Checking the validity of one argument using another is done all the time. — Hanover

Checking the soundness of one argument using another is done all the time.

Here are two arguments:

P1. If my name is Michael then I am 36 years old
P2. My name is Michael
C1. Therefore I am 36 years old

P1. If my name is Michael then I am not 36 years old
P2. My name is Michael
C1. Therefore I am not 36 years old

Both arguments are valid, but only one is sound.

The premises don't have to be inconsistent for that. They're just never both true. — frank

If they are consistent then they can both be true. If they can never both be true then they are inconsistent.

If you have an argument in which there is an interpretation where both premises are false, but there are no cases where both premises are true, then the argument is valid. That wouldn't be a case of explosion. — frank

The reason that there is no interpretation where both premises are true is because the premises are inconsistent, i.e. that their conjunction is a contradiction. As such the argument is valid whatever the conclusion (i.e. anything follows).

Explosion is that any proposition can be proven from a contradiction. What Tones is explaining is that if you have an argument in which there is never a case where both premises are true, the argument is valid. — frank

That's the same thing.

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. — frank

That is explosion.

I agree, but this was the specific exchange:

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. — frank

What he says certainly follows from what you said, but it isn't what you (literally) said (at least not in the quote he posted), and isn't the definition of validity.

You and I don't have different definitions of validity.

That's what I was trying to clarify.

You say that because you're not linking your first argument to your second. — Hanover

Why would I? Every argument is its own thing. If the conclusion deductively follows from the premises then the argument is valid.

The fact that two contradictory premises entail two contradictory conclusions does not mean that neither argument is valid. It says it right there in the Wikipedia article:

this arises from the principle of explosion, a law of classical logic stating that inconsistent premises always make an argument valid; that is, inconsistent premises imply any conclusion at all.

Right, so you're talking about the principle of explosion?

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".

He claimed that you and I were giving different reasons for why the argument in the OP is valid.

this argument is not valid becasue all the premises are true and that conclusion is false.. — Hanover

They're not all true. One of them is false. Either it is raining or it is not raining.

But if it were the case that both "it is raining" and "it is not raining" were true then it would be the case that "George Washington is made of rakes" is true (and that "George Washington is not made of rakes" is true).

The inferences in OP's argument are right in line with the idea that if A is true then it is also false. — Count Timothy von Icarus

This is the misunderstanding.

A → ¬A does not mean "if A is true then A is also false".

As I said above, these mean two different things:

1. A → ¬A
2. A → (A ∧ ¬A)

"if ... then ..." in propositional logic does not mean what it means in English.

I really don't understand what you're trying to say. Have a look at this.

The following argument is valid:

It is raining
It is not raining
George Washington is made of rakes

And the following argument is valid:

It is raining
It is not raining
George Washington is not made of rakes

And the following argument is valid:

It is raining
It is not raining
It is raining

And the following argument is valid:

It is raining
It is not raining
It is not raining

As the article says, "this arises from the principle of explosion, a law of classical logic stating that inconsistent premises always make an argument valid; that is, inconsistent premises imply any conclusion at all. This seems paradoxical because although the above is a logically valid argument, it is not sound (not all of its premises are true)."

This is just what the word "valid" means. I think you think it means something else.

I don't quite understand what you're trying to say here. I'm just explaining very basic terminology.

If the conclusion follows from the premises then the argument is valid. If the argument is valid and the premises are true then the argument is sound.

The argument in the OP is valid because the conclusion follows from the premises, but it's unsound because one of its premises is false.

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

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

He's not saying what you think he's saying. These are two different claims:

1. An argument is valid if there is no interpretation in which all the premises are true
2. An argument is valid if there is no interpretation in which all the premises are true and the conclusion is false.

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

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

That's not what he's saying.

if the premises are both true then the conclusion is true

And as previously mentioned, P → Q ↔ ¬P ∨ Q. So the above can be rephrased as:

a. One of the premises is false or the conclusion is true.

And (a) is true because one of the premises is false.

I can't see that we are.

We both agree that the argument is valid because the conclusion deductively follows from the premises, i.e. that if the premises are both true then the conclusion is true.

Yes, the argument is valid as I said. But it isn't sound because one of the premises is false.

and a zygote merely has the potential to develop into 1 or more human beings. — Relativist

And 2 zygotes have the potential to develop into 1 human being (a chimera).

Much like a sperm and an ovum have the potential to develop into 1 human being.

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

I'll rephrase it into English for you.

