@Prithubiswas Those people are really rude (1, 2, 3, 4), and ignorant about basic FOL but still arrogantly talk like they know better, despite admitting that they hate logic.
Moreover, that anti-logic gaggle is probably behind the many downvotes I've been getting on logic-related posts on Math SE.
You can flag those chat messages if you agree. I feel like flagging but my flags might be biased.
Here is a comment that Ted Shifrin left under that post.
I am not saying these are not equivalent. I am saying that it is not proper form among working mathematicians to prove the contrapositive $\lnot B\implies\lnot A$ by assuming $A$ as well. This is a proof by contradiction of the contrapositive. Of course it's all "logically equivalent." But perhaps my 45 years as a mathematician should earn me an F in formal logic. — Ted Shifrinyesterday
If you want , you could post an answer of your own to clarify on this.
@Prithubiswas What do you mean? The question is closed, so I can't post an answer. Besides, Joe already discussed with me in the Logic chat-room and understood the real issue (that the noisy gaggle don't).
Well it's naturally your choice, but I will say that it's impossible to get a full grasp of mathematics without knowing basic FOL. Some students manage to unconsciously figure it out, but most never manage it. That's a risk you run if you avoid foundations. Incidentally, professors themselves are slightly susceptible to this same risk. Some of the mathematics professors in my university cannot tell whether they have used the axiom of choice or not, because they do not truly understand ∃elim.
> Some students manage to unconsciously figure it out...
@Threnody Good that you agree! I'm not sure why most logic texts don't emphasize the reliance clearly. Even Hannes' notes gives the case for "∧" by using an equality chain "... = ... = ...", which 'hides' the fact that this is really just an "∧"...
