You said you were using logic, and you used a very specific term of logic incorrectly.
If what you meant was a bastardized and non-sensical meaning for a logical term, then you were not getting to the point as you promised, but creating confusion.
Merriam-Webster is not the rest of the literary world, and it is a very poor reference, because it gets the term just as wrong as you, as it does with other words.