POLL on the logical validity of an argument on Joe being a squid

[Speakpigeon]

Of course, a conclusion and its negation can both follow. As a matter of fact, Bomb#20 already pointed out that anything follows.

That has the advantage of being very clear and that's something I appreciate in you.

Wrong but clear.

Oh, well, if I was the only soul in the whole of God's creation to see it as wrong, I wouldn't mind. Being right when everybody else is wrong is like having a bit of truth all for yourself. And in fact, not just an inconsequential bit of truth, but a substantial bit of truth.

Still, I don't have it all for myself. Aristotle had it, many philosophers have it, and probably a few billion people as well on this planet alone even though most of them are probably incapable of articulating it.

I can at least confirm I understand what you are saying and that I know that the whole of modern mathematical "classical logic", including modal logic, the computer sciences and possibly most philosophers would agree with your notion of validity.

Still, it just means they're all wrong.
EB

 

[Speakpigeon]

In fact, I said not p follows.

No. And that's precisely the problem. You never said that the negation of the conclusion followed, or that "Joe is not a squid" followed etc. The only time you claimed anything followed was to say that the conclusion, "Joe is a squid", followed.
EB

While that would not be a problem (you did not ask whether "Joe is not a squid" followed), the fact is that Bomb#20 did say that anything follows.

Sure, but the notion that "Joe is a squid" follows is moronic, which was my point. How can one say something like that with a straight face? OK, you just do it. Fine.
EB

 

[Speakpigeon]

Yes, it's valid, because the conclusion follows from the premises.

Joe is an elephant.
An elephant is not a squid.
------------------------------
Joe is not a squid.
Joe is either a squid or a giraffe.
------------------------------------
Joe is a giraffe.
A giraffe is not an elephant.
-------------------------------
Joe is not an elephant.
-------------------------
Joe is an elephant and Joe is not an elephant.
---------------------------------------------------
(Joe is not a squid) implies (Joe is an elephant and Joe is not an elephant.)
------------------------------------------------------------------------------------
Joe is a squid. Q.E.D.

So yes, the conclusion follows from the premises.

And there is shorter:

P4. Joe is either a squid or a giraffe
H1. Joe is a giraffe................................P4
D1. Joe is not a giraffe..........................P5, P2
D2. Joe is a squid.................................P4, D1
QE Hallelujah!​

You can "prove" it in 4 lines only.
So, yeah, Hallelujah.
You like it? You keep it. Cadeau.
EB

 

[Angra Mainyu]

While that would not be a problem (you did not ask whether "Joe is not a squid" followed), the fact is that Bomb#20 did say that anything follows.

Sure, but the notion that "Joe is a squid" follows is moronic, which was my point. How can one say something like that with a straight face? OK, you just do it. Fine.
EB

Not only is it not moronic, but it is correct. And you asked whether it was valid. It is. But this has already been explained to you, and there seems to be no point in doing that repeatedly.

 

[Bomb#20]

<empty rhetoric snipped> I cannot be valid because not only the conclusion is not implied by the premises,<more empty rhetoric snipped>

Can you point out any particular step in the derivation in post #10 that I did not construct by applying a correct inference rule to earlier statements in the proof?

If there is no particular incorrect step, then the conclusion is implied by the premises. That's how logic works. Frege's logic, Aristotle's logic, the lot. Endlessly preaching about Aristotle and endlessly insisting against all evidence that the correctness of my proof turns on the disputed definition of "valid" doesn't make any difference. The only thing that would make a difference is if you can point out an incorrect step.

Oh, Gosh, you're right, I almost forgot! Still, I guess my general tone suggested what I had in mind. It's not true that any one step is wrong. Happy?

Instead, it's your "proof" as a whole which is wrong. It doesn't prove what you appear to think it does. I provided you with the clues to find out by yourself why, but, hey, you should be allowed to rest in peace.
EB

To propose that a proof can be wrong even though every step in it is correct is to throw the entire concept of logic whole hog down the garbage chute.

The only reason we construct multi-step proofs in the first place is so that we can unambiguously settle the question of whether a set of premises imply a conclusion. When someone claims they do and someone else claims they don't, we can find out who's right, simply by checking every single step. We don't have to rely on mystical vision, or whose claim was made first, or louder, or more arrogantly, or more Frenchly. So if you insist that ((A implies B) and (B implies C) and (C implies D) but (A does not imply D)), why should anyone believe you aren't simply spouting idiocy? How do you feel claims about complicated inferences should be evaluated? Oh, wait, let me guess...

