Improved Squid Argument

[Angra Mainyu]

I need you to have your people look into having this logic thing revamped. Have them give it an overhaul. It’s the new millineum already and the speakpigeons of the world doesn’t want to lose what sembalance or normalcy that used to come with the traditional notion of validity. Heck, I can throw something on the grill, he’ll bring the music, you make a few text book alterations; everyone’ll be happy.

Actually, Speakpigeon's own position is self-contradictory. And we're not trying to come up with a new version of validity. An argument is valid if the conclusion follows from the premises. In the case you mentioned,

If there are only two people in the building, we’ll only need one fire truck
There are only two people in the building.
Eight more people enter the building
Therefore, we’ll only need one fire truck.

in a normal situation, you no longer have the premise "there are only two people in the building".
But consider how unreasonable Speakpigeon's claim that you cannot choose just a subset of the premises is. Speakpigeon says:

Its still deductive. Most people might put together a 200 piece puzzle. This is a three piece puzzle. If all my pieces are there to make the picture, bam, I can do it. You can put it together too. What’s weird about this is you’ve opened up your very own three piece puzzle set and threw two of your pieces onto my table.

So, here I am sitting with five pieces trying to make the picture on the box (the conclusion), so not only do I have to work out which pieces don’t belong, I have to put together the ones needed to make the picture. Thanks a lot!

Valid just means I can get to where I want with what I got. If that can happen, then there is a flow or path from premise world to conclusion world. The bridge can be built. That don’t make it sound, but it does make it valid.

LOL. This shows you are just ignoring two of the premises. Sorry, you can't do that. You have to get to the conclusion of the five premises of the argument, not that of some arbitrary subset of them. You are effectively validating a different argument. The premise asserting that Joe is an elephant cannot be ignored.

EB

With that criterion, consider the following arguments:


Argument 6:


Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Conclusion: Tom is a mollusc.

That is valid, right. But now, consider the following argument:

Argument 7:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Premise 3: Tom is not a mollusc.
Conclusion: Tom is a mollusc.


Now, Speakpigeon's criterion says that the new argument is not valid, because apparently you can't ignore some of the premises. But Speakpigeon accepted weakening!!!
So, addition of more premises should not invalidate an argument.

 

[Speakpigeon]

Can you produce an example of a justification by professional logicians, i.e. mathematicians, philosophers, computer scientists etc., that ANY definition of validity used in mathematical logic is correct?
EB

Angra Mainyu has given a justification that I would cosign. Have you responded to it, yet?

Here is the question I asked:

Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that the definition of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?
Here is the definition:

Validity
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.
Internet Encyclopedia of Philosophy - https://www.iep.utm.edu/val-snd/

AM never provided a justification that the definition is correct.

By correct, I mean true of something. What thing is the mathematical definition of validity true of? Whatever it is, I am asking a justification that the definition is true of it.

And of course, I meant a justification proposed by some well-known specialists of logic. I wasn't asking for AM's own justification.

The justification proposed by AM is that the mathematical definition of validity is logically consistent, i.e. that it is valid according to itself. Clearly, that's not what I asked. I asked what according to mathematicians makes it true. I couldn't find mself any well-known mathematician saying anything to the effect that the definition is true. Look at any logic textbook. Nobody even claim anything to the effect that the mathematical definition of validity would be true.

Yet, the world over, mathematicians behave as if they were the specialists of logic. They are not. They are the specialist of mathematical logic and there is no reason whatsoever to accept that mathematical logic is logic itself. First, this would be a circular claim since, as AM did, it would justify mathematical logic by mathematical logic. And second, all the empirical evidence shows that mathematical logic isn't even close to being a true model of logic. The principle of explosion is one major difference but there are others. One poster here unwittingly exhibited what is in effect a valid implication for mathematical logic but not for us human beings. Neither of you even noticed. You think you're a specialist? Whoa. I'm not impressed. What is impressive, though, is that you think you can pick and choose. No. If you refuse to answer a straightforward question, then that's it. You're disqualified. Is my squid argument valid? What is the justification proposed by well-known logicians that ANY of the definitions of validity used in mathematical logic is correct, i.e. true of human logic? The 19th century mathematicians Boole and Frege both clearly believed their formal logic modelled the human deductive reasoning. But, apparently, that's no longer something mathematicians are prepared to claim. And you two are completely irrelevant here.

