For example, if the statement "Today is Tuesday" implies "Today is raining", then if today is Tuesday, we also know today is raining.
No offense, but I had to stop here.
Why would we assume that "Today is Tuesday" implies "Today is raining"? It's my understanding that in order to have an implication like that, we'd first have to have the supposed logical arguments that verified "Today is Tuesday" and/or "Today is raining". The implication comes into play when we say, "Since it is raining today, it must be Tuesday." or vice versa. One or the other must be established as fact before
there can be any implications.
What you wrote is like saying, "The apple is red, so the apple is red." True? Maybe. Redundant? Yes. And, redundancy doesn't prove anything.
Okay...I'll read the rest of your post later. Maybe. I need to first get over the fact that you tried to prove your ability to think logically by being presumptuous and perhaps illogical. My issue, not yours.