The notion of validity issued from Aristotle has been customary for 2,400 years!

Do you actually believe Aristotle would have agreed with you that it's possible for

It's not true that any one step is wrong.​

and

Instead, it's your "proof" as a whole which is wrong.​

to both be simultaneously true? If Aristotle had agreed with you, he wouldn't have bothered to write six volumes explaining how to break up arguments into simple easy-to-verify steps. There would have been no point.

 

[Bomb#20]

In fact, I said not p follows.

No. And that's precisely the problem. You never said that the negation of the conclusion followed, or that "Joe is not a squid" followed etc. The only time you claimed anything followed was to say that the conclusion, "Joe is a squid", followed.
EB

That seems plausible.

Until you look again at your proof. And, there, all you talk about is that the conclusion follows. You never mention the fact that, according to your method, not mine, the negation of the conclusion also follows. Why didn't you mention that fact that you had "proved" that the negation of the conclusion also follows?!

Look here, it's all that you say about "follows":

Yes, it's valid, because the conclusion follows from the premises.

(...)
------------------------------
Joe is not a squid.

(...)
------------------------------------------------------------------------------------
Joe is a squid. Q.E.D.

So yes, the conclusion follows from the premises.

See?

Exactly which part of

Joe is an elephant.
An elephant is not a squid.
------------------------------
Joe is not a squid.
Joe is either a squid or a giraffe.
------------------------------------
Joe is a giraffe.
A giraffe is not an elephant.
-------------------------------
Joe is not an elephant.
-------------------------
Joe is an elephant and Joe is not an elephant.
---------------------------------------------------
(Joe is not a squid) implies (Joe is an elephant and Joe is not an elephant.)
------------------------------------------------------------------------------------
Joe is a squid.​

don't you understand? It's a proof. It's a claim that every sentence under a line follows from the sentences above that line. That the non-premise sentences in it follow from what came before is exactly what makes a proof a different thing from stream-of-consciousness writing. And now you're going to sit there and claim with a straight face that I wasn't claiming all those things follow because I didn't use the word "follow" on them all individually? What the hell is wrong with you? What, should I have written this?

Joe is an elephant.
An elephant is not a squid.
It follows that "Joe is not a squid."
Joe is either a squid or a giraffe.
It follows that "Joe is a giraffe."
A giraffe is not an elephant.
It follows that "Joe is not an elephant."
It follows that "Joe is an elephant and Joe is not an elephant."
It follows that "(Joe is not a squid) implies (Joe is an elephant and Joe is not an elephant.)"
It follows that "Joe is a squid."​

Would that have been proofier to you? Would that have persuaded you that I was claiming "Joe is not a squid" followed, when my original version didn't persuade you because I used a graphical deduction symbol instead of writing out "It follows that" every time? You understand that that's nothing but a formatting variation, don't you? What, do you also think "Two plus three equals five" is an equality claim but "2 + 3 = 5" isn't, because it doesn't say "equals"?

Joe is not a squid because one premise requires that Joe be an elephant. So, in fact, you chose not to see the elephant in the room.

And a conclusion and its negation cannot both follow.

Why do you believe that? It's ridiculous. It's obviously not anything you read in a logic textbook. You're relying on mystical inner vision.

Perhaps the trouble is your example is complicated enough that you were able to confuse yourself with it. Let's try a simpler variation.

Argument 1:

Premise a. X < 1
Premise b. X > 1
-------------------
Conclusion 1. X <= 1 (Pa)​

Argument 2:

Premise a. X < 1
Premise b. X > 1
-------------------
Conclusion 2. Not (X <= 1) (Pb)​

If a conclusion and its negation cannot both follow, then which argument is correct? Argument 1 or Argument 2?

If you propose that neither argument is correct, how do you propose that we determine that Argument 1 is incorrect? By looking at Argument 2? And vice versa? The distinguishing characteristic of validity is, as you have already said yourself, that we can determine whether an argument is valid by checking only the form of the argument.

 

[Bomb#20]

Of course, a conclusion and its negation can both follow. As a matter of fact, Bomb#20 already pointed out that anything follows.

...
Oh, well, if I was the only soul in the whole of God's creation to see it as wrong, I wouldn't mind. Being right when everybody else is wrong is like having a bit of truth all for yourself. And in fact, not just an inconsequential bit of truth, but a substantial bit of truth.

