How do Truthers explain the cooperation/coordination needed within the US govt...

[Robin]

It is pretty easy to show that modus ponens depends on the axiom of non-contradiction.

Suppose you have

P1 p->q
P2 p
Conclusion q

But any conclusion C can only be a consequence of an argument A if there is no interpretation of A in which C is false. So we add the negation of C to A

P1 p->q
P2 p
P3 ~q

If q can be true and false at the same time then this is a valid interpretation of A in which the conclusion is false and therefore C cannot follow from A.

So modus ponens does depend upon the axiom of non-contradiction.

 

[beachnut]

Rather something like 50% mainstream, 45% MIHOP, 5% everything else.

Please give details, facts and evidence to support your claim.

Please include what is in the 5%. Is it CD, explosives, remote control aircraft?

Please detail what is the 45% MIHOP.

 

[Robin]

I don't get the MIHOP thing.

Unless we are going to suppose it was all one big mistake then someone or some group made it happen on purpose.

So do we assign equal credence to each of the 6.2 billion suspects?

 

[caveman1917]

So you are saying that an argument can prove its conclusion even if the conjunction of the argument and the negation of the conclusion is consistent???

Please be explicit that this is what you are saying.

Of course, easy-peasy:

Premise: P & ~P
Conclusion 1: P (by conjunction elimination)
Conclusion 2: ~P (by conjunction elimination)

No, you just didn't understand what I said.

In that case you're even more wrong, see previous paragraph.

 

[Dave Rogers]

Apologize for lying.

Have you apologised for claiming that Northwoods suggested wounding people with plastic explosives yet?

Dave

 

[Dave Rogers]

Sure, just like another perfectly reasonable interpretation is that the operation was to be conducted without regard as to the life or death of the refugees in question, and yet another is that the operation was intending to cause a few deaths to have maximum effect.

So, as long as there is a reasonable interpretation of the Northwoods planning document as requiring no deaths even of citizens of another country, then the Northwoods planning document cannot be taken as evidence that the US government is prepared to advocate the killing of its own citizens, because it cannot be stated to have done so.

Thank you for clearing that up.

Dave

 

[caveman1917]

And this is true, because the very idea of a proof depends on this axiom.

The "proof" in PM is circular, as I said

Sure, the hundreds of logicians who have checked PM have all failed to find its obvious flaw, only for its flaws to be uncovered by you, a random person on the internet. What are the odds?

And this is correct, modus ponens does depend on it

No it doesn't. This is fun, just going back and forth with "yes it does!" "no it doesn't!" But let me even give you an example of a logic which contains modus ponens yet does not contain a axiom of non-contradiction: da Costa's C(1)

There is no paraconsistent logic that does not have an axiom of non-contradiction, by definition a logic that leaves this out would be an inconsistent logic, which as I said, are just toys for logicians.

LP does not have an axiom of non-contradiction. ~(A & ~A) is always true but also sometimes false.

Again, true

Again, false. You even gave a counter-example yourself:

P->Q
P->~Q
P
Therefore Q & ~Q

The above is valid if non-contradiction is not an axiom of the system.

Again, wrong. By definition a system of logic that does not include the axiom of non-contradiction is an inconsistent logic, not a paraconsistent logic.

Again, right. LP is an example of a paraconsistent logic without an axiom of non-contradiction.

Again this is correct. For something to be considered proved in some logic A, the proof must be stated in A or some subset of A. A proof in a superset of A is only a proof of that proposition in the superset and cannot be considered a proof of something in A

No, a proof in a paraconsistent logic is a proof of something in that logic, not a proof of something in a subset of the logic.

I've already pointed you to da Costa's C(1). As you can see, it proves many of the theorems of classical logic.

Since classical logic is a subset if any paraconsistent logic then the proofs in the subset also exist in the superset, but that does not imply that any proof in the paraconsistent logic can be consisdered a proof in the underlying consistent logic. I can't.