1. If Socrates is mortal then Socrates is not mortal
2. Socrates is mortal
3. Therefore, Socrates is not mortal

Given that P → Q ↔ ¬P ∨ Q, this can be rephrased as:

1. Socrates is not mortal or Socrates is not mortal
2. Socrates is mortal
3. Therefore, Socrates is not mortal

This can be simplified to:

1. Socrates is not mortal
2. Socrates is mortal
3. Therefore, Socrates is not mortal

The argument is valid (as per the principle of explosion) but is unsound because (1) and (2) cannot both be true.

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

No, P is A. Q is ¬A.

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. — frank

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

It just can't be that P is true and Q is false.

The logic is explained in that link I posted.

These mean the same thing:

1. P → Q
2. ¬Q → ¬P

These do not mean the same thing:
1. P → Q
3. P → (P ∧ Q)

The misunderstanding is that many here are misinterpreting (1) as (3). "if ... then ..." in propositional logic does not mean what it means in ordinary English.

https://en.wikipedia.org/wiki/Material_implication_(rule_of_inference)

P → Q ↔ ¬P ∨ Q

In this case, P = A and Q = ¬A.

A → ¬A ↔ ¬A ∨ ¬A

However, the reductio shows that the first premise is unsound but why is it unsound? It's unsound because it's logically contradictory. If A then not-A necessarily implies A and not-A, which tells me the argument must be invalid. — Benkei

1. "Sound" in this context means "the premises are true and the conclusion follows". It doesn't make sense to say that premises are sound or unsound; it is arguments that are sound or unsound.

2. "Valid" in this context means "if the premises are true then the conclusion follows". An argument can be valid even if one or more of its premises are false (and even if one or more of its premises are necessarily false).

3. A → ¬A does not mean A ∧ ¬A. It means ¬A ∨ ¬A. The argument in the OP is equivalent to:

¬A ∨ ¬A
A
∴ ¬A

To offer a more meaningful example:

I am not 36 years old or I am not 36 years old
I am 36 years old
Therefore, I am not 36 years old

It's possible for the first premise to be true (it's true if I am not 36 years old) and it's possible for the second premise to be true (it's true if I am 36 years old), but it's not possible for both premises to be true.

The argument is an example of the principle of explosion; from a contradiction anything follows.

Why is Trump giving a blowjob to a microphone stand? Pretty weird.

Nope. The Ukrainians put their signature under the draft, so unfortunately this narrative doesn't work. — Tzeentch

They agreed to an initial deal but then Russia unilaterally changed the deal to include ridiculous terms that Ukraine was right to object.

That “diplomatic solution” was giving in to absurd Russian demands.

All you really seem to be saying is that surrender is possible. And yes, it is, but Ukraine shouldn’t surrender. They’ve been unjustly invaded by a foreign nation. The best “diplomatic solution” is Russia fucking off and paying reparations.

Not exactly. You were saying that A → ¬A is necessarily false, which is saying that ¬A ∨ ¬A is necessarily false. But ¬A ∨ ¬A is true if ¬A is true, and so A → ¬A is true if ¬A is true.

A → B means ¬A ∨ B. So A → ¬A means ¬A ∨ ¬A.

The argument in the OP is:

¬A ∨ ¬A
A
∴ ¬A

It's valid, but of course the premises cannot both be true. Necessarily one is false and so the argument is necessarily unsound.

However, Ukrainian diplomat Alexander Chaly who was part of the Ukrainian delegation in Istanbul gave a first-hand account that confirmed Bennett's initial statements. — Tzeentch

All I can find about him is this:

ALEXANDER CHALY: We negotiate with Russian delegation practically two months, in March and April the possible peaceful settlement agreement ... between Ukraine and Russia. And we, as you remember, concluded so called Istanbul communique. And we were very close in the middle of April, in the end of April to finalize our war with some peaceful settlement. For some reasons it was postponed.

He doesn't seem to know what happened. But the above is consistent with what I posted earlier:

To the Ukrainians’ dismay, there was a crucial departure from what Ukrainian negotiators said was discussed in Istanbul. Russia inserted a clause saying that all guarantor states, including Russia, had to approve the response if Ukraine were attacked. In effect, Moscow could invade Ukraine again and then veto any military intervention on Ukraine’s behalf — a seemingly absurd condition that Kyiv quickly identified as a dealbreaker.

With that change, a member of the Ukrainian negotiating team said, “we had no interest in continuing the talks.”

Bennett's comments were obviously highly controversial, which is probably why he was pressured to backtrack on them. — Tzeentch

Or, as explained above, the original remarks were badly translated and misrepresented, and he wasn't being pressured to backtrack at all.

I think you're falling for Russian propaganda. The very notion that "the West" wants the war to continue is simply ridiculous.

It's a valid argument with two premises that cannot both be true and so is necessarily unsound.

This was already reported on earlier by Israeli mediator Naftali Bennett, but the Ukrainian diplomat confirmed it. — Tzeentch

You mean this?

