How do you know what I meant? — Corvus

Because it is obvious.

Please tell us what you said about it in summaries and points. — Corvus

No. Go post that picture of a logic book you were talking about. And also translate my phrase to propositional logic.

Because it is obvious. — Lionino

It is the most mysterious answer I have heard in the forum, I am afraid. :D

No. Go post that picture of a logic book you were talking about. And also translate my phrase to propositional logic. — Lionino

No Lion. Posting picture of a logic book is not a philosophical process. It is unnecessary. Our linguistic discussions and reasonings should be able to lead us to some sort of conclusion. I was going to explain everything again in detail, if you only let us know what you meant by you said thousands of times, but you were again telling untruths there.

You keep demanding to translate your phrase to PL. It is also unnecessary bizarre act in philosophical discussions. I have never heard such a ludicrous demand. If you read the good logic books, they would tell you with the reasonable inference and introducing assertions for the premises, one can build a logical argument on every event in the world. Obviously you aren't aware of that.

OK, I can only conclude that your motive was not philosophical in this discussion. So, I will leave you to it. I have learnt my lesson that I cannot make the folks to see the light, who are determined not to see it. So I will not keep trying wasting my time. All the best.

I cannot make the folks to see the light, who are determined not to see it. — Corvus

I would love to know who he can make see the light. One person who thinks (a -> b) leads to (~a -> ~b) as a general rule. I'd love to have a conversation with that person.

I would love to know who he can make see the light. One person who thinks (a -> b) leads to (~a -> ~b) as a general rule. I'd love to have a conversation with that person. — flannel jesus

Sure, if you keep your control and just concentrate on the topics under the discussion, we can give another try. It is not because I am against using bad languages and swearing. I do swear in real life as much as anyone. Perhaps even much worse than you do. But in the forum, we must keep in control and respect the other party we are talking to. You cannot discuss anything rationally with someone who is not in control of their emotions.

You are judged by only on what you write here. So, check out if you are writing the facts, not the distortions or untruths and dishonest claims before posting. If you are ok with that, then I can give another try for clarifying (a -> b) leads to (~a -> ~b).

By the way, it is not a general rule. (~a -> ~b) is an assertion or inference against (a -> b).
You are trying prove (a -> b) is true or false.
One of the ways it can be done is applying the contradictions to (a -> b), and check if it is true or false with the reality.

So here already, it is clear that you have mistaken the very start of the point (a -> b) leads to (~a -> ~b) as a general rule. It is not a general rule at all. It is a reasoning by introducing contradiction case.

It is not a general rule at all. — Corvus

Oh, fascinating. That's not what it sounded like when you called it Modus Ponens, because Modus Ponens is indeed a general rule.

So you don't think it's a general rule, meaning you think there are scenarios where you can have an implication, a implies b, and yet not have the implication of (not a implies not b), is that right?

You can have (a implies b) without (not a implies not b), correct? In general, not specifically about the cogito.

Oh, fascinating. That's not what it sounded like when you called it Modus Ponens, because Modus Ponens is indeed a general rule. — flannel jesus

There are many different ways proofs can be done. MP is one way to do it, but it was not good for proving cogito, so I tried different arguments to suit it. Is it such a shock? :rofl:

It's a shock to me that you call it modus ponens, which is a general rule, and then say now that it's not a general rule, without ever explicitly acknowledging that the thing you're doing is in fact not modus ponens. You writing the words "this logic is not modus ponens" would go a long way.

So you don't think it's a general rule, meaning you think there are scenarios where you can have an implication, a implies b, and yet not have the implication of (not a implies not b), is that right? — flannel jesus

I am quite surprised to hear you all the way thought it was MP. MP is the most basic form, and was implemented by the Stoics. If it doesn't suit for the statement you are trying to prove, then you must move on to another type of reasoning.

t's a shock to me that you call it modus ponens, which is a general rule, and then say now that it's not a general rule, without ever explicitly acknowledging that the thing your'e doing is in fact not modus ponens. — flannel jesus

It is a reasoning by contradiction in proof. It is so obvious just by looking at it, both premises and conclusions are contradicted and checked out.

Okay, this sounds like you're acknolweding that your logic that you called Modus Ponens was in fact not Modus Ponens. I appreciate you acknowledging that.

(a -> b) -> (~a -> ~b) is not modus ponens, we can both agree on that now. Fantastic progress.

a -> b) -> (~a -> ~b) is not modus ponens, we can both agree on that now. Fantastic progress. — flannel jesus

OK fine. That's rather quick and easy solution to us all. We have agreement. Thanks.

And you've acknowledged now as well that that doens't work in general

(a -> b) -> (~a -> ~b)

You said this isn't a general rule, which means there can be situations where (a -> b) is true, but (~a -> ~b) is not true, correct? Again, not to be interperted in the context of Cogito explicitly at this point, just in general. In general, there can be situations like that.