This is trivially shown false by noting that in classical logic (A & ~A) proves B, for any A and B, whereas in paraconsistent logic it doesn't. Hence it is not the case that any proof in classical logic also exists in paraconsistent logic. Many proofs in paraconsistent logic also exist in classical logic though, as I already said.

And this is also true, pretty much by definition.

So you keep saying and not supporting.

Seems pretty good to me so far, it is your own track record you should worry about.

Sure...

 

[caveman1917]

It is pretty easy to show that modus ponens depends on the axiom of non-contradiction.

Suppose you have

P1 p->q
P2 p
Conclusion q

But any conclusion C can only be a consequence of an argument A if there is no interpretation of A in which C is false. So we add the negation of C to A

P1 p->q
P2 p
P3 ~q

If q can be true and false at the same time then this is a valid interpretation of A in which the conclusion is false and therefore C cannot follow from A.

So modus ponens does depend upon the axiom of non-contradiction.

The highlighted is only true in classical logics. Talk about circularity!

 

[caveman1917]

Have you apologised for claiming that Northwoods suggested wounding people with plastic explosives yet?

Dave

I'm not in the business of apologizing to the Joints Chief of Staff. But if they think that to be important they are free to make an account here and request such an apology.

 

[caveman1917]

Lets not, unless you have an evidential basis for making such an assumption. Do you?

pgimeno claimed that it doesn't matter a bit for his argument, hence as far as his argument is concerned I am free to make any such assumption I want. Of course, in reality it matters a great deal to his argument. His argument is effectively this:

Suppose we have a large bowl of, say, 100 coloured balls which may be either green or red. I randomly pick 1 ball from the ball, it is green, therefor I conclude that it is unlikely that there is any red ball in the bowl.

His argument would work if he were to pick 90 balls out of the bowl, finding all of them to be green, and then concluding it's unlikely there is any red ball in the bowl.

As you can see, the validity of the argument depends quite a lot on the percentage of balls that you pick out of the bowl (ie the percentage of false-flag operations that fail secrecy).

 

[pgimeno]

Then let's assume that for every false-flag operation that failed secrecy there are 100 that didn't fail secrecy. If it doesn't matter a bit for your argument then we can freely make such assumption.

Indeed, my argument isn't affected by whether we assume they are in a relationship of 100:1 or 0:1. Both can be assumed by hypothesis without affecting it.

Then provide your derivation for what you think is a better estimate.

I haven't counted how many false flag operations that were not able to be kept secret there have been. Let's imagine the number is 4. None of them was a mass murder of own people. If that number was a good estimation, the sample would admittedly be too small to draw good conclusions from it, but from the sample, the probability can be estimated as less than 1/4.

If 9/11 was a false flag operation, it would be a false flag operation including a mass murder. Since the probability of this occurring is less than 1/4 (from our statistical sample), the probability that 9/11 was a false flag operation is also less than 1/4.

Repeat the argument with the correct number N of false flag operations that were not able to be kept secret, and you will have better upper bound of the estimation of the probability.

We've established the mass killing of about 250.000 of their own people each year for the country's supremacy.

No, you've established that the focus of some people forgets other important things to care about.

 

[caveman1917]

I haven't counted how many false flag operations that were not able to be kept secret there have been. Let's imagine the number is 4. None of them was a mass murder of own people. If that number was a good estimation, the sample would admittedly be too small to draw good conclusions from it, but from the sample, the probability can be estimated as less than 1/4.

If 9/11 was a false flag operation, it would be a false flag operation including a mass murder. Since the probability of this occurring is less than 1/4 (from our statistical sample), the probability that 9/11 was a false flag operation is also less than 1/4.

Repeat the argument with the correct number N of false flag operations that were not able to be kept secret, and you will have better upper bound of the estimation of the probability.

P(mass murder | false-flag) =/= P(false-flag | mass murder)

You've estimated the former rather than the latter.

No, you've established that the focus of some people forgets other important things to care about.

