Improved Squid Argument

[Angra Mainyu]

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.

Then you do not accept weakening. Weakening means that the addition of premises to a valid argument cannot make it invalid.

Next you're going to claim that true is false and false is true.

That is simply an insult, uttered with reckless disregard from the truth.

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.

First, by that criterion, many are indeed mistaken, because either those who say that they are not valid are mistaken, or those who say that are meaningless are mistaken (or both, but at least one of the two answers is mistaken, since the two answers are mutually incompatible).

Second, that is not what I said. As I already explained, colloquial language does not usually need a fine-grained classification of deductive arguments, so maybe the same word can properly be used for an argument that has false premises and one in which the conclusion does not follow from the premises. Some posters might be using "invalid" to encompass both, whereas others might be using more fine-grained vocabulary, and making a distinction, and then making a logical mistake.

If, instead of asking whether the argument is valid, you asked whether the conclusion follows from the premises, that would provide more information about whether they are making logical errors or not on the basis of their answers. Still, it would be better to talk to them to get, in each particular case, whether they are mistaken, or whether it's a terminology issue.

That aside, in order to assess the evidence, one has to take a look not merely at the votes, but at what happened later.

For example, I convinced fast that the argument is valid. So, that vote should not count as you are counting it. People are capable of learning, and some do learn.

As for Cheerful Charlie, I grant I was unable to persuade him, unfortunately, but reading his posts clearly shows that he is making mistakes.

As for bigfield (who voted 'invalid') and Tom Sawyer (who voted 'doesn't make sense'), I did not have the opportunity to reply to them and try to persuade them, as they did not post in the thread explaining why they made the assessments that they made, so they don't think it's valid in the sense in which they understand the word 'valid', but we do not know what that sense is. In particular, we do not know whether bigfield believes that the conclusion does not follow from the premises.

 

[Angra Mainyu]

No elephant is a squid.
Joe is an elephant.

Joe then cannot be a squid.

Therefore, Joe is a squid
Any sort of "logic" that can conclude Joe is a squid is obviouslt flawed.

Let me try to persuade you otherwise.

Argument 3:

P1: No giraffe is an elephant.
P2: Joe is either a squid or a giraffe.
P3: Joe is an elephant.
C: Therefore, Joe is a squid.​

Is that valid?

Consider, for example, the following argument:

Argument 4:

P1: No giraffe is a mollusc.
P2: Joe is either a squid or a giraffe.
P3: Joe is an mollusc.
C: Therefore, Joe is a squid.​

If you take a look, you will see that Argument 4 and Argument 3 have exactly the same form. Before I go on, I would like to ask you whether you think Argument 3 and Argument 4 are both valid, or neither, or only one (depending on the answer, I might or might not try to convince you that the original OP argument is valid).

Joe is an elephant.
No elephant can be a squid.

Therefore Joe is either a giraffe or a squid is invalid.

Joe is defined as an elephant.

That is not what I asked you, though. Please take a look at the arguments above. Are they valid? More to the point, in Argument 3 and in Argument 4, does the conclusion follow from the premises?

 

[fast]

If A, then B (which is true)
A (which is true)
Some nonconflicting P (which is false)
Conclusion: B

Argument is valid
Weakening is present
Argument accepted as valid by speak pigeon— but wouldn’t if P was conflicting
Argument unsound —but only because a premise is false —despite P’s irrelevancy to validity

There doesn’t seem to be any important reason to consider the truth or falsity of an irrelevant nonconflicting premise for either validity or soundness. The truth of the conclusion is preserved regardless of the truth or falsity of the nonconflicting and irrelevant premise.

 

[Speakpigeon]

If A, then B (which is true)
A (which is true)
Some nonconflicting P (which is false)
Conclusion: B

Argument is valid
Weakening is present
Argument accepted as valid by speak pigeon— but wouldn’t if P was conflicting
Argument unsound —but only because a premise is false —despite P’s irrelevancy to validity

There doesn’t seem to be any important reason to consider the truth or falsity of an irrelevant nonconflicting premise for either validity or soundness. The truth of the conclusion is preserved regardless of the truth or falsity of the nonconflicting and irrelevant premise.

