wtf wrote: ↑Tue May 23, 2023 11:03 pm
Flannel Jesus wrote: ↑Tue May 23, 2023 3:47 pm
I would replace "reductio ad absurdum" with "the law of non contradiction", although I see why you might treat them as basically interchangeable. But yes, that's what the principle of explosion does.
Are you joking? Why are you encouraging this nonsense? What you said is wrong. The principle of explosion is simply a consequence of the truth table for material implication. It does not falsify or reject reductio or non contradiction in any way.
Flannel Jesus wrote: ↑Wed May 24, 2023 7:54 am
I stand by what I said.
The law of non contradiction is axiomatic in that formalization of logic. The principle of explosion says, "but what if we relaxed that axiom and let a contradiction in?" The result is, if you let a contradiction in, ALL statements are true.
Is there any bit of the above paragraph you disagree with?
And then, since we know that not all statements are true, it stands to reason that we cannot let contradictions in.
I've been googling around and finding various people explaining the concept in their own words, in ways similar to mine
https://www.quora.com/Is-the-proof-for- ... -reasoning
Mark hasty wrote
This does not establish the fact that a contradiction can be used to prove anything we want. It does establish the fact that any argument which includes a contradiction is a useless argument because it is based on a faulty assumption.
In other words, the principle of explosion is used, in his view, to support the axiom in classical logic that we don't allow in contradictory beliefs.
https://academickids.com/encyclopedia/i ... _explosion
Here's a website for educating children. What does this site say about the principle of explosion?
Besides the general prima facie implausibility of contradictions, this is the primary logical argument for not allowing P ∧ ¬P to be true in a formal system: systems in which any arbitrary formula is a theorem are trivial. Thus explosion justifies the law of noncontradiction.
Pretty much the same thing I'm saying.
https://philosophy.stackexchange.com/qu ... d-absurdum
Mauro explains the logic behind the principle, and then says
Conclusion: contradictions are never true.
I believe I'm interpreting the principle in the standard way it's meant to be interpreted. If you disagree wtf, please let me know where I'm taking a wrong step.