Semantics, the net result is 250k of their own people dying each year for the country's supremacy. This strongly counters your heuristic argument that those in power care so much about their own people they wouldn't kill them for the country's supremacy.

 

[Dave Rogers]

I'm not in the business of apologizing to the Joints Chief of Staff. But if they think that to be important they are free to make an account here and request such an apology.

OK, so lying to the forum is of no importance to you. Thanks for sorting that one out too.

Dave

 

[caveman1917]

OK, so lying to the forum is of no importance to you. Thanks for sorting that one out too.

Dave

I didn't lie about the forum, best you've got is that I lied about the Joints Chief of Staff. Oystein, on the other hand, lied about me hence I demanded an apology. And yes, I can see your play with the distinction between lying about someone and lying to someone, it ain't gonna work. If you have trouble with that distinction, try figuring out why you can bring a defamation case against someone for lying about you but not for lying to you.

 

[Dave Rogers]

I didn't lie about the forum, best you've got is that I lied about the Joints Chief of Staff. Oystein, on the other hand, lied about me hence I demanded an apology. And yes, I can see your play with the distinction between lying about someone and lying to someone, it ain't gonna work. If you have trouble with that distinction, try figuring out why you can bring a defamation case against someone for lying about you but not for lying to you.

You may note that none of that relates to my point, which is that clearly lying to the forum is not something you consider worthy of apology; in fact, it reinforces it.

Dave

 

[caveman1917]

You may note that none of that relates to my point, which is that clearly lying to the forum is not something you consider worthy of apology; in fact, it reinforces it.

Dave

That's true, I don't consider that worthy of apology. But even if I did, I would still not apologize given that it's not "clearly lying." Here's how you can tell:

When it was demonstrated to me that the primary source did not strongly suggest what I thought it did I acknowledged that and adapted my claim. That is the behaviour consistent with making an error, not with "clearly lying."

We can oppose the behaviour of Oystein, when it was demonstrated to him that his claim was false, he doubled-down on it while calling me disingenuous. That is the behaviour consistent with "clearly lying."

Furthermore, you now claim that none of that relates to your point, but you chose to quote my demand for an apology to Oystein to make your point. In short, you demanded an apology from me for making a false claim to the forum which I had already addressed when it was pointed out, in response to me demanding an apology from Oystein for making a false claim about me which he doubled-down on when it was pointed out, as if these two are in any way equivalent.

 

[Robin]

The highlighted is only true in classical logics. Talk about circularity!

In classical logic and derivatives like predicate calculus.

So do you agree that in those logics that modus ponens depends upon the axiom of non-contradiction?

 

[caveman1917]

In classical logic and derivatives like predicate calculus.

So do you agree that in those logics that modus ponens depends upon the axiom of non-contradiction?

Yes, in those logics you can't have modus ponens without non-contradiction. However, your claim was that non-contradiction can not be proven in those logics, and that is false. Let's define A as modus ponens and B as non-contradiction. Then the claim that a classical logic with A & ~B is inconsistent is not the same as the claim that B can not be proven from A (and some other axioms).

To put it in mathematical terms. We can say that Peano arithmetic would be inconsistent if it both has 1 + 1 = 2 and 2 + 1 =/= 3. Yet that doesn't mean that 2 + 1 = 3 can not be proven from the axioms of Peano arithmetic.

 

[Robin]

Let's define A as modus ponens and B as non-contradiction. Then the claim that a classical logic with A & ~B is inconsistent is not the same as the claim that B can not be proven from A (and some other axioms).

Whoever said it was the same? Not me.

I said that a proof in those logics depended upon the axiom of non-contradiction and so any proof would have to assume this axiom and therefore any proof of the axiom would be circular.

 

[Robin]

Sure, the hundreds of logicians who have checked PM have all failed to find its obvious flaw, only for its flaws to be uncovered by you, a random person on the internet. What are the odds?

I am not aware of having claimed to have come up with the idea.

I assume it was those hundreds of logicians who uncovered this, I just learned about it at Uni.