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

[bigfield]

a contradiction implies anything

Can someone elaborate on this particular point? It doesn't make sense to me. I feel like it must be possible for all of the premises and the conclusion to be true in order for the argument to be valid.

That's not the customary definition of "valid". After all, it's possible for all of the premises and the conclusion to be true in all manner of illogical arguments, such as "All men are mortal; Socrates is dead; therefore Socrates is a man." So that's not a useful property to give a name to.

"Valid" is conventionally defined as "It must be impossible for all of the premises to be true and the conclusion to be false." That's why "All men are mortal; Socrates is immortal; Socrates is a man; therefore all women are from Venus." is a valid argument: it actually satisfies the definition. When it's impossible for all the premises to be true, period, that means for all the premises to be true and the conclusion to be false is also impossible. Once things are impossible, adding additional conditions doesn't make them become possible. So even when the conclusion really is false the argument still satisfies the criterion.

Does that help at all? I know it's kind of counterintuitive. You have to stare at it sideways for a bit.

Yes, it's just counterintuitive.

You showed that "Joe is not a squid" cannot be true because it leads to a contradiction, therefore its negation, "Joe is a squid" must be true, but that leaves us with "Joe is a squid", "Joe is an elephant", and "An elephant is not a squid", which can't all be true at the same time.

Your new example is also counterintuitive. "All men are mortal; Socrates is immortal; Socrates is a man; therefore all women are from Venus." Isn't that just a non-sequitur? How can a fallacious argument be valid? Just doesn't seem right to me, although I do see it fits the customary definition of "valid".

 

[untermensche]

There are valid arguments and there are valid arguments with utility.

No utility in just saying Socrates is immortal from thin air.

No utility will ever come from it.

It is a waste of time.

 

[Speakpigeon]

Mathematical logic, as it is recognised by most mathematicians today as the standard method of logical calculus, says the argument is valid. The validity of the argument is in effect a trivial consequence of how the material implication is defined using a truth table, and how validity is defined to coincide with this definition of the material implication. According to this definition, any argument whose premises cannot be true--i.e. premises which are false in all logical cases, as is indeed the case here--will be valid, and this irrespective of what the premises say, of what the conclusion says, and of the existence or not of a relation between what the premises say and what the conclusion says, provided the premises and the conclusion make sense as being either true or false, which they do here.

Oh, so we are going with antonyms of valid for your definition of valid.

Writing several rambling paragraphs doesn’t automatically allow you to redefine words in such a way that all people must bow to your wisdom.

The argument is valid only in the sense that you have listed six sequential statements.

I didn't provide in this post any definition of validity. The one I favour already exists.

I was showing why voting that the argument doesn't make sense doesn't make sense.
EB

 

[Speakpigeon]

A squid is not a giraffe
A giraffe is not an elephant
An elephant is not a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

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

I understand how some people come to claim the argument is valid on the basis of the definition of validity accepted in modern mathematical "classical logic", but I find it really embarrassing that you should say here with a straight face that the conclusion "follows" from the premises. What follows from the premises here is that the conclusion is necessarily false.
EB

 

[Speakpigeon]

1. A is not B

2. B is not C

3. C is not A

4. D = A or B

5. D = C

Therefore: D = A

Invalid.

D cannot = A because D = C (5) and C does not = A (3)

Excellent!

Still, you've unmasked yourself as a perfectly logical person after successfully passing during so many years for a logical moron.

There are other ways to invalidate this.

Please explain.

You mean premise 1 and 4, perhaps? Which makes this argument doubly invalid.
EB

 

[Jimmy Higgins]

a contradiction implies anything

Can someone elaborate on this particular point? It doesn't make sense to me. I feel like it must be possible for all of the premises and the conclusion to be true in order for the argument to be valid.

That's not the customary definition of "valid". After all, it's possible for all of the premises and the conclusion to be true in all manner of illogical arguments, such as "All men are mortal; Socrates is dead; therefore Socrates is a man." So that's not a useful property to give a name to.

This is the issue I am having. Your example has a conclusion that doesn't contradict the previous statements. It flies off into the woods, but it doesn't contradict anything.

Where as the OP's lines 4 and 5 contradict each other and then the conclusion violates the previous statement 5, primarily. I don't see the equivalence between your example and the OP. The OP's 4, 5, and 6 seem unresolvable.