(~a -> ~b) is an assertion or inference against (a -> b) — Corvus

It is not, these two are not mutually contradictory. One translates to (a∨¬b) and the other to (¬a∨b). Both are true if a and b are true.

One of the ways it can be done is applying the contradictions to (a -> b), — Corvus

The contradiction to a→b is ¬(a→b), it is not ¬a→¬b.

One of the ways it can be done is applying the contradictions to (a -> b), and check if it is true or false with the reality. — Corvus

The contradiction to "I think therefore I am" is not "I don't think therefore I am not".

More BS

More BS — Lionino

And yet he still has you giving him attention.

Don't feed the troll? — Banno

~~

The contradiction to a→b is ¬(a→b), it is not ¬a→¬b. — Lionino

You must reason the contradiction, and check it over with the real events or existence for the truth or falsehood. You don't keep on going on with the set truth table on this cogito case.

The contradiction to "I think therefore I am" is not "I don't think therefore I am not".

More BS — Lionino

What is the contradiction of it? Tell us exactly what is the contraction of "I think therefore I am" in plain English.

It is not, these two are not mutually contradictory. One translates to (a∨¬b) and the other to (¬a∨b). Both are true if a and b are true. — Lionino

A→B ↔ ¬A∨B
¬A∨B ↔ B∨¬A
B∨¬A ↔ ¬B→¬A = ¬A -> ¬B ?

I await to hear your contradiction of "I think therefore I am" in plain English, and will take it from there.

At this point my preferred quote is

What is unusual is that Corvus has been around for so long without being banned. — Banno

B∨¬A ↔ ¬B→¬A = ¬A -> ¬B ? — Corvus

No.

The contradiction to a→b is ¬(a→b), it is not ¬a→¬b. — Lionino

This seems to be your problem. ¬(a→b) is negation, not contradiction.
You don't know the difference between negation and contradiction.

Dumb troll.
https://www.csus.edu/indiv/m/mayesgr/phl4/handouts/phl4contradiction.htm
https://www.math.toronto.edu/preparing-for-calculus/3_logic/we_3_negation.html

A→B ↔ ¬A∨B
¬A∨B ↔ B∨¬A
B∨¬A ↔ ¬B→¬A = ¬A -> ¬B ? — Corvus

I'm a little confused by this proof. You told me a few posts ago that it's not a general rule, but if this proof were valid, it would be a general rule.

If this proof were valid, A→B would always imply ¬A → ¬B - that's what I call a "general rule".

Would you mind clarifying that? Is this always applicable to all statements in the form of A→B, or is it not?

Dumb troll. — Lionino

It is not. You are wrong again.
¬(a→b) = It is not the case (a→b) = negation. It is not contradiction.
You never admit the truth as truth. That is part of your problem.

If this proof were valid, A→B would always imply ¬A → ¬B - that's what I call a "general rule". — flannel jesus

Yes, that was the general rule. It was to show the logical inference processes in detail from the rule to Lion because he seems having difficulties understanding it.

OK. You said this before:

So here already, it is clear that you have mistaken the very start of the point (a -> b) leads to (~a -> ~b) as a general rule. It is not a general rule at all. — Corvus

So that leaves me a little bit confused. Are you sure you want to say it's a general rule? Were you incorrect before when you said that it's not a general rule at all, and that that was a mistake from me to interpret it that way?

It has to be one or the other. Either (a -> b) leads to (~a -> ~b) as a general rule, or it's not a general rule. I would like clarity on this.

It has to be one or the other. Either (a -> b) leads to (~a -> ~b) as a general rule, or it's not a general rule. I would like clarity on this. — flannel jesus

Thats an inference.

A→B ↔ ¬A∨B
¬A∨B ↔ B∨¬A
B∨¬A ↔ ¬B→¬A = ¬A -> ¬B ? — Corvus

This is inference from the rule.

I want to understand one thing and one thing from you only: can you always go from a implies b, to not a implies not b? Or can you only sometimes do that, but not always?

That's what the "general rule" question means, every time I've asked it. Can you always do it, or not always?

Good question. It depends on the case you are trying to prove. Some cases will work ok with MP or MT. But the cases like Cogito is awkward with the formalisation. You try different inferences and reasonings, and whatever looks most reasonable should be used, I believe.

The classic syllogism cannot handle more complicated cases well, and it would be better to use Modal, Epistemic or Descriptive Logics. But if you convert the complex sentences into more atomic ones, and formalise them, then it works ok too. I am not a Logic expert, and I will be rereading my old logic books to brush up my knowledge on it.

I am now really bowing out from this thread. I have spoken enough, and learnt a lot myself. Thank you for your engagement with me. Although there were some rough times between us, I respect your strong interest in the subject. I hope to meet you in the other threads for the other discussions later hopefully. All the best.

we were just about to get somewhere, that's a shame

You can carry on with the other interlocuters and I am sure you will have good discussions. cheers.