In effect, AM, by striving so hard to exhibit some sort of clumsy and inadequate justification, confirmed he couldn't find what I asked. There is no such justification.
EB

 

[Speakpigeon]

With that criterion, consider the following arguments:

Argument 6:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Conclusion: Tom is a mollusc.

That is valid, right. But now, consider the following argument:

Argument 7:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Premise 3: Tom is not a mollusc.
Conclusion: Tom is a mollusc.

Now, Speakpigeon's criterion says that the new argument is not valid, because apparently you can't ignore some of the premises. But Speakpigeon accepted weakening!!!
So, addition of more premises should not invalidate an argument.

Listen, I like to answer explicit claims. What you are claiming is just confused. It's not up to me to assume what you mean. So, please exhibit in one short sentence what you mean here, something of the form A implies B. You should be able to do that, right?

But I can already tell you, you're argument is not valid.
EB

 

[A Toy Windmill]

Actually, Speakpigeon's own position is self-contradictory.

I'm beginning to see why Speakpigeon has a problem with the principle of explosion.

And I'm beginning to see why the preference for Aristotelian logic. Speakpigeon doesn't appear to be able to follow a rule for more than a few steps, so I see why they are more comfortable with something as simple as syllogisms.

The rest is just the ramblings of a crank, complete with the idea that the establishment is brainwashed and that if they attempted to reveal the truth, the men in black would have to silence them.

 

[Jimmy Higgins]

Just to check, this argument is not valid, correct?

Premise) Joe is not squid.
Conclusion) Therefore, Joe is a squid.

 

[Speakpigeon]

Just to check, this argument is not valid, correct?

Premise) Joe is not squid.
Conclusion) Therefore, Joe is a squid.

LOL. Excellent. Thanks for that.
EB

 

[fast]

Just to check, this argument is not valid, correct?

Premise) Joe is not squid.
Conclusion) Therefore, Joe is a squid.

New rule: if we can “not use premises given, then we can “use premises not given.” Fair’s fair, right!

So, the premise not given is that “Joe is a squid.”

Given that, and some TNT, we can conclude (validly) that all three legged raccoons are unicorns.

 

[Angra Mainyu]

Just to check, this argument is not valid, correct?

Premise) Joe is not squid.
Conclusion) Therefore, Joe is a squid.

Correct.

 

[Angra Mainyu]

With that criterion, consider the following arguments:

Argument 6:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Conclusion: Tom is a mollusc.

That is valid, right. But now, consider the following argument:

Argument 7:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Premise 3: Tom is not a mollusc.
Conclusion: Tom is a mollusc.

Now, Speakpigeon's criterion says that the new argument is not valid, because apparently you can't ignore some of the premises. But Speakpigeon accepted weakening!!!
So, addition of more premises should not invalidate an argument.

Listen, I like to answer explicit claims. What you are claiming is just confused. It's not up to me to assume what you mean. So, please exhibit in one short sentence what you mean here, something of the form A implies B. You should be able to do that, right?

But I can already tell you, you're argument is not valid.
EB

Look, what I am saying is not confused at all. It is very precise. I will address it later, but first, I have another false and unwarranted claim of yours to deal with (because you made that other claim first, so I have already written the reply and will post it first).

 

[Angra Mainyu]

To readers: Speakpigeon once again grossly misrepresents my position, with utter disregard for the truth. Below, I will show this, and explain my defense of what Speakpigeon claims the definition of validity in mathematical logic is.

The justification proposed by AM is that the mathematical definition of validity is logically consistent, i.e. that it is valid according to itself.

That is false. It should be obvious to Speakpigeon that it is false, as anyone can see by reading this thread.