 

[Speakpigeon]

a contradiction implies anything

Can someone elaborate on this particular point? It doesn't make sense to me. I feel like it must be possible for all of the premises and the conclusion to be true in order for the argument to be valid.

The arbitrary definition of the material implication, through an arbitrary truth table, gives this result that a false antecedent implies everything else. So, "A and not A" implies both that the Moon is made of green cheese and that reality just doesn't exist. That's called the paradox of the material implication because it is so obviously contrary to how we feel intuitively about it. In other words, it's just mindbogglingly untrue. Russell understood that, which is why he called this strange implication "material" rather than "logical".

The definition of validity used by Bomb#20 is that of modern mathematical "classical logic", which was initiated by Frege and Russell barely more than a century ago. But this definition isn't "customary" at all outside mathematical logic, computer sciences and probably some dark corners of philosophy. In fact, it doesn't reflect anybody's intuitive notion of validity and it doesn't reflect the customary definition of validity based on Aristotle's formal logic, which has for itself not a paltry century of poor service like modern mathematical logic does but an astonishing 2,400 years of good service. I have yet to hear of any well-known rationalist or empiricist prior to the inception of modern mathematical logic at the very end of the 19th century who would have criticised the notion of validity as based on Aristotle's syllogistic.

So, as far as I am concerned, the only customary definition of validity is that based on Aristotle. And, it does deliver the goods, namely that this idiotic argument is not valid, which is what our intuition tells us. I cannot be valid because not only the conclusion is not implied by the premises, but it is the negation of the conclusion which is implied by the premises. The premises imply that Joe is not a Squid, and at least in two different ways. So definitely not a valid argument.

Bomb#20 here says the argument is valid because the definition of validity he relies on says that the argument is valid if it is impossible for the premises to be all true and the conclusion false. Since the premises cannot be all true because they contradict each other, it is in effect impossible for the premises to be all true and the conclusion false, hence validity. A kind of trivial and stupid validity to be sure. This definition is nonetheless necessary if you don't want to let go of the material implication. Adopting validity a la Aristotle would be inconsistent with the material implication.

Hence, most people trained in formal logic as based on the material implication will tend to declare this argument valid on the strength of their commitment to modern mathematical "classical logic", denying thereby their own logical intuition that tells them the argument is not valid. That's pretty heroic. Dumb, but heroic.

Most people who are obviously untrained in formal logic will on the contrary declare the argument not valid. Most of them can't explain why exactly they say the argument is invalid, and some will just declare it "nonsense". This can be explained by the fact that they rely on their logical intuition alone. This in turn is empirical evidence that Aristotle got it right.
EB

 

[Speakpigeon]

That's not the customary definition of "valid". After all, it's possible for all of the premises and the conclusion to be true in all manner of illogical arguments, such as "All men are mortal; Socrates is dead; therefore Socrates is a man." So that's not a useful property to give a name to.

This is the issue I am having. Your example has a conclusion that doesn't contradict the previous statements. It flies off into the woods, but it doesn't contradict anything.

Where as the OP's lines 4 and 5 contradict each other and then the conclusion violates the previous statement 5, primarily. I don't see the equivalence between your example and the OP. The OP's 4, 5, and 6 seem unresolvable.

The pair of premises 3 and 5 together imply that the conclusion is false and hence the argument is not valid.

Independently, the pair of premises 1 and 4 together imply that the conclusion is false and hence the argument is not valid.

So, the conclusion is twice falsified.

Show

Oh, wait, twice falsified, double negation, not not p is equivalent to p!!! QED!!! The argument is valid!!!

Show

This was an ironic comment

EB

 

[Speakpigeon]

a contradiction implies anything

Can someone elaborate on this particular point? It doesn't make sense to me. I feel like it must be possible for all of the premises and the conclusion to be true in order for the argument to be valid.

That's not the customary definition of "valid". (...) "Valid" is conventionally defined as "It must be impossible for all of the premises to be true and the conclusion to be false."

And your definition here is the "customary" definition of validity only for modern mathematical "classical logic", computer sciences and maybe some young philosophers paid by universities to work with mathematicians and scientists. It's been "customary" in this very limited sense for only 120 years, if that.

The notion of validity issued from Aristotle has been customary for 2,400 years! And it is a notion which is intuitive and as such shared by all human beings, provided they haven't been trained like puppies to adopt the paradox of the material implication as the 11th commandement.