Still, I don't have it all for myself. Aristotle had it, many philosophers have it, and probably a few billion people as well on this planet alone even though most of them are probably incapable of articulating it.

I can at least confirm I understand what you are saying and that I know that the whole of modern mathematical "classical logic", including modal logic, the computer sciences and possibly most philosophers would agree with your notion of validity.

Still, it just means they're all wrong.
EB

You seem to be under the impression that Aristotle would have agreed with you. There's nothing non-Aristotelian about any of the reasoning steps I used. A conclusion and its negation can both follow in Aristotelian logic; that's why his reductio ad absurdum proofs work.

If you're objecting to the concept that "Anything follows from a contradiction", keep in mind that that's an observation, not an inference rule. It's not something my proofs rely on. It just turns out that you won't be able to name any C that I can't get to from your five contradictory premises, using normal uncontroversial* reasoning steps.

If it's your and a few billion other people's unalterable conviction that a conclusion and its negation can't both follow, how do you propose we decide which one follows when a fully Aristotelian proof of each has been exhibited? Is whichever proof was put on display first the winner?

(* There are philosophers called "intuitionists" to whom some of those reasoning steps may be controversial. They are called "intuitionists" because of their rejection of the popular but apparently counterintuitive rule that "Not (Not P)" implies "P".)

 

[Speakpigeon]

And you asked whether it was valid. It is.

Me, I like empirical evidence best. The empirical evidence is that a few people say it is valid and a few people say it is not.

It is also a well-known fact that many people object to all arguments that have contradictory premises or simply empirically false premises. That much is well-know, publicly available empirical evidence.

The fact that arguments with false premises, and more generally all implications with a false antecedent, are said to be valid by the current standard mathematical theory of logic is called the "paradox of the material implication", which is straightforwardly an admission that most people are certain that this kind of arguments and implications are in fact not valid. That much is also publicly available empirical evidence.

It is also empirical evidence that people who say this kind of argument is valid are more likely people who had some training in formal logic, so they are definitely more likely to be biased. Most people with no training in formal logic say that kind of argument is not valid, and as untrained, they are less likely to be biased.

So, I accept you say the argument is valid but that in itself is just one isolated data without much value, as explained. And, me, I'm sure the argument is not valid and most people would feel the same.

But this has already been explained to you, and there seems to be no point in doing that repeatedly.

There is nothing to explain. The question was: Is this argument valid?

I asked those who replied "yes" to this question to explain why they say it is valid and most of them can explain themselves and all end up giving the same kind of justification which an be traced back to the current standard mathematical theory of logic, thereby demonstrating they are probably biased in their assessment.

Not only is it not moronic, but it is correct.

Based on what?

I've looked for a justification of the current standard mathematical theory of logic for a long time now, including here, and I didn't find any rational justification whatsoever.

All you have to support your position is your own unsupported assumptions and your smug certainty that your view is backed up by the whole mathematical establishment.

And your position is moronic because it straightforwardly flies in the face of the notion of validity we all have intuitively and as all interested intellectuals have thought of it since Aristotle. 2,400 years of formal logic. The current moronic standard mathematical theory of logic is 120 years old and it is also easy to understand which mathematicians have adopted this standard and it has little to do with trying to express logical validity

And I have yet to see convincing empirical evidence that my interpretation is wrong.

Your insistence that the argument is valid won't be enough.
EB

 

[Speakpigeon]

Oh, Gosh, you're right, I almost forgot! Still, I guess my general tone suggested what I had in mind. It's not true that any one step is wrong. Happy?

Instead, it's your "proof" as a whole which is wrong. It doesn't prove what you appear to think it does. I provided you with the clues to find out by yourself why, but, hey, you should be allowed to rest in peace.
EB

To propose that a proof can be wrong even though every step in it is correct is to throw the entire concept of logic whole hog down the garbage chute.

The only reason we construct multi-step proofs in the first place is so that we can unambiguously settle the question of whether a set of premises imply a conclusion. When someone claims they do and someone else claims they don't, we can find out who's right, simply by checking every single step. We don't have to rely on mystical vision, or whose claim was made first, or louder, or more arrogantly, or more Frenchly. So if you insist that ((A implies B) and (B implies C) and (C implies D) but (A does not imply D)), why should anyone believe you aren't simply spouting idiocy? How do you feel claims about complicated inferences should be evaluated? Oh, wait, let me guess...

