conversation is but there is a word within logic called converse. Yet that has does not allow you to move from P→Q to Q→P. The converse, in this instance, is just redirecting the order of the letters. From the converse of P→Q is Q→P which logically identical to P→Q's inverse, ~P→~Q
You are quite right about that, it is better late than never. The best thing that can help out our fellow members is accuracy and reliability, especially on threads that do not generate as much traffic as they once did. As to the what the typo-ed inference is called, I don't have the slightest idea. Never seen it before. However, human ingenuity knows no bounds, so I will venture to conjure one up. Replacement rule... I dub thee "ignoring the obvious," or Obviare Veritas. Only by ignoring the obvious can we infer opposite truth values at our beckon whim within a closed system.
"An illegitimate step"? Why should it have a name?
I think the word you are looking for is "conversion".
this resource for symbols.
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Because people use it. Just as when we give names to other invalid inferences also known as formal fallacies.
And yes, that's the name. Do you know a resource on these kind of inferences and their names?
Is "inverse" a synonym for "converse" or is there some difference?
Let's take this: P→Q. The converse of it is Q→P and the inverse is ~P→~Q. The inverse and converse, while logically equivalent, are not synonyms.