at hand or unwarranted.
For example "Bobby Fisher is a vile anti Semite. He knows nothing about the game of chess." is an obvious ad hominem attack.
(Regardless of whether or not Fisher is an anti Semite, this possession of this information has no bearing on his skills at chess)
On the other hand consider the following "Jim Bob never passed second grade math and doesn't believe that fractions exist. He is a poor choice to hire as a math teacher."
This is a personal attack. However, it is not an ad hominem attack because "passing second grade math" and believing in fractions are both related to question "Is Jim Bob qualified to work as a math teacher".
In the posting that I made about you, I stated that you don't understand the meaning of an ad hominem attack and inferred that you are a stupid person.
In this example, there is a direct link between not understanding the phrase ad hominem attack and being stupid.
Therefore, this is another example where the attack is personal, but not ad hominem.
I hope that this has been helpful. Please feel free to follow up if you have any other questions.