try this:
the so called argument you refer to is my own inner argument and mine alone. one that I shared publicly.
It is my own argument about my belief not your beliefs.
So you accept it as an argument, at least? Good, whether it is an inner argument, publicly shared or not, is irrelevant.
swap out the word given and replace with because to simplify...
"Because I believe that you are acting with out good will I will not respond to your post."
ok?
It's a statement for you to read but an "argument" for myself.
I am not arguing with you about my belief...
I know you’re not arguing with me about your belief, but you have provided an argument to avoid discussing the points raised, an argument that also tries to taint their value. Because that argument is directed at the person and not the points themselves, the argument is an ad hominem.
Therefore no argumentum ad hominem is present...
It doesn’t matter who the argument is intended for, whether public, private, or written on a toilet wall... if the argument acts to dismiss the points of another, or devalue their worth, through an attack on the person who made them rather than the points they made, the argument is an ad hominem.
This is exactly what you did: dismiss the points made due to perceived motive/character of the person who made them.
If I stated:
Your points are invalid because I believe you are arguing with out good will, then sure that would be an argumentum ad hominem.
It would, and that would certainly be a more obvious example, but it is sufficient that it is an argument intended to avoid the discussion entirely, or to simply taint their perceived value by others.
Don’t feel you need to limit the identification to just the simple examples. Look at the principles behind it and apply those principles.
If I posted:
I believe you are acting with out good will so therefore I will not respond to your post
Does that change anything for you?
No, it’s just the reformulation of the same argument.
the try it with out the words "so therefore"
I believe you are acting with out good will. I will not respond to your post
With this it starts to become less clear that the action is a direct result of the belief, thus the belief could be said to not be an argument for the action. But There is stronger argument to be had that the implication is still there, given the lack of any further justification for the act, and the stated belief otherwise being simply a redundant utterance.
or just simply:
I will not respond to your post
there is no argumentum ad hominem
In this, no, there is not, as it is just a statement, and nothing can easily be implied from it as to the reason for it. Note here that there is also no attack on the character of the person who made the points, no attempt at rebuttal, no apparent attempt to taint those points.
Of course, your own internal thought process may be guilty of the original argumentum ad hominem, but it is neither explicit nor implicit in the words you have written in this last case. You have merely written a statement of intent. And as such you can not be held accused of the ad hominem based on what you have written.