Does that help at all? I know it's kind of counterintuitive. You have to stare at it sideways for a bit.

You bet.
EB

 

[untermensche]

1. A is not B

2. B is not C

3. C is not A

4. D = A or B

5. D = C

Therefore: D = A

Invalid.

D cannot = A because D = C (5) and C does not = A (3)

Excellent!

Still, you've unmasked yourself as a perfectly logical person after successfully passing during so many years for a logical moron.

There are other ways to invalidate this.

Please explain.

You mean premise 1 and 4, perhaps? Which makes this argument doubly invalid.
EB

All that has happened is you understand something I easily understand.

That isn't always the case.

Like thinking the nature of an infinite series by magic changes by calling it a set.

 

[Bomb#20]

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

I understand how some people come to claim the argument is valid on the basis of the definition of validity accepted in modern mathematical "classical logic", but I find it really embarrassing that you should say here with a straight face that the conclusion "follows" from the premises.

Well, sorry to embarrass you, but the facts are what they are. You snipped the part of my post where I demonstrated that it follows, but that doesn't make the demonstration go away. I realize English isn't your first language. Do you know what the word "follow" means? Do you understand why a conclusion is said to "follow" from a set of premises when it's a logical implication of them? "Follow" means "come after". In the context of logic, it means the conclusion "comes after" the premises within a sequence of proof steps each of which is derived from earlier steps. So to deny that a conclusion "follows" from premises, when the derivation has been exhibited, is equivalent to asserting that some step in the derivation other than a premise was not constructed by applying a correct inference rule to earlier statements in the proof.

So you can smirk at my straight face all you like, but 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?

What follows from the premises here is that the conclusion is necessarily false.
EB

You say that as though only one thing were allowed to follow from any given set of premises. That's not how it works. It's okay if the conclusion you wrote in post #1 follows from the premises, and the conclusion you wrote in post #24 also follows from the premises. There's a sequence of correct deductions leading to the former, and there's a different sequence of correct deductions leading to the latter. Deal with it.

 

[Speakpigeon]

Do you know what the word "follow" means? Do you understand why a conclusion is said to "follow" from a set of premises when it's a logical implication of them?

I don't smirk, I cringe.

Here is your proof:

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.

I'm very impressed. Badly impressed, but impressed.

So, your proof takes no less than 10 lines...

Pretty hard work! Quite a job! Not exactly obvious...

So, here is mine. It's very easy to find it because it's just glaringly obvious. You can't miss it. It takes only 3 lines:

Joe is an elephant......................P5
An elephant is not a squid...........P3
Therefore, Joe is not a squid........P3, P5, (x=a) ∧ (a≠b) → (x≠b)

So, the premises contradict the conclusion.

So, now, could you explain how come you were able prove that the conclusion follows while, using apparently the same method, I proved it doesn't follow?

And how come you could find a difficult proof requiring no less than 10 lines without apparently finding first the glaringly obvious one I give here, which also contradicts your result?

Oh, but you did find it first! Your proof starts with my proof! Funny, isn't it?

So, I would surmise that you don't understand what it means that the consequence should follow from the premises.

And yet, you explained it yourself here, though, in your own words, "a conclusion is said to follow from a set of premises".

Apparently, not quite.

Your proof is evidence that you believe that if you can prove that not p doesn't follow, then p follows!!! Marvellous. Magical!!!

Well, I don't remember reading anything about that myself.

And my proof, the first three lines of your own proof, shows this is not true.

I don't smirk, I cringe.

So, amusingly, instead of just assuming the negation of the conclusion as you should have done, your proof starts with the three lines of my proof which effectively contradict the conclusion you nonetheless believe you proved:

Joe is an elephant.
An elephant is not a squid.
------------------------------
Joe is not a squid.

Joe is not a squid, see? That's not just an assumption you could just disprove, as you obviously believe, it's a consequence of the premises and as such it's here to stay no matter what!

So, you start by showing that the set of premises contradicts the conclusion and then proceed to show that the premises also contradict the negation of the conclusion. And instead of putting 2 and 2 together, you choose to forget the first three lines of your proof proving unwittingly that the conclusion is false, and just assume endearingly that proving that not p doesn't follow proves p follows.

I hope you understand that if we follow your method here, we end up contradicting ourselves. Indeed, your proof contains two proofs that contradict each other.

The way I do it, we don't end up in a contradiction.

