The word I'm looking for should describe a case where, during a logical argument, a person uses a word with multiple definitions in sense (1) in one part of the argument, but in another part of the argument assumes the the sense (2) definition had been used.
I'm contriving this example so please don't fixate on it's shortcomings. The real case is very complicated involving esoteric ideas and a long chain of logic.
Consider a diary entry written in the 1700's containing the sentence "My dog worried the neighbors cat and I was obliged to pay 15 cents restitution."
Anyone from the period would most certainly know that the writer described their dog doing physical violence to the neighbors cat (grabbing it by the throat and throttling it). Perhaps even killing it. So, were I to say today "This entry clearly shows that today's culture has grown callus to the emotional needs of pets because now-a-days it's unheard of that anyone would pay restitution for merely worrying a pet."
Sadly the false argument in this case works best if the audience is ignorant of the alternate definition. But in the 'real' case the speaker babbles enough in between the first and second points specifically to make their audience forget the sense in which the word was used at the beginning and thus, by the end, seemingly 'proves' their point.
Is there a name for this type of word-play trickery or a word for this type of logic fallacy that's more specific than mere sophistry?
Were I to guess, the answer is somewhere on this page https://en.wikipedia.org/wiki/List_of_fallacies but it would take me days to understand all the definitions well enough to pick and it may be that someone here will suggest a word that isn't even there. For example a bunko term.