First, I asked Speakpigeon in the other thread whether she believed all mathematical statements were either true or false. She replied:
https://talkfreethought.org/showthr...ct-mathematics&p=683824&viewfull=1#post683824

I think all statements are either true or false.

I will grant this for the sake of the argument.

Note that it follows from the hypothesis that all statements are either true or false, that in particular all mathematical statements are either true or false.
Note also that I am making no claims that all mathematical statements are either true or false, or that this is not so.
Rather, I am granting for the sake of the argument Speakpigeon's own claim.

So, let us continue. Speakpigeon says:

https://talkfreethought.org/showthr...Squid-Argument&p=693333&viewfull=1#post693333

Here is the question I asked:

Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that the definition of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?
Here is the definition:

Validity
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.
Internet Encyclopedia of Philosophy - https://www.iep.utm.edu/val-snd/

I will also grant for the sake of the argument Speakpigeon's claim that that is the definition of logical validity used in mathematical logic since the beginning of the 20th century.
Note that I do not claim that that is the definition of validity. Nor do I claim it is not. Nor do I claim there is a single definition of validity in mathematics. Nor do I claim otherwise. Rather, so far I am merely conceding some of Speakpigeon's own claims, for the sake of the argument, and not making any further claims.

Let us continue, then. By 'CML-valid' or 'valid according to classical mathematical logic' or similar expressions, I mean that a deduction (or argument, inference, or whatever one calls it) is valid according to the definition provided by Speakpigeon and quoted above. Namely, a deduction is CML-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.

Here's the first important point:

Suppose A is a CML-valid mathematical argument, with premises P1,...,Pn and conclusion C. Further, suppose all of the premises are true. Then, so is the conclusion C. Why? Because the premises are true, and the argument takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Therefore, C is not false. Given the previous hypothesis (i.e., every mathematical statement is either true or false), C is true.

This gives us an important feature of CML-validity: it is truth-preserving. If one starts with truths, by CML-valid arguments one gets only more truths.

Note that I am not remotely saying that I assume CML is correct in any sense, or that it is valid "according to itself" (whatever that means). Rather, I have just shown that CML-valid arguments are truth-preserving.

Let us now suppose we have another definition of validity; let's call it V-validity. Suppose, further, that V-validity is also truth-preserving, and that A2 is an argument that is V-valid, with premises Q1,..Qm, and conclusion C2. Then, A2 is also CML-valid. Why? Because if A2 were not CML-valid, then - by definition of CML-validity -, it would follow that it is not the case that A2 takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. But then - since the argument takes some form -, then it takes a form that makes it possible for the premises to be true but the conclusion nevertheless to be false. Hence, it would follow that V-validity fails to be truth-preserving. That would contradict our assumption. It follows then that A2 is CML-valid (because if we assume it is not CML-valid, that implies a contradiction).

So, we have established that CML-validity is the strongest form of truth-preserving validity, in the sense that any argument valid according to a truth-preserving definition of validity, is CML-valid.

As a result, CML-validity gives us the strongest tool for finding mathematical truth. This is because definitions of validity that are not truth-preserving would surely not be conducive to finding mathematical truth (because you might start with true premises and get a false conclusiion), and because any truth-preserving definition of validity V2 that is not equivalent to CML is weaker: there will be inferences that are CML-valid but not V2-valid, whereas every V2-valid definition of validity will be CML-valid.

So, we have the strongest definition of validity, and with that, our strongest means of finding mathematical truths.

But wait, might that be a problem? If the deductive method is very strong, there is a risk that you start with false premises, and you get a lot of falsehoods. Is that a problem? Not for mathematics, for the following reasons:

First, while mathematicians sometimes make logical errors in applying CML, that is usually corrected before a paper is published, because the authors and other mathematicians check it repeatedly. Moreover, if some errors make it into a paper, readers - who are nearly always also mathematicians - will almost certainly sooner or later (very probably sooner, if the paper has readers) spot it. So, while the system is not perfert, it is generally very reliable in getting CML-validity right.

Now, since CML-validity is truth-preserving, as long as the the most basic, starting points are true (i.e., those not resulting from previous arguments in previous papers), that guarantees that we have an extremely strong method - in fact, the strongest - for finding mathematical truth.