So, the way you do it, you have to accept my proof. The way I do it, I don't have to accept your proof, because it contradicts itself.

Something tells me, you're not going to understand, even though you explained it yourself here, in your own words, "a conclusion is said to follow from a set of premises".

Please, do me a favour. Take your own words seriously.
EB

 

[Bomb#20]

I don't smirk, I cringe. ...
Please, do me a favour. Take your own words seriously.

Your post is a perfect storm of ignorance and arrogance. It is the Dunning-Kruger effect in action.

Joe is an elephant......................P5
An elephant is not a squid...........P3
Therefore, Joe is not a squid........P3, P5, (x=a) ∧ (a≠b) → (x≠b)

So, the premises contradict the conclusion.

So, now, could you explain how come you were able prove that the conclusion follows while, using apparently the same method, I proved it doesn't follow?

No you didn't. You proved the negation of the conclusion follows. Only in your amateurish imagination is that the same thing as proving the conclusion doesn't follow. You're making rookie mistakes.

And how come you could find a difficult proof requiring no less than 10 lines without apparently finding first the glaringly obvious one I give here, which also contradicts your result?

Oh, but you did find it first! Your proof starts with my proof! Funny, isn't it?

Yeah, pretty funny. So why did you claim I apparently didn't first find the glaringly obvious one you give here? You really need to fact-check the things you say about other people.

So, I would surmise that you don't understand what it means that the consequence should follow from the premises.

I'm sure you would. You're in the habit of surmising things you don't have a logical basis for.

Your proof is evidence that you believe that if you can prove that not p doesn't follow, then p follows!!!

No it isn't. You made that up out of whole cloth. At no point in my proof did I say anything equivalent to "not p doesn't follow". In fact, I said not p follows. In fact, that was the very first inference in my proof. In fact, you quoted it back to me. You really need to fact-check the things you say about other people.

So, amusingly, instead of just assuming the negation of the conclusion as you should have done,

As I "should have done"?!? You say that as though only one logical proof can be constructed from a given set of premises. When A implies B there are usually many many ways to write a proof that gets from A to B. "Think for yourself, and let others enjoy the privilege to do so, too."

your proof starts with the three lines of my proof which effectively contradict the conclusion you nonetheless believe you proved:

Joe is an elephant.
An elephant is not a squid.
------------------------------
Joe is not a squid.

Joe is not a squid, see? That's not just an assumption you could just disprove, as you obviously believe, it's a consequence of the premises and as such it's here to stay no matter what!

Where on earth do you imagine I indicated it's an assumption? Look again. See that line of hyphens I wrote above it? I clearly marked it as a consequence. You just decided I believe it's an assumption, based on your own prejudices, because you aren't very good at this.

So, you start by showing that the set of premises contradicts the conclusion and then proceed to show that the premises also contradict the negation of the conclusion.

Yes, exactly. The set of premises prove both the conclusion and the negation of the conclusion. Such is life.

And instead of putting 2 and 2 together, you choose to forget the first three lines of your proof proving unwittingly that the conclusion is false, and just assume endearingly that proving that not p doesn't follow proves p follows.

I understand that condescension is a way of life with you, but save it for when you're right. At no point did I assume that proving that not p doesn't follow proves p follows, and you have zero reason to think I did. You really need to fact-check the things you say about other people.

I hope you understand that if we follow your method here, we end up contradicting ourselves. Indeed, your proof contains two proofs that contradict each other.

Your premises contradict each other.

The way I do it, we don't end up in a contradiction.

The way you do it? You mean, "P5, P3, therefore not C.", simply leaving out three premises? What, are P5 and P3 more premisy than your other premises? What, when conflicting proofs can be constructed from the same set of premises, whichever one you like better wins? Did you read a logic textbook that told you that was a legitimate form of deductive reasoning?

So, the way you do it, you have to accept my proof. The way I do it, I don't have to accept your proof, because it contradicts itself.

All proofs from contradictory premises contradict themselves. Garbage in, garbage out. But both proofs are logical. I have to accept your proof because I'm logical. You don't have to accept my proof because you're not logical. Nobody has to accept any proof. People are allowed to be illogical. Suit yourself.

Please, do me a favour. Take your own words seriously.

Please do me a favor. Stop making false claims about me.

Oh, one more thing. There was a line from my post you snipped. For your convenience, here it is again.

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?