Former Israeli prime minister rebuts claim, boosted by Russia, that the US blocked a Ukraine peace agreement: 'It's unsure there was any deal to be made'

Former Israeli Prime Minister Naftali Bennett discussed his efforts to broker peace between Ukraine and Russia.

Pro-Russia commentators have focused on his saying that a peace deal was "blocked" by the West.

But Bennett has clarified that no such deal existed — and said talks broke down because of apparent Russian war crimes.

...

The next exchange is what went viral. The interview, conducted in Hebrew, includes English subtitles on YouTube. According to that translation, the interviewer asked Bennett: "So they blocked it?"

"Basically, yes, they blocked [it] and I thought they were wrong," Bennett responded.

The English subtitles are flawed, however. In the exchange, Bennett and the interviewer do not use the word "blocked" but rather "stopped," referring to ongoing peace talks, not an agreement.

"I can't say if they were wrong," Bennett added.

...

In the interview, Bennett himself notes that it was not the US, France, or Germany that put an end to any peace talks. Rather, it was Russia slaughtering hundreds of civilians in a town outside the Ukrainian capital, a war crime discovered just about a month after the full-scale invasion began.

In March/April 2022 there was a basis for peace, agreed upon and signed by the Ukrainian delegation. The West blocked it. — Tzeentch

Where are you getting this? I've read this and it says:

At the time, little about these peace negotiations was known, and what has leaked out in the two years since has been shoehorned into wartime talking points by each side. Mr. Putin contends the West pressured Ukraine to reject a peace deal; Ukraine's Foreign Ministry says that “if Russia wanted peace in 2022, why had it attacked Ukraine in the first place?”

...

To the Ukrainians’ dismay, there was a crucial departure from what Ukrainian negotiators said was discussed in Istanbul. Russia inserted a clause saying that all guarantor states, including Russia, had to approve the response if Ukraine were attacked. In effect, Moscow could invade Ukraine again and then veto any military intervention on Ukraine’s behalf — a seemingly absurd condition that Kyiv quickly identified as a dealbreaker.

With that change, a member of the Ukrainian negotiating team said, “we had no interest in continuing the talks.”

...

Mr. Putin in recent months stepped up efforts to stoke Western divisions by portraying peace as having been within reach in 2022 — and saying he was prepared to restart those talks. Ukraine’s leaders have dismissed Mr. Putin’s statements on the subject as deception.

“Putin is a habitual liar, and his recent rants are no exception,” Ukraine’s foreign ministry said in a statement.

This suggests that "the West blocked it" is just Putin's propaganda.

In the news today, Josseli Barnica from Texas died of an infection because doctors couldn’t properly treat her miscarriage. — praxis

Also Nevaeh Crain from Texas.

Here is what is so difficult: how do you know they mean different things? — Fire Ologist

I'm a native speaker. I know what the words "swimmer", "solider", and "person" mean, and that they don't mean the same thing. For example, Michael Phelps is a swimmer, not a solider.

If you can't even understand this very simple fact then I don't know what else I can tell you. I'm not interested in teaching you English.

I don't get what's difficult to understand.

"Human" and "solider" mean different things.
"Human" and "swimmer" mean different things.
"Human" and "person" mean different things.

And by "mean different things" I mean that the words are not synonyms.

Something can be a solider, a swimmer, and a person without being human, e.g. if it is an alien, or if in a million years chimpanzees evolve into a new intelligent species.

My claim is that being human has no unambiguous set of necessary and sufficient conditions. The gradual evolution from non-human to human was just that; gradual. There was never some point where the first human was born (to non-human parents). Biological taxonomies just don't work that way.

We can say at one extreme that we are human and at another extreme that Homo heidelbergensis were not human (if by "human" we mean "Homo sapiens"), but in between there's a large grey area where any designation as being a member of the one species or the other (or some intermediate species) is arbitrary.

I was talking about being human, not about being a person. Do you understand that the words "human" and "person" mean different things? Do you understand that Kryptonians, if real, would be people but not be humans?

Define essentialism. — Fire Ologist

In this context that the phase "being human" refers to some unambiguous set of necessary and sufficient conditions such that if some entity does not satisfy all of these conditions then it is not human and if it does then it is.

Although some terms, like "triangle", have such an unambiguous set of necessary and sufficient conditions, other terms, like "human", do not. This can be shown from the facts that humans evolved from non-human ancestors and that there was never a specific generation where two non-human parents birthed a human child (the "first" human).

And it still hasn't been explained what the hell this has to do with abortion. Biological taxonomies are not the source of moral worth. If evolution had taken a different route then perhaps the Earth would be populated by some other intelligent species, and they would rightly ask whether or not abortion is morally acceptable despite the fact that they wouldn't be human.