What if the most basic, starting points, are false? Well, if that is the case, mathematics is a hopeless endeavor regardless of what definition of validity one uses, so this is not a particular problem for CML. Still, perhaps we can make a more fine-grained argument here: in the past, naive set theory was considered very basic, and yet it was inconsistent. However, that is not a problem with the system: on the contrary, it is a case in which the system worked: mathematicians did find the error. When I say "basic points", it has to be the most elementary things one can think of (mathematics does not work quite like that, but remember I am granting Speakpigeon's claim that all statements are either true or false, for the sake of the argument).

So, by CML, we find new mathematical truths, and we can find any truth that could be found from the same starting points by another truth-preserving method, but also more truths than any weaker method.

So, that's a good reason to adopt CML-validity as the way of deriving statements from others: we find true statements from true statements, and it's the strongest method for doing that.

Additionally, I would add that CML is intuitively right, for most mathematicians. This is not so because they were told so. Where I live, most mathematicians never take a course in mathematical logic (I think it would be a good thing if they did, but anyway), but those who do (or who decide to study it on their own), when they first encounter it, usually find it very intuitive, and in particular, they find the definition very intuitive.

Now, as you can see, Speakpigeon's claim that

The justification proposed by AM is that the mathematical definition of validity is logically consistent, i.e. that it is valid according to itself.

is false. It does not even come close to the truth, and it ought to be obvious to anyone being rational that this is so.

Also, note that the defense I just gave above of CML-validity does not depart from the defense I had already given here in any substancial way, and only adds further details.

Finally, note that anyone who carefully reads the defense I had already given here and is being rational will not going to reckon that the justification proposed by me " is that the mathematical definition of validity is logically consistent, i.e. that it is valid according to itself." That is a gross misrepresentation of what I did, which Speakpigeon persists in doing, with reckless disregard for the truth.

Now, Speakpigeon also says:

AM never provided a justification that the definition is correct.

By correct, I mean true of something. What thing is the mathematical definition of validity true of? Whatever it is, I am asking a justification that the definition is true of it.

That is a very different claim. Note that even if Speakpigeon were correct that I never provided a justification that the definition is correct, it would remain the case that the justification I provided would not be what Speakpigeon claims it is, and furthermore, that a reader who is being rational would realize that. Indeed, even if Speakpigeon were correct that I never provided a justification that the definition is correct, it would remain the case that

The justification proposed by AM is that the mathematical definition of validity is logically consistent, i.e. that it is valid according to itself.

is false, it does not even come close to the truth, and it ought to be obvious to anyone being rational that this is so.

Finally, someone might suggest that in my defense of CML-validity above, I'm using arguments that are Aristotelian-invalid, or whatever. Let me make this clear: my defense of CML-validity above is using my own faculties, my own sense of logic, not assuming some specific definition beforehand.

All that said, let us now consider Speakpigeons further claim, that

AM never provided a justification that the definition is correct.

By correct, I mean true of something. What thing is the mathematical definition of validity true of? Whatever it is, I am asking a justification that the definition is true of it.

Well, actually, I did. I argued - under the assumption that all statements are either true or false; more below - that it is the strongest method for finding mathematical truth. So, what is true of? It is true that it is the strongest method for finding mathematical truth. Now, this is not an argument against using more restrictive definitions (say, an intuitionistic definition) as a means of, say, obtaining a sort of proof that is perhaps more useful for some practical applications. Sometimes, we don't only need to know that something is the case, but it's interesting the way in which it follows from something else. At any rate, the arguments I give above (and others) would still support adopting that definition in the meta-theory.

Moreover, I argued that "CML is intuitively right, for most mathematicians." That also provides a justification for adopting it. I mean, if it were counterintuitive, maybe even if it's the strongest method, a somewhat weaker but more intuitive one would in practice work better. But no, most mathematicians do find it intuitive, in my experience.