The notion of validity issued from Aristotle has been customary for 2,400 years!

Do you actually believe Aristotle would have agreed with you that it's possible for

It's not true that any one step is wrong.​

and

Instead, it's your "proof" as a whole which is wrong.​

to both be simultaneously true? If Aristotle had agreed with you, he wouldn't have bothered to write six volumes explaining how to break up arguments into simple easy-to-verify steps. There would have been no point.

Wrong assumption.

It is your method which is wrong.

The mere fact that you can't even think of this pretty obvious possibility shows the limitation of your rationality. You're much too emotional.

You're like the Pope at the time of Copernicus. The Pope had a "proof", too. His proof was that you only need to look at the Sun throughout the day to see that it is going round and round around us. Yep, it sure does look like it does.
EB

 

[Speakpigeon]

Exactly which part of

Joe is an elephant.
An elephant is not a squid.
------------------------------
Joe is not a squid.
Joe is either a squid or a giraffe.
------------------------------------
Joe is a giraffe.
A giraffe is not an elephant.
-------------------------------
Joe is not an elephant.
-------------------------
Joe is an elephant and Joe is not an elephant.
---------------------------------------------------
(Joe is not a squid) implies (Joe is an elephant and Joe is not an elephant.)
------------------------------------------------------------------------------------
Joe is a squid.​

don't you understand? It's a proof.

Yeah, and I produced a better, shorter, "proof":

P4. Joe is either a squid or a giraffe
H1. Joe is a giraffe................................P4
D1. Joe is not a giraffe..........................P5, P2
D2. Joe is a squid.................................P4, D1
QE Hallelujah!​

So, the conclusion "Joe is a squid" does "follow from".

You like it, you keep it.

It's a claim that every sentence under a line follows from the sentences above that line.

And what does it mean exactly that a sentence "follows from". Please, articulate clearly what it means for a sentence to follow from another sentence.

Why do you believe that? It's ridiculous. It's obviously not anything you read in a logic textbook. You're relying on mystical inner vision.

???

How could you possibly know that? You must believe you possess extra-sensory perception to know that.

Perhaps the trouble is your example is complicated enough that you were able to confuse yourself with it. Let's try a simpler variation.

Argument 1:

Premise a. X < 1
Premise b. X > 1
-------------------
Conclusion 1. X <= 1 (Pa)​

The conclusion does not follow from Pa.

Not sure what you are trying to say here.

What seems obvious to me, assuming ordinary arithmetic relations, is that there is no value of X that would "follow from" here.

Argument 2:

Premise a. X < 1
Premise b. X > 1
-------------------
Conclusion 2. Not (X <= 1) (Pb)​

OK, good, assuming X is a number, then the conclusion follows from Pb (it doesn't follow if e.g. X is a colour).

See, we agree here.

If a conclusion and its negation cannot both follow, then which argument is correct? Argument 1 or Argument 2?

Should be obvious by now.

we can determine whether an argument is valid by checking only the form of the argument.

That's what I do. You don't.
EB

 

[Angra Mainyu]

Me, I like empirical evidence best. The empirical evidence is that a few people say it is valid and a few people say it is not.

That is part of the empirical evidence. The empirical evidence is that nearly everyone who studies the matter - if they study logic, math, philosophy, etc. - reckon it is valid.

It is also a well-known fact that many people object to all arguments that have contradictory premises or simply empirically false premises. That much is well-know, publicly available empirical evidence.

Some people do that. Some of them later take a course of logic somewhere, and nearly all of those who do realize they were wrong.

The fact that arguments with false premises, and more generally all implications with a false antecedent, are said to be valid by the current standard mathematical theory of logic is called the "paradox of the material implication", which is straightforwardly an admission that most people are certain that this kind of arguments and implications are in fact not valid. That much is also publicly available empirical evidence.

Words have meaning, and the word 'valid' does as well. In a Logic and Epistemology Forum, words are generally understood in their technical sense. That technical sense also is generally used by people who defer to the experts when it comes to the meaning of that particular term. If there is another meaning of "valid", then you should argue for there being such a meaning, and clarify what you mean.

It is also empirical evidence that people who say this kind of argument is valid are more likely people who had some training in formal logic, so they are definitely more likely to be biased. Most people with no training in formal logic say that kind of argument is not valid, and as untrained, they are less likely to be biased.

