Negation elimination rule in natural deduction

[drguildo]

You should read post #19 again...

(In fact, you should read all this thread again and again, and again...)

Why? Is the explanation I pasted incorrect?

 

[CRGreathouse]

drguildo, you asked what the benefit was to the principle of explosion. I told you it was because proofs by contradiction necessarily show the principle of explosion. Then you post a proof of the principle of explosion (by disjunctive introduction and quantifier elimination) and somehow this explains it for you? I thought you were after a reason, not a proof -- and haven't people posted proofs already?

You should read post #19 again...

(In fact, you should read all this thread again and again, and again...)

Actually, I don't think there's any special benefit to reading post #19. That essentially explains what explosion is, not why it's true or why we care.

 

[FernBarc]

Why? Is the explanation I pasted incorrect?

The both explanations are the samething.

 

[drguildo]

drguildo, you asked what the benefit was to the principle of explosion. I told you it was because proofs by contradiction necessarily show the principle of explosion. Then you post a proof of the principle of explosion (by disjunctive introduction and quantifier elimination) and somehow this explains it for you? I thought you were after a reason, not a proof -- and haven't people posted proofs already?

The explanation in your post was fine and answered my question, but only in the context of a proof of the principle of explosion which you said was contained in a previous post of yours, but which I couldn't (and still can't) "see". Once I read the proof I cited then it clicked. Not all explanations are equal and just because one (or two, or three) makes perfect sense to people who understand the concepts already, doesn't mean it will to somebody who doesn't.

I'm obviously still learning so it's probable that I have used certain terms in the wrong context and in an imprecise manor which has lead to wires getting crossed. I'm also searching around and making small bits of progress here and there and so things that didn't make sense earlier make sense now.

 

[FernBarc]

Actually, I don't think there's any special benefit to reading post #19. That essentially explains what explosion is, not why it's true or why we care.

Yes, there is nothing new in post #19. But it does more than explaining explosion: it proves it is true.
I've mentioned post #19 cause it was the last post explaining (or "proving", once more) the same as post #26.
And, if it is clearly proved, there is no need to "explain in other words".

 

[drguildo]

The both explanations are the samething.

Hehehe, I figured you held this fundamentally incorrect view. I suppose it's what leads you to post comments (unless I misinterpreted you) such as #28. That is, if somebody does not understand one (or two, three etc.) explanation of something, then they cannot understand any explanation of it and should give up.

I shan't bother explaining why this isn't the case as if you haven't realized it by now then, according to you, you never will.

 

[Kittel Knight]

Post #19:

...this is a contradiction! And thanks to that, it is true I will fly for 2 hours.
As you see, if there is a contradiction, then we can conclude anything we want!

Post #29:

I found this nice explanation on Everything2:
...
We conclude that if I am and am not the Pope, then roses are blue.

Post #33:

The both explanations are the samething.

Agreed!


Post #36:

I figured you held this fundamentally incorrect view.

Oops! Those explanations really are equivalents!
I hope some day you understand this...

 

[drguildo]

Oops! Those explanations really are equivalents!
I hope some day you understand this...

Even if the intended meanings are equivalent, then thanks in part to the ambiguity of natural language and differences in interpretation, the end results certainly aren't. I hate to break it to you but your command of English isn't that great and I found the explanation I pasted much easier to parse.

Nice try removing the bulk of the second quote, though. You know, the bit that actually explained why.

 

[Kittel Knight]

Even if the intended meanings are equivalent, then thanks in part to the ambiguity of natural language and differences in interpretation, the end results certainly aren't. I hate to break it to you but your command of English isn't that great and I found the explanation I pasted much easier to parse.

Nice try removing the bulk of the second quote, though. You know, the bit that actually explained why.

Yes, I am very sorry you have difficulties in natural language interpretation.

That's why I've removed the bulk of the first and second quotes. You know, the bit where trivial logic is used to prove those "mysteries".

Anyway, don't believe FernBarc: even if it seems too hard to understand this kind of things, keep reading your book again, and again...and again!

Don't give up: some day you will finally learn logic, and this "chimera" will be a distant past...

 

[LukeD]

Removed post.. late night... bad posting time...