What about the assumption?
After all, one might say I did not defend CML-validity, but only did so under the assumption that every statement (or at least, every mathematical statement) is either true or false. Now, this is true, but remember, Speakpigeon says

https://talkfreethought.org/showthr...ct-mathematics&p=683824&viewfull=1#post683824

I think all statements are either true or false.

, so it is proper to make that assumption in this context - in fact, I am merely granting one of Speakpigeon's claims, for the sake of the argument.

Now, Speakpigeon might later say that by "correct" she meant something else. What then? Well, then, it would remain the case that regardless of whether my defense of CML is a justification that the definition is correct in whatever sense of "correct" Speakpigeon has in mind, Speakpigeon's claim that

The justification proposed by AM is that the mathematical definition of validity is logically consistent, i.e. that it is valid according to itself.

is false, it does not even come close to the truth, and it ought to be obvious to anyone being rational that this is so. In fact, even if my justification of CML-validity were flawed in whatever sense, it would certainly not be the case that "The justification proposed by AM is that the mathematical definition of validity is logically consistent, i.e. that it is valid according to itself." - as Speakpigeon claims.

 

[Angra Mainyu]

With that criterion, consider the following arguments:

Argument 6:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Conclusion: Tom is a mollusc.

That is valid, right. But now, consider the following argument:

Argument 7:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Premise 3: Tom is not a mollusc.
Conclusion: Tom is a mollusc.

Now, Speakpigeon's criterion says that the new argument is not valid, because apparently you can't ignore some of the premises. But Speakpigeon accepted weakening!!!
So, addition of more premises should not invalidate an argument.

Listen, I like to answer explicit claims. What you are claiming is just confused. It's not up to me to assume what you mean. So, please exhibit in one short sentence what you mean here, something of the form A implies B. You should be able to do that, right?

But I can already tell you, you're argument is not valid.
EB

What I claim is not remotely confused to a sufficiently intelligent person who is being rational. Why should I even bother with you? I was not speaking to you, but to fast.

But regardless, here goes:

Argument 6:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Conclusion: Tom is a mollusc.
​

Argument 6 is valid. Now, weakening says that the addition of premises to a valid argument cannot make it invalid. Hence, from "Argument 6 is valid" and "Weakening is true", we conclude that Argument 7 is valid, , where Argument 7 is

Argument 7:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Premise 3: Tom is not a mollusc.
Conclusion: Tom is a mollusc.​

Given that you accept the validity of Argument 6 (it follows from your own claims about validity), and that you also accept weakening (you said so yourself), then it follows from claims that you accept that Argument 7 is valid. However, you are now implying that Argument 7 is not valid, apparently because you can't ignore some of the premises. So, some of your claims imply that Argument 7 is valid, whereas some of your claims imply that Argument 7 is not valid.

 

[fast]

Validity preserves truth, and that’s important, yet I’d like to articulate a justification for the definition (explanation for the usage/meaning of the term). Recall my earlier stance that there’s a great divide between that of deductive arguments and non-deductive arguments. We speak not of nondeductive arguments as valid or invalid. They are not valid, but not invalid either.

With a deductive argument (with true premises), the addition of validity must be such that the divide is maintained. An argument to be deductive cannot have a meaningful difference between “invalid” and “not valid.” There’s a preservation—guarenteed entailment.

There is an underlying categorization that must take on a collectively exhaustive construct such that it’s impossible for the leakage of truth or the infusion of falsehood.

That was esoteric. We have two pieces. One is true premises. The only thing we have left (validity) has to be such that the guarentee of truth must follow with NO possibility of error. Otherwise, the divide becomes skewed.

Anyhow, some two cents.

On a side note:

P1. If Joe is a person, then joe is alive
P2. Joe is a person
P3. No dog has ever barked
C: Joe is alive

Is that sound?

 

[Angra Mainyu]

Validity preserves truth, and that’s important, yet I’d like to articulate a justification for the definition (explanation for the usage/meaning of the term). Recall my earlier stance that there’s a great divide between that of deductive arguments and non-deductive arguments. We speak not of nondeductive arguments as valid or invalid. They are not valid, but not invalid either.