<crickets>

 

[Bomb#20]

That's not the customary definition of "valid". (...) "Valid" is conventionally defined as "It must be impossible for all of the premises to be true and the conclusion to be false."

And your definition here is the "customary" definition of validity only for modern mathematical "classical logic", computer sciences and maybe some young philosophers paid by universities to work with mathematicians and scientists. It's been "customary" in this very limited sense for only 120 years, if that.

The notion of validity issued from Aristotle has been customary for 2,400 years! And it is a notion which is intuitive and as such shared by all human beings, provided they haven't been trained like puppies to adopt the paradox of the material implication as the 11th commandement.

Where on earth do you imagine you see me, at any point in my arguments upthread, relying on material implication?

You keep reciting "2,400 years" like a mantra, as though 19th-century logicians' transition from Aristotelian logic to predicate calculus were a fashion trend. It was progress. Mathematicians switched away from using Aristotelian logic for exactly the same reason we switched from Euclid's venerable 2,000-year-old compass-and-straightedge constructions to Descartes' analytical geometry: because it's a more powerful proof system. There are clearly correct logical inferences that Aristotelian logic is too bloody weak to generate. "Daisy is one of my farm animals. All my livestock are cows or horses. All cows have hooves. All horses have hooves. Therefore, Daisy has hooves." Do that using Aristotle's syllogisms. It's trivial in predicate calculus.

 

[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.

 

[Speakpigeon]

<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

 

[Speakpigeon]

Your post is a perfect storm of ignorance and arrogance. It is the Dunning-Kruger effect in action.

So, the premises contradict the conclusion.

So, now, could you explain how come you were able prove that the conclusion follows while, using apparently the same method, I proved it doesn't follow?

No you didn't. You proved the negation of the conclusion follows. Only in your amateurish imagination is that the same thing as proving the conclusion doesn't follow. You're making rookie mistakes.

And how come you could find a difficult proof requiring no less than 10 lines without apparently finding first the glaringly obvious one I give here, which also contradicts your result?

Oh, but you did find it first! Your proof starts with my proof! Funny, isn't it?

Yeah, pretty funny. So why did you claim I apparently didn't first find the glaringly obvious one you give here? You really need to fact-check the things you say about other people.

So, I would surmise that you don't understand what it means that the consequence should follow from the premises.

I'm sure you would. You're in the habit of surmising things you don't have a logical basis for.

Your proof is evidence that you believe that if you can prove that not p doesn't follow, then p follows!!!

No it isn't. You made that up out of whole cloth. At no point in my proof did I say anything equivalent to "not p doesn't follow". In fact, I said not p follows. In fact, that was the very first inference in my proof. In fact, you quoted it back to me. You really need to fact-check the things you say about other people.

So, amusingly, instead of just assuming the negation of the conclusion as you should have done,

As I "should have done"?!? You say that as though only one logical proof can be constructed from a given set of premises. When A implies B there are usually many many ways to write a proof that gets from A to B. "Think for yourself, and let others enjoy the privilege to do so, too."

your proof starts with the three lines of my proof which effectively contradict the conclusion you nonetheless believe you proved:

Joe is an elephant.
An elephant is not a squid.
------------------------------
Joe is not a squid.

Joe is not a squid, see? That's not just an assumption you could just disprove, as you obviously believe, it's a consequence of the premises and as such it's here to stay no matter what!

Where on earth do you imagine I indicated it's an assumption? Look again. See that line of hyphens I wrote above it? I clearly marked it as a consequence. You just decided I believe it's an assumption, based on your own prejudices, because you aren't very good at this.

So, you start by showing that the set of premises contradicts the conclusion and then proceed to show that the premises also contradict the negation of the conclusion.

Yes, exactly. The set of premises prove both the conclusion and the negation of the conclusion. Such is life.

And instead of putting 2 and 2 together, you choose to forget the first three lines of your proof proving unwittingly that the conclusion is false, and just assume endearingly that proving that not p doesn't follow proves p follows.

I understand that condescension is a way of life with you, but save it for when you're right. At no point did I assume that proving that not p doesn't follow proves p follows, and you have zero reason to think I did. You really need to fact-check the things you say about other people.

I hope you understand that if we follow your method here, we end up contradicting ourselves. Indeed, your proof contains two proofs that contradict each other.

Your premises contradict each other.

The way I do it, we don't end up in a contradiction.

