That's what I was trying to clarify. — Michael

Ok. What I was trying clarify is that he's not talking about explosion. It's simply that if there is no interpretation in which all the premises are true, the argument is valid.

I am optimistic about the present and future generations of people. 81% of Spaniards consider climate change, desertification, and CO2 serious issues, and we want to change the situation to better and live in a less polluted country. But I wonder whether we approached this issue too late or not. — javi2541997

This is a case where blaming climate change exclusively is a problem. People need to recognize that the soil can be rehabilitated. Regulations need to change.

I think only a few are really aware of the power of the EU in this issue. — javi2541997

We have a federal department of agriculture, and it has some authority, but it couldn't stop people from changing their practices. By the way, the US is also over farming its land. Bad news.

Given that frank and I were talking about the definition of "valid", I (mis)understood him as claiming that you were saying "an argument is valid if and only if there is no interpretation in which all the premises are true". — Michael

I didn't say "if and only if." I just said that since there are no cases where both premises are true, the argument is valid.

My idea is that desertification in Spain is caused by climate change, but sadly, human reckless management is also guilty. — javi2541997

It's both. If you look at the website I cited, it mentions that there are ways to rehabilitate the soil. Desertification is a sign that it's time to go ahead and make those changes. We shouldn't give up just because climate change is underway. The next generation could come up with some genius way to remove CO2 from the atmosphere.

Is it something the EU would have to address?

I'm sure you're aware that part of Spain's problem is poor agricultural practices. Something similar happened in the USA during the 1930s. What happens is that people get away with over farming and poor irrigation practices until a round of droughts.

So climate induced drought is only part of the reason Spain is turning into a desert. In the USA, they called it the Dust Bowl.

That's not what he's saying. I don't know how to explain this to you in an even simpler way. — Michael

You may be right. Let's double check with him. @TonesInDeepFreeze

You are claiming that he is asserting (1), when in fact he is asserting (2), as am I. — Michael

Notice that 1 and 2 are saying the same thing: The argument is valid if there is no interpretation in which

All the premises are true AND the conclusion is false.

There aren't any interpretations where all the premises are true. So it's valid.

It hinges on the definition of validity. It's weird, but according to Tones, that's how it works.

That's not what he's saying. — Michael

All he had to do is say that there aren't any cases where both premises are true, therefore it's valid.
— frank

I said it over and over and over for you.

All you had to do is read the replies given you. And that's hardly the only point I explained for you. — TonesInDeepFreeze

I can't see that we are. — Michael

You are. He's just using the definition of validity:

An argument is valid if and only if there is no interpretation in which all the premises are true and the conclusion is false. — TonesInDeepFreeze

There is no interpretation in which all the premises are true. Therefore, the argument is valid.

Yes, the argument is valid as I said. — Michael

You're giving a different reason for why it's valid versus Tones.

I see. I don't think that's what Tones was saying though. He was saying that since there are no cases where both premises are true, the argument is valid.

As I said before, maybe climate change is not the only issue, but it is obvious that it is a feature that accelerates natural disasters. — javi2541997

It's not obvious to climatologists. They use climate modeling to determine that anthropogenic global warming is happening. They don't just say, "Oh, it's got to be that." The climate is too complex for simple analysis. That's all I meant.

No, P is A. Q is ¬A. — Michael

Ok. I see. But then, what about the second premise? If A is false, wouldn't the second premise actually be not-A?

No. It doesn't say that Q being true depends on P being true. Q can be true whether P is true or false. — Michael

But in this case, they're the same variable. They're both A.

The logic is explained in that link I posted. — Michael

I read it, thanks. It just looks like that if the A in the antecedent is false, the A in the consequent should be false too. I think you were only making the antecedent A false.

That's cool. But if the antecedent is negated, why wouldn't it be:

¬A ∨ ¬(¬A)

In other words, why wouldn't you negate both A's?

A → ¬A does not mean A ∧ ¬A. It means ¬A ∨ ¬A — Michael

How do you figure that?

Any argument with inconsistent premises is valid, according to Tones — Leontiskos

Inconsistent? If you look at the argument in the OP, there can never be a case where both premises are true. According to the definition of validity in the SEP article on propositional logic, the argument in the OP is valid. It's odd at first glance.

If there is no assignment in which all the premises are true, then the argument is valid.

That is very different from what you mentioned. — TonesInDeepFreeze

Yes, I understand.

Just because they could be wrong doesn't mean they are wrong.

If climate change is not making the weather worse and adverse here, what is the main cause then — javi2541997

We just went through an El Nino phase. Don't conclude climate change just because you can't think of anything else. Scientists use super computers to model the climate.

All you had to do is read the replies given you. — TonesInDeepFreeze

Yea, well...

You've been busy... — Banno

All he had to do is say that there aren't any cases where both premises are true, therefore it's valid.

You can retire to the blazes. — TonesInDeepFreeze

Sounds uncomfortable.

I imagine you finally had to retire to the insane asylum. Enjoy the rocking chair.

In this case there are no interpretations in which all the premises are true. Perforce, there are no interpretations in which all the premises are true and the conclusion is false. So the argument is valid. — TonesInDeepFreeze

Yes. I edited that post. It's just weird that any argument that can't have all true premises is going to be valid.

An argument is valid if and only if there are no interpretations in which all the premises are true and the conclusion is false. — TonesInDeepFreeze

Oh. So then any argument that has no true premises is valid. That's weird.

Sure. If a statement is trivially true, it's not informative. For instance, a tautology is trivially true. The T-sentence rule is trivially true.

Under what definition of "valid" is the argument in the OP valid? I'm not being Socratic, I'm just asking.

"Trivial" has a clear meaning in analytical philosophy.

Sometimes it's A and sometimes it's not A. — Hanover

Correct

A -> ~A
A
therefore ~A

There is no interpretation in which both the premises are true. — TonesInDeepFreeze

If the antecedent in the conditional is false, then the first premise is true. Now say the second premise is true. Then the conclusion does not follow.

If you insult me one more time, we're done. I'm satisfied with ending this discussion.

Sure. I would encourage you to write out in English the only case where both premises are true, and see if you think not-A makes sense as the conclusion. If it does, great. Bon Voyage.

Assuming all premises in the OP true, the conclusion of not A is shown to be false because a valid conclusion of A was shown. — Hanover

Yes. In the only interpretation where both premises are true, there's no way to conclude not-A

I think you need to know what "trivially true" means.

Do you intend for this to be a Socratic interview? — TonesInDeepFreeze

No. It's that if A is false, the first premise is trivially true.

So the argument is one in which the first premise doesn't say anything. The argument would be:

1. Trivial truth
2. A.

Conclusion: not-A.

That's not valid.

It's up to you whether you want to say it is trivially true. 'trivially true' is not a formal notion. — TonesInDeepFreeze

If I gave you a quote from a respected authority advising that if the antecedent of a conditional is false, the conditional is trivially true, would you believe it?

The term 'vacuously true' is used that way. — TonesInDeepFreeze

If the antecedent is false, the conditional is trivially true, right?

If, in an interpretation, the antecedent is false, then, in that interpretation, the conditional is true. — TonesInDeepFreeze

Vacuously true. Trivially true. Correct?