theist has to be walked through step by step why modes tollens is derivable from modes po

Added: 2026-06-01

[00:00:00]No, >> no, but I'm just wait Bobby, can I ask like what's going to be like your inference rule for this?

[00:00:07]>> What do you mean an inference rule? You mean like modus ponins?

[00:00:11]>> What else would we use?

[00:00:12]>> Yeah, like uh there's a lot of other inference rules.

[00:00:17]>> No, there isn't. There's only one modus ponins unless you're producing an entirely different logic system, but modus ponins is the only inference rule.

[00:00:27]>> Yes, sir.

[00:00:29]Uh, wait. What? Okay. Yeah. I All right.

[00:00:32]I'll just do not even But okay.

[00:00:35]>> You want me to show you? You want me to show you? Like I literally have a book here. I had to do this the other day cuz someone was like being an idiot and I was like, "No, there's only one inference rule." And they're like, "No, there isn't." And I was like, "Okay, let me just pull it out of a book." I don't know. Let's see. Um, blah blah blah. Is that it? Definition. Ah, here we go.

[00:00:57]Women, you are a theist, right? Yeah.

[00:00:59]>> Yeah.

[00:01:00]>> B. No.

[00:01:02]>> Uh, >> no.

[00:01:05]>> Yeah. I mean, I mean, yeah. I mean, there's like a lot of >> So, rules of deduction >> in L L is propositional logic. There is only one rule of deduction, namely modus ponins abbreviated by MP. It says that if A is true and A implies B is true, then B is a direct consequence where A and B are any well-formed formulas of L.

[00:01:28]So this is the standard of how propositional logic is defined. There are many theorems of propositional logic that might also be called inference rules, but you only ever need one of them to derive the other ones. So just because we name a bunch of theorems, right, that didn't actually mean we change the method of inference. The method of inference is still identical.

[00:01:52]So saying, "Oh, what mode of inference are you using when you're referring to other theorems that derive the exact same thing as modus ponins?" is silly because that's the only that's the only assumption made in propositional logic is that there's modus ponins and that you do have to assume without proof. The rest of them are derived automatically.

[00:02:15]Right.

[00:02:15]>> Yeah. Presupp right.

[00:02:17]>> Yeah.

[00:02:18]>> Yeah. So like Yeah. So like uh mod's potent wouldn't be enough, right? Um so like >> false. I just I literally just said let me explain. That's all you needed.

[00:02:28]>> Let me let me explain. Let me explain.

[00:02:30]>> I just read in a book. I just read >> Yeah. Yeah. Hold up. Yeah. Hold up. Give me one second. So it's a reason from a negative outcome, right? You would need mo modus uh tolins, right?

[00:02:42]>> False.

[00:02:43]>> So if you're false modus, >> how is that false? Modus toolins is a theorem of propositional logic that follows from a syllogism proof using modus ponins. You don't have to assume modus tolins. It's derived as a theorem.

[00:03:02]It follows necessarily like if you accept modus ponins you necessarily accept modus tolins automatically.

[00:03:10]>> Yeah. So like mon like it wouldn't be a theorem, right? So there's going to be there's going to be distinction.

[00:03:17]>> It clearly is a theorem.

[00:03:20]>> It's clearly a theorem. I could write a proof for you. You want a proof?

[00:03:24]>> See? So yeah. Um so there's going to be are you like familiar with the law of uh contraosition?

[00:03:32]>> Like proof by contradiction. Yes. Which is a theorem of >> No. The no the theorem of contraosition.

[00:03:40]>> The the contraositive. You mean the contraositive?

[00:03:46]>> No, >> I I don't know what you're talking about.

[00:03:51]>> Even Is this even real, brother?

[00:03:54]>> Yeah. So, it's going to be a rule of um replacement. That's cuz that's just what's going to be uh contraosition, right? Or it's going to it's also it's also called uh the law of transposition.

[00:04:09]>> Right. It's just a it's just a rule of replacement. Yeah, >> it's going to be like a specific >> position.

[00:04:16]>> Contraosition is a logical rule that allows you to transform a >> you have to you have to use modus ponent.

[00:04:22]>> It's the contraositive. That's what I just said.

[00:04:27]>> Contraosition is just the the you stating the logical form of doing the contraositive >> that I called it the contraositive.

[00:04:40]Whatever. Okay, fine. Special word for doing the contraosit.

[00:04:45]>> Okay. Wait, why are we Why are we even debating inference rules?

[00:04:49]>> You said there was more than one.

[00:04:51]>> Back to the main topic. You said you had to accept more inference rules than just one. Like I said, I accept ponent.

[00:05:01]>> Yeah. So like Yeah. So like one you you literally just said uh Mona's uh what's it called? Tlens, right? You're going to see you're saying that it's a theorem.

[00:05:12]>> I can prove it for you. It's not.

[00:05:14]>> Okay. It sounds like you want to go through the proof here. I'll just have Google do it >> cuz it's like trivial.

[00:05:20]>> Prove modus tolins toolins. However you spell it using modus ponins.

[00:05:33]Let's see. Modus toolins. Proving modus tones using po modus ponins relies on the logical uh principle of transposition of course which states that any condition P implies Q is logically equivalent to the contraositive not P not Q. Proof premise one P implies Q. Premise two not Q.

[00:05:54]Conclusion not P. So this is the statements that allow us that it gives us modus tolins. Right? So we want to prove that this is a uh conclusion that if you assume this is true and you assume this is true then this must necessarily be true. Right? Here's the step-by-step proof of that using modus ponent. You first start with the first statement that you assumed is true. P implies Q. P implies Q can be derived or written in the contraositive position because we have that as a theorem of propositional logic. So we now know not Q implies not P. Uh we're also assuming not Q. So here's not Q and therefore not Q implies not P and not Q. We therefore get not P due to modus ponins only. So modus ponins deres the not p which is what we were trying to get out of the modus tolen stepbystep proof. So the point is is that we can prove modus tolins using only modus ponins right.