YEC: The people who say that humans and mosquitoes have a common ancestor are more likely people who studied biology, so they're definitely more likely to be biased.


Regardelss, it is people who are familiar with the definition of 'valid' who say it is valid, so of course it's usually people who had some training in formal logic. The people who aren't but defer to the experts when it comes to the definition of a technical term are much more likely to be mistaken - but they still tend to yield to the experts, because it's a technical term.

So, I accept you say the argument is valid but that in itself is just one isolated data without much value, as explained. And, me, I'm sure the argument is not valid and most people would feel the same.

The argument is valid regardless of whether you accept or not, but in this case, you should be able to figure that out on your own.

There is nothing to explain. The question was: Is this argument valid?

Sure, there was something to explain, namely why the argument is valid. It has already been explained to you. Maybe you did not want anyone to explain it to you. But it has been explained regardless.

I asked those who replied "yes" to this question to explain why they say it is valid and most of them can explain themselves and all end up giving the same kind of justification which an be traced back to the current standard mathematical theory of logic, thereby demonstrating they are probably biased in their assessment.

YEC: I asked those who said that humans and mosquitoes had a common ancestor to explain why they say so, and most of them can explain themselves and all end up giving the same kind of arguments that can be traced back to the current evolutionist theory of origins of humans, thereby demonstrating they are probably biased in their assessment.

Based on what?

I've looked for a justification of the current standard mathematical theory of logic for a long time now, including here, and I didn't find any rational justification whatsoever.

All you have to support your position is your own unsupported assumptions and your smug certainty that your view is backed up by the whole mathematical establishment.

And your position is moronic because it straightforwardly flies in the face of the notion of validity we all have intuitively and as all interested intellectuals have thought of it since Aristotle. 2,400 years of formal logic. The current moronic standard mathematical theory of logic is 120 years old and it is also easy to understand which mathematicians have adopted this standard and it has little to do with trying to express logical validity

And I have yet to see convincing empirical evidence that my interpretation is wrong.

Your insistence that the argument is valid won't be enough.
EB

It is not my insistence. It has already been explained to you why it is valid. But nothing will be enough to persuade you, apparently.

 

[Speakpigeon]

Not only is it not moronic, but it is correct.

Based on what?
I've looked for a justification of the current standard mathematical theory of logic for a long time now, including here, and I didn't find any rational justification whatsoever.

It has already been explained to you why it is valid. But nothing will be enough to persuade you, apparently.

Believe me, I would have been convinced if there was a convincing justification supporting the definition of logical validity as used in the current standard mathematical theory of logic.

So, what is the justification supporting the definition of logical validity as used in the current standard mathematical theory of logic?
EB

 

[Angra Mainyu]

It has already been explained to you why it is valid. But nothing will be enough to persuade you, apparently.

Believe me, I would have been convinced if there was a convincing justification supporting the definition of logical validity as used in the current standard mathematical theory of logic.

So, what is the justification supporting the definition of logical validity as used in the current standard mathematical theory of logic?
EB

Actually, the definition is what it is, regardless of the motivation for those defining it.
Even so, I would say that it is an interesting property of an argument that "it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false" (one of the equivalent ways of giving the definition). Purely for example, it is very a very useful concept in mathematics. In fact, a mathematical paper with an invalid proof would almost certainly not pass peer review, and the only way it would pass peer review would be for the reviewers to make a mistake and fail to realize it is invalid.

It's hard to overstate how important this is. It's everywhere in mathematics, in pretty much every paper. Purely for example, here the author proves that every semi-greedy Schauder basis for an infinite-dimensional Banach space is almost greedy, and leaves an open question of whether the condition that the basis be Schauder can be removed, so that the result holds for all Markushevich bases. Suppose one wants to figure whether the answer to the question is affirmative. How would one go about that? Well, if one suspects it is, one would try to modify the proof in the paper so that one gets a valid proof, which uses the hypothesis that a Markushevich basis is semi-greedy and reaches the conclusion that it is almost greedy. If that does not work, one might try to come up with a different valid proof, or else one might try to come up with counterexamples if one suspect the answer is negative (side note: I'm not suggesting there is a counterexample here; I'm just saying how one would go about it). . But in order to show that something is a counterexample, one would likely also assume the basis is almost greedy, and reach a contradiction - after proving that it is semi-greedy, using a valid proof again.