The way you do it? You mean, "P5, P3, therefore not C.", simply leaving out three premises? What, are P5 and P3 more premisy than your other premises? What, when conflicting proofs can be constructed from the same set of premises, whichever one you like better wins? Did you read a logic textbook that told you that was a legitimate form of deductive reasoning?

So, the way you do it, you have to accept my proof. The way I do it, I don't have to accept your proof, because it contradicts itself.

All proofs from contradictory premises contradict themselves. Garbage in, garbage out. But both proofs are logical. I have to accept your proof because I'm logical. You don't have to accept my proof because you're not logical. Nobody has to accept any proof. People are allowed to be illogical. Suit yourself.

Please, do me a favour. Take your own words seriously.

Please do me a favor. Stop making false claims about me.

Oh, one more thing. There was a line from my post you snipped. For your convenience, here it is again.

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?

<crickets>

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?

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.
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

 

[Angra Mainyu]

Your post is a perfect storm of ignorance and arrogance. It is the Dunning-Kruger effect in action.


No you didn't. You proved the negation of the conclusion follows. Only in your amateurish imagination is that the same thing as proving the conclusion doesn't follow. You're making rookie mistakes.


Yeah, pretty funny. So why did you claim I apparently didn't first find the glaringly obvious one you give here? You really need to fact-check the things you say about other people.

So, I would surmise that you don't understand what it means that the consequence should follow from the premises.

I'm sure you would. You're in the habit of surmising things you don't have a logical basis for.

Your proof is evidence that you believe that if you can prove that not p doesn't follow, then p follows!!!

No it isn't. You made that up out of whole cloth. At no point in my proof did I say anything equivalent to "not p doesn't follow". In fact, I said not p follows. In fact, that was the very first inference in my proof. In fact, you quoted it back to me. You really need to fact-check the things you say about other people.

So, amusingly, instead of just assuming the negation of the conclusion as you should have done,

As I "should have done"?!? You say that as though only one logical proof can be constructed from a given set of premises. When A implies B there are usually many many ways to write a proof that gets from A to B. "Think for yourself, and let others enjoy the privilege to do so, too."

your proof starts with the three lines of my proof which effectively contradict the conclusion you nonetheless believe you proved:

Joe is an elephant.
An elephant is not a squid.
------------------------------
Joe is not a squid.

Joe is not a squid, see? That's not just an assumption you could just disprove, as you obviously believe, it's a consequence of the premises and as such it's here to stay no matter what!

Where on earth do you imagine I indicated it's an assumption? Look again. See that line of hyphens I wrote above it? I clearly marked it as a consequence. You just decided I believe it's an assumption, based on your own prejudices, because you aren't very good at this.

So, you start by showing that the set of premises contradicts the conclusion and then proceed to show that the premises also contradict the negation of the conclusion.

Yes, exactly. The set of premises prove both the conclusion and the negation of the conclusion. Such is life.

And instead of putting 2 and 2 together, you choose to forget the first three lines of your proof proving unwittingly that the conclusion is false, and just assume endearingly that proving that not p doesn't follow proves p follows.

I understand that condescension is a way of life with you, but save it for when you're right. At no point did I assume that proving that not p doesn't follow proves p follows, and you have zero reason to think I did. You really need to fact-check the things you say about other people.

I hope you understand that if we follow your method here, we end up contradicting ourselves. Indeed, your proof contains two proofs that contradict each other.

Your premises contradict each other.

The way I do it, we don't end up in a contradiction.

The way you do it? You mean, "P5, P3, therefore not C.", simply leaving out three premises? What, are P5 and P3 more premisy than your other premises? What, when conflicting proofs can be constructed from the same set of premises, whichever one you like better wins? Did you read a logic textbook that told you that was a legitimate form of deductive reasoning?

So, the way you do it, you have to accept my proof. The way I do it, I don't have to accept your proof, because it contradicts itself.

All proofs from contradictory premises contradict themselves. Garbage in, garbage out. But both proofs are logical. I have to accept your proof because I'm logical. You don't have to accept my proof because you're not logical. Nobody has to accept any proof. People are allowed to be illogical. Suit yourself.

Please, do me a favour. Take your own words seriously.

Please do me a favor. Stop making false claims about me.

Oh, one more thing. There was a line from my post you snipped. For your convenience, here it is again.

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?

<crickets>

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?

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.
EB

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

 

[Angra Mainyu]

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.