With a deductive argument (with true premises), the addition of validity must be such that the divide is maintained. An argument to be deductive cannot have a meaningful difference between “invalid” and “not valid.” There’s a preservation—guarenteed entailment.

There is an underlying categorization that must take on a collectively exhaustive construct such that it’s impossible for the leakage of truth or the infusion of falsehood.

That was esoteric. We have two pieces. One is true premises. The only thing we have left (validity) has to be such that the guarentee of truth must follow with NO possibility of error. Otherwise, the divide becomes skewed.

Anyhow, some two cents.

On a side note:

P1. If Joe is a person, then joe is alive
P2. Joe is a person
P3. No dog has ever barked
C: Joe is alive

Is that sound?

No, but it is valid. It is not sound because not all of the premises are true. At least P3 is false. I do not know whether P2 is true (who is Joe?). As for P1, it is ambiguous, as the word "person" has more than one meaning.

 

[fast]

Validity preserves truth, and that’s important, yet I’d like to articulate a justification for the definition (explanation for the usage/meaning of the term). Recall my earlier stance that there’s a great divide between that of deductive arguments and non-deductive arguments. We speak not of nondeductive arguments as valid or invalid. They are not valid, but not invalid either.

With a deductive argument (with true premises), the addition of validity must be such that the divide is maintained. An argument to be deductive cannot have a meaningful difference between “invalid” and “not valid.” There’s a preservation—guarenteed entailment.

There is an underlying categorization that must take on a collectively exhaustive construct such that it’s impossible for the leakage of truth or the infusion of falsehood.

That was esoteric. We have two pieces. One is true premises. The only thing we have left (validity) has to be such that the guarentee of truth must follow with NO possibility of error. Otherwise, the divide becomes skewed.

Anyhow, some two cents.

On a side note:

P1. If Joe is a person, then joe is alive
P2. Joe is a person
P3. No dog has ever barked
C: Joe is alive

Is that sound?

No, but it is valid. It is not sound because not all of the premises are true. At least P3 is false. I do not know whether P2 is true (who is Joe?). As for P1, it is ambiguous, as the word "person" has more than one meaning.

P1 If more than 30 people enter a building with a maximum allowable capacity of 30 people, the buildings allowable capacity will be exceeded.
P2 more than 30 people entered a building with a maximum capacity of 30 people.
P3 some dogs bark
C the buildings allowable capacity has been exceeded

At any rate, it’s my intent for all three premises and the conclusion to be true.
It’s strange that the irrelevant premise must be true for the conclusion to be sound when the truth of the third premise is irrelevant for the argument to be valid.

 

[Jimmy Higgins]

Just to check, this argument is not valid, correct?

Premise) Joe is not squid.
Conclusion) Therefore, Joe is a squid.

Correct.

Okay, I think I understand this madness.

 

[Angra Mainyu]

Validity preserves truth, and that’s important, yet I’d like to articulate a justification for the definition (explanation for the usage/meaning of the term). Recall my earlier stance that there’s a great divide between that of deductive arguments and non-deductive arguments. We speak not of nondeductive arguments as valid or invalid. They are not valid, but not invalid either.

With a deductive argument (with true premises), the addition of validity must be such that the divide is maintained. An argument to be deductive cannot have a meaningful difference between “invalid” and “not valid.” There’s a preservation—guarenteed entailment.

There is an underlying categorization that must take on a collectively exhaustive construct such that it’s impossible for the leakage of truth or the infusion of falsehood.

That was esoteric. We have two pieces. One is true premises. The only thing we have left (validity) has to be such that the guarentee of truth must follow with NO possibility of error. Otherwise, the divide becomes skewed.

Anyhow, some two cents.

On a side note:

P1. If Joe is a person, then joe is alive
P2. Joe is a person
P3. No dog has ever barked
C: Joe is alive

Is that sound?

No, but it is valid. It is not sound because not all of the premises are true. At least P3 is false. I do not know whether P2 is true (who is Joe?). As for P1, it is ambiguous, as the word "person" has more than one meaning.