Is there an alternative way to go about that?
Well, there are variants, but always a key point is to have valid proofs, i.e., proofs such that the premises imply the conclusion.

 

[Speakpigeon]

It has already been explained to you why it is valid. But nothing will be enough to persuade you, apparently.

Believe me, I would have been convinced if there was a convincing justification supporting the definition of logical validity as used in the current standard mathematical theory of logic.

So, what is the justification supporting the definition of logical validity as used in the current standard mathematical theory of logic?
EB

Actually, the definition is what it is, regardless of the motivation for those defining it.
Even so, I would say that it is an interesting property of an argument that "it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false" (one of the equivalent ways of giving the definition). Purely for example, it is very a very useful concept in mathematics. In fact, a mathematical paper with an invalid proof would almost certainly not pass peer review, and the only way it would pass peer review would be for the reviewers to make a mistake and fail to realize it is invalid.

It's hard to overstate how important this is. It's everywhere in mathematics, in pretty much every paper. Purely for example, here the author proves that every semi-greedy Schauder basis for an infinite-dimensional Banach space is almost greedy, and leaves an open question of whether the condition that the basis be Schauder can be removed, so that the result holds for all Markushevich bases. Suppose one wants to figure whether the answer to the question is affirmative. How would one go about that? Well, if one suspects it is, one would try to modify the proof in the paper so that one gets a valid proof, which uses the hypothesis that a Markushevich basis is semi-greedy and reaches the conclusion that it is almost greedy. If that does not work, one might try to come up with a different valid proof, or else one might try to come up with counterexamples if one suspect the answer is negative (side note: I'm not suggesting there is a counterexample here; I'm just saying how one would go about it). . But in order to show that something is a counterexample, one would likely also assume the basis is almost greedy, and reach a contradiction - after proving that it is semi-greedy, using a valid proof again.

Is there an alternative way to go about that?
Well, there are variants, but always a key point is to have valid proofs, i.e., proofs such that the premises imply the conclusion.

???

It seems you failed to understand my question, or, if you did, that you decided to elude it.

So, I repeat, what is the justification supporting the definition of logical validity as used in the current standard mathematical theory of logic?

If you can't provide the justification I'm asking for, please fuck off.
EB

Note
I never suggested validity was anything less than crucial, and not just for mathematics but for, I think, everything our brain does. So, your piece here is a moronic derail. This is also typical. You don't even quote the bit that might have justified your assumption here that I pooh-pooh validity. I don't, and in fact exactly the contrary, I value it as absolutely essential to all that we do. Even people like you who say something wrong probably do it on the basis of a valid inference.

Still, you've as much as admitted you don't know whether there is any proper justification. So, basically, you've just admitted that the definition you use either is essentially arbitrary or that it is exclusively founded on the intuition of those who produced the definition. Recall that mathematicians make mistakes. So, in effect, whether this definition is correct is anybody's guess and therefore your claim to proceed from some authoritative definition is bollocks.

Well, given your derail here, I can only reasonably assume you're probably no longer capable of having a rational debate on this.

 

[Angra Mainyu]

So, I repeat, what is the justification supporting the definition of logical validity as used in the current standard mathematical theory of logic?

If you don't make your questions clear enough, you should not expect others to figure out from starters what you mean - or at all.

By "as used" do you mean the justification for using it not in "the mathematical theory of logic"? What does "the mathematical theory of logic" even mean?
I took it you meant to challenge the definition used in mathematics, logic, philosophy, etc., and I provided a good justification in mathematics. But if you do not like that, I will provide a justification of the use of that definition in other contexts as well.

If you can't provide the justification I'm asking for, please fuck off.

You are being obscure, so it's a challenge to figure out what you mean, but I surely I do not feel inclined to do you the favor of fucking off given your behavior towards others and towards me.

Still, you've as much as admitted you don't know whether there is any proper justification.

False. I would suggest readers take a look at the exchange.

So, basically, you've just admitted that the definition you use either is essentially arbitrary or that it is exclusively founded on the intuition of those who produced the definition.

False.

Recall that mathematicians make mistakes. So, in effect, whether this definition is correct is anybody's guess and therefore your claim to proceed from some authoritative definition is bollocks.

First, that is an absurd argument. From "mathematicians make mistakes" to "whether this definition is correct is anybody's guess..." is just absurd. It's not deductively valid, but also it does not provide any good evidence at all. It's like your Copernicus nonsense.

