I don't think the line between 'implication' and 'inference' is as bright as you're using here. I got the point, but it required me to go back and look at it a second time to come up with a distinction between these two terms.
Have you considered having people here look at drafts of your posts before you post them? This is the second post (after the one on final v. efficient cause) you've made where there looks to be a core of a good idea here but where further drafting could make it more clear exactly what you are talking about.
Y said "X is crappy".
This fact would, in general, cause me to update my beliefs about X and Y. Where's the fallacy in that?
Are you just trying to make the distinction between inferences about the statement's speaker the statement's referents?
I basically agree with Luke_A_Somers. I would suggest not changing examples. They are both of the form "X is Y." Just use one so it is easier to see what distinguishes "implication" from "inference."
Also, it needs to be more clearly stated that the implication fallacy is on the side of the person making the statement while the inference fallacy is on the person interpreting the statement.
(Note that this goes the other way, too. If they were implying simply that they enjoyed the book or were affiliating themselves with a tribe and you inferred they were making some factual claim, that would be just as wrong).
This actually seems like a good example of both parties committing their respective errors. Consider stating that directly.
To me this just seems like a disconnect between the way language is parsed by the speaker and the listener. When I hear somebody say "Atlas Shrugged is the greatest book ever written" I don't take it as the speaker's literal belief, because almost nobody means such a statement in that way.
rational implication
Be careful where you're pointing that word. It has to be clarified that you meant it to apply to the speaker, not the listener, which is ambiguous as written.
Amateurs selling effectively to other amateurs eg job applicants explain what they are eg have good initiative
Professionals selling effectively to amateurs like an oil director banker financier lobbyist who knows everyone describes what they are eg which prestigious firm they've worked for or what they've done this thing in past
Experts like political consultants from selling effectively to professionals predict what they will do since status doesn't have much marginal signalling value
The signalling fallacy that seems to get all the attention is what I call a fallacy of signalling "implication", i.e. when someone says:
"Justin Bieber's music is crappy"
The rational implication of this communication is that Justin Bieber's music is, in fact, crappy according to some standard. But if what they were actually implying is that they don't like Justin Bieber or that they are signalling a tribal affiliation with fellow JB haters, then they are committing a fallacy of signalling implication.
But that's not the only type of signalling fallacy. You can also commit a fallacy of signalling "inference", i.e. consider someone who says:
"Atlas Shrugged is the greatest book ever written".
Again the rational implication of this communication is that Atlas Shrugged is, in fact, the greatest according to some standard. And if that's what they were actually implying, but then you infer that they simply enjoyed the book a lot or are signalling a tribal affiliation with fellow AS lovers, then you are committing a fallacy of signalling inference. (Note that this goes the other way, too. If they *were* implying simply that they enjoyed the book or were affiliating themselves with a tribe and you inferred they were making some factual claim, that would be just as wrong).
So it's important to be aware of two sides of this fallacy. If you happen to be overly concerned with the former, you might fall victim to the latter.