P1 If more than 30 people enter a building with a maximum allowable capacity of 30 people, the buildings allowable capacity will be exceeded.
P2 more than 30 people entered a building with a maximum capacity of 30 people.
P3 some dogs bark
C the buildings allowable capacity has been exceeded

At any rate, it’s my intent for all three premises and the conclusion to be true.
It’s strange that the irrelevant premise must be true for the conclusion to be sound when the truth of the third premise is irrelevant for the argument to be valid.

Soundness is a property of the argument, not the conclusion. But the truth of any of the premises is irrelevant to the argument to be valid, whereas the truth of all of them is relevant for it to be sound. I'm not sure why that would be strange. Sometimes, it is useful to distinguish between the question of whether a conclusion follows from some premises, and questions of truth.

 

[fast]

I misspoke. I meant to say to argument, not conclusion. But yes, the way you put it, it makes sense.

 

[Koyaanisqatsi]

As I pointed out second post itt, it's just a confusion over esoteric definitions. Colloquially, whenever someone uses the word "valid" they usually mean "true" or "accurate" or "I affirm such a position." But in formal logic, "valid" applies strictly to form.

ALL of this nonsense could easily be avoided if instead of using the word (and subsequently the esoteric definition) "valid" logicians instead used the phrase "properly formatted." Which is really what the word denotes.

 

[Speakpigeon]

What I claim is not remotely confused to a sufficiently intelligent person who is being rational. Why should I even bother with you? I was not speaking to you, but to fast.

But regardless, here goes:

Argument 6:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Conclusion: Tom is a mollusc.
​

Argument 6 is valid. Now, weakening says that the addition of premises to a valid argument cannot make it invalid. Hence, from "Argument 6 is valid" and "Weakening is true", we conclude that Argument 7 is valid, , where Argument 7 is

Argument 7:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Premise 3: Tom is not a mollusc.
Conclusion: Tom is a mollusc.​

Given that you accept the validity of Argument 6 (it follows from your own claims about validity), and that you also accept weakening (you said so yourself), then it follows from claims that you accept that Argument 7 is valid. However, you are now implying that Argument 7 is not valid, apparently because you can't ignore some of the premises. So, some of your claims imply that Argument 7 is valid, whereas some of your claims imply that Argument 7 is not valid.

Good, thanks for explaining. That will save time.

However, you're making an incorrect assumption. I do accept weakening but only as A implies A or B, as I indeed explained somewhere, and not as A implies B implies A and C implies B. The later kind of "weakening" doesn't work ... when C contradicts A.

Anyway, thank you for being so candid about mathematical logic. However, it only gets worse and worse as you come to reveal your surprising justifications for your initial claims. I now realise there isn't even the smallest point of agreement. Next you're going to claim that true is false and false is true. At this juncture, there isn't any ground left for any understanding. Most posters here, and indeed elsewhere, take arguments with contradictory premises either as not valid or meaningless. Your only objection to this result is to claim that people are logically incompetent. That's not true. Most people easily understand Aristotle's syllogisms and see them as valid even when they don't have any formal training.

As I said already a while ago, we don't have anything to talk about.

You don't even understand my request for a justification of the definition of validity. The mere fact that you could only provide a clumsy attempt at justification cooked in your own kitchen shows you don't know of even one well-known mathematician who proposed such a justification. QED as far as I am concerned.
EB

 

[Speakpigeon]

ALL of this nonsense could easily be avoided if instead of using the word (and subsequently the esoteric definition) "valid" logicians instead used the phrase "properly formatted." Which is really what the word denotes.

Yeah, I support this idea. Mathematical logic should say "properly formatted".

It should also eschew the word "logic" in "mathematical logic", that would clarify since mathematical logic obviously isn't logic at all.

Again, my thread on my squid argument was about logic and validity, not about the mathematicians' view of logic or about being "properly formatted".

There is no difficulty with the notion of validity. Dictionaries give a straightforward definition that we can all understand.

Valid
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.

Most people understand that a logical argument isn't necessarily one with true premises and a true conclusion, especially when the argument is about whether Joe is a squid or an elephant.

EB