Second, what are you even asking?
The definition in logic, in mathematics, and in philosophy is what it is. In which context are you saying that the mathematicians in question might be making a mistake? In the usefulness of the definition in mathematics?
If you are talking about whether to use it in other contexts, well, some of us are interested in whether an argument "takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false". It is really useful not only in mathematics, but in science as well - obviously, because science uses a lot of mathematics -, and in philosophy too, because philosophy is concerned with finding truths (and it is also useful for refuting people behaving in a hostile and irrational manner on the internet).

By the way, it is not only mathematicians who would reject an invalid argument in a paper. A paper with an invalid argument would not be published in physics, or philosophy, etc., barring an error by the people who check it, because precisely one of the things they check deductive arguments for is validity, and that is for the obvious reason they want to guarantee that truth is preserved, and valid arguments have the form that allow them to do that.

Well, given your derail here, I can only reasonably assume you're probably no longer capable of having a rational debate on this.

That is a mistaken and epistemically irrational assumption on your part.

 

[Speakpigeon]

If you don't make your questions clear enough, you should not expect others to figure out from starters what you mean - or at all.

By "as used" do you mean the justification for using it not in "the mathematical theory of logic"? What does "the mathematical theory of logic" even mean?
I took it you meant to challenge the definition used in mathematics, logic, philosophy, etc., and I provided a good justification in mathematics. But if you do not like that, I will provide a justification of the use of that definition in other contexts as well.


You are being obscure, so it's a challenge to figure out what you mean, but I surely I do not feel inclined to do you the favor of fucking off given your behavior towards others and towards me.

Still, you've as much as admitted you don't know whether there is any proper justification.

False. I would suggest readers take a look at the exchange.

So, basically, you've just admitted that the definition you use either is essentially arbitrary or that it is exclusively founded on the intuition of those who produced the definition.

False.

Recall that mathematicians make mistakes. So, in effect, whether this definition is correct is anybody's guess and therefore your claim to proceed from some authoritative definition is bollocks.

First, that is an absurd argument. From "mathematicians make mistakes" to "whether this definition is correct is anybody's guess..." is just absurd. It's not deductively valid, but also it does not provide any good evidence at all. It's like your Copernicus nonsense.

Second, what are you even asking?
The definition in logic, in mathematics, and in philosophy is what it is. In which context are you saying that the mathematicians in question might be making a mistake? In the usefulness of the definition in mathematics?
If you are talking about whether to use it in other contexts, well, some of us are interested in whether an argument "takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false". It is really useful not only in mathematics, but in science as well - obviously, because science uses a lot of mathematics -, and in philosophy too, because philosophy is concerned with finding truths (and it is also useful for refuting people behaving in a hostile and irrational manner on the internet).

By the way, it is not only mathematicians who would reject an invalid argument in a paper. A paper with an invalid argument would not be published in physics, or philosophy, etc., barring an error by the people who check it, because precisely one of the things they check deductive arguments for is validity, and that is for the obvious reason they want to guarantee that truth is preserved, and valid arguments have the form that allow them to do that.

Well, given your derail here, I can only reasonably assume you're probably no longer capable of having a rational debate on this.

That is a mistaken and epistemically irrational assumption on your part.

???

What is the justification supporting the definition of logical validity as used in the current standard mathematical theory of logic?

By "the current standard mathematical theory of logic", I mean 1st order ZFC.
EB

 

[fast]

If (just if, mind you) we were dealing with a lexical definition of the word, “valid” and suspected an error had been reported (and believing the definiens inaccurately explains the definiendum),I would question the lexicographer about the procedures behind their rendention. After all, a lexical definition is a function of how a word is COLLECTIVELY used by FLUENT speakers of a language, and if an error has been reported, I turn not to the speakers but to reporters for an explanation for the error.

The meaning of the term “valid” as used by logicians, however, is explained with a stipulative definition. That’s a big deal different. While we rely on lexicographers to provide definitions we can trust with words as used in our general lexicon, we have only the logicians to turn to for an explication for the definition they made up.

There is no etymological fallacy equivalence at play here with his question. If I wanted to know the lexical meaning of a word, I cannot examine the history in guarantee of a mistake free answer. The thing is, with stipulative definitions, there is no mistake to make. Any of us can stipulate a definition. I can define the word ‘valid’ as meaning containing at least three words in an argument. It doesn’t by any means change the lexical definition, but it does add another stipulative definition to the mix.

A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.​

I don’t know if the definition is in fact arbitrary or not. I’d like to think a whole hell of a lot went into its creation. Some methodologically-backed protocols as opposed to haphazard thought like the one I posed for illustration.

And the question is:

What went on in their minds when they decided on this? Sure, the definition is what it is (a fine trivial truism), and the motivation behind it is distinct, but it’s that (the motivation) that gets us closer to understanding the question.

The motivation for the question is another matter. I suspect the issue of arbitrariness is floating about—as if validity is not truly apart of the world or some such since it was made up, but I think the definition of logical “validity” is just as much as something real as poetry in a book. It exists.

 

[GenesisNemesis]

How can you have two conclusions, that Joe is an elephant, and Joe is a squid? It doesn't follow from "Joe is an elephant" that Joe is a squid.

 

[GenesisNemesis]

Also "Joe is either a squid or a giraffe" is incompatible with "Joe is an elephant" because it was already established that a giraffe is not an elephant.

 

[Speakpigeon]

If (just if, mind you) we were dealing with a lexical definition of the word, “valid” and suspected an error had been reported (and believing the definiens inaccurately explains the definiendum),I would question the lexicographer about the procedures behind their rendention. After all, a lexical definition is a function of how a word is COLLECTIVELY used by FLUENT speakers of a language, and if an error has been reported, I turn not to the speakers but to reporters for an explanation for the error.

The meaning of the term “valid” as used by logicians, however, is explained with a stipulative definition. That’s a big deal different. While we rely on lexicographers to provide definitions we can trust with words as used in our general lexicon, we have only the logicians to turn to for an explication for the definition they made up.

There is no etymological fallacy equivalence at play here with his question. If I wanted to know the lexical meaning of a word, I cannot examine the history in guarantee of a mistake free answer. The thing is, with stipulative definitions, there is no mistake to make. Any of us can stipulate a definition. I can define the word ‘valid’ as meaning containing at least three words in an argument. It doesn’t by any means change the lexical definition, but it does add another stipulative definition to the mix.

A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.​

I don’t know if the definition is in fact arbitrary or not. I’d like to think a whole hell of a lot went into its creation. Some methodologically-backed protocols as opposed to haphazard thought like the one I posed for illustration.

And the question is:

What went on in their minds when they decided on this? Sure, the definition is what it is (a fine trivial truism), and the motivation behind it is distinct, but it’s that (the motivation) that gets us closer to understanding the question.

The motivation for the question is another matter. I suspect the issue of arbitrariness is floating about—as if validity is not truly apart of the world or some such since it was made up, but I think the definition of logical “validity” is just as much as something real as poetry in a book. It exists.

We all understand what the word "valid" means. For those who are no so sure, here is a good dictionary definition:

Validity
4. Logic
a. Containing premises from which the conclusion may logically be derived: a valid argument.
b. Correctly inferred or deduced from a premise: a valid conclusion.

Obviously not good enough to prove anything much but it does identify what it is we talk about when we use the word "validity".

The question is logically simple. Two possibilities. Either the procedural definition of validity, i.e. how to prove an argument or an implication valid, is completely arbitrary or it is not.

First possibility, if the definition is arbitrary, then no definition can be said to be correct and there's no rationale for deciding that the one used by mathematicians today is the correct one. Any definition is as good as any other. In this case, I say my definition, as I use it here, is that of Aristotle, and in this case, it is as good as any because all definitions are arbitrary.

Second possibility, the definition of validity is not arbitrary. Good, if it's not arbitrary, then it must have a justification, so, what is the justification supporting the definition of logical validity as used in the current standard mathematical theory of logic, given that by "the current standard mathematical theory of logic", I mean 1st order ZFC?

And of course, the crucial point is whether validity exists or not independently of our definitions of it. I agree with you, validity exists. We perhaps disagree as to how it exists. Me, I think it is a natural property of the human brain resulting from something like 550 million years of natural selection of our nervous system. As such, it has good credentials in terms of efficiency in our natural environment and it means that we all have an intuitive notion of validity and we can all assess intuitively whether arguments are valid or not, as Locke for example observed. And the point of this thread is to highlight the fact that most people not biased by training in formal logic see the Squid argument as not valid, contrary to those who had a training who will tend to favour validity, and precisely because they are biased. So, now, let's see what might be the justification of the definition these people favour.
EB