That's correct. Most of the time, adding a premise or two will preserve the validity of the conclusion. However, this is tricky. It is not necessarily particularly obvious that the added premise conflicts with the others. So, in effect, each time you add a premise, you have to check that the argument is still valid. Thus, for all practical purposes, there's really no benefit in the idea that adding a premise may not affect the validity of th conclusion.

Further, the added premise may be self-contradictory. In this case, the conclusion is not valid (indeed, there's no conclusion that would be valid).
EB

 

[Speakpigeon]

First, by that criterion, many are indeed mistaken, because either those who say that they are not valid are mistaken, or those who say that are meaningless are mistaken (or both, but at least one of the two answers is mistaken, since the two answers are mutually incompatible).

Unless...

Your logic is failing you here. Both are right.

No surprise here.
EB

 

[Speakpigeon]

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.

You understand that if Joe is an elephant, and that he is a squid, and that an elephant is not squid, then Joe is necessarily squid and nothing else?! And indeed also is an elephant and nothing else... And indeed a cup of tea and nothing else. And indeed Donald Trump himself. And...

Wait.

I know Jimmy;
I don't know Jimmy;
Therefore, I know for sure that Jimmy is a Nazi and thus I can go on the Internet repeating that the conclusion that I know that Jimmy is a Nazi is valid.

Do you understand that to the point that you agree it's valid?!
EB

 

[Angra Mainyu]

First, by that criterion, many are indeed mistaken, because either those who say that they are not valid are mistaken, or those who say that are meaningless are mistaken (or both, but at least one of the two answers is mistaken, since the two answers are mutually incompatible).

Unless...

Your logic is failing you here. Both are right.

No surprise here.
EB

No, of course my logic is not failing. If some people say the argument does not make sense, and others say it is invalid, then one of them is correct, and the others are not - assuming they mean the same; of course, which you (given your assumption of a shared common understanding of "valid") do believe, so I can go with your that. In reality, they might not mean the same. But for that matter, some of those who say "invalid" might mean "unsound".

Also, keep in mind that those voting "invalid" do not believe the answer is "doesn't make sense" (otherwise, they would have voted that!), and the same goes in the other direction.

 

[Angra Mainyu]

Okay, I think I understand this madness.

You understand that if Joe is an elephant, and that he is a squid, and that an elephant is not squid, then Joe is necessarily squid and nothing else?! And indeed also is an elephant and nothing else... And indeed a cup of tea and nothing else. And indeed Donald Trump himself. And...

Wait.

I know Jimmy;
I don't know Jimmy;
Therefore, I know for sure that Jimmy is a Nazi and thus I can go on the Internet repeating that the conclusion that I know that Jimmy is a Nazi is valid.

Do you understand that to the point that you agree it's valid?!
EB

Obviously, the conclusion that Jimmy is a Nazi can be drawn from many premises, which do not need to be contradictory. For example:

P1: Either Jimmy is a Nazi, or it is not the case that 2+2=4.
P2: 2+2=4.
C: Jimmy is a Nazi.

Obviously, that argument is valid, and has no contradictory premises. So, the fact that one can derive the conclusion that Jimmy is a Nazi from some premises, without making any logical errors, has nothing to do with whether contradictions imply everything.
Also, obviously, the fact that there are infinitely many valid deductive arguments with the conclusion "Jimmy is a Nazi" do not provide any information about Jimmy, and it would be immoral to go around promoting the idea that Jimmy is a Nazi just because of that. It is also immoral to deliberately engage in equivocation, using the fact that the word "valid" has more than one meaning to then say that it's a valid conclusion that Jimmy is a Nazi, which taken out of context will likely be interpreted as saying something about Jimmy, not just stating a trivial fact about deductive arguments.

 

[Jimmy Higgins]

Okay, I think I understand this madness.

You understand that if Joe is an elephant, and that he is a squid, and that an elephant is not squid, then Joe is necessarily squid and nothing else?! And indeed also is an elephant and nothing else... And indeed a cup of tea and nothing else. And indeed Donald Trump himself. And...

Wait.

I know Jimmy;
I don't know Jimmy;
Therefore, I know for sure that Jimmy is a Nazi and thus I can go on the Internet repeating that the conclusion that I know that Jimmy is a Nazi is valid.

Do you understand that to the point that you agree it's valid?!
EB

As long as you show your work, I’m fine with that.

 

[Angra Mainyu]

Incidentally, deductions with contradictory premises are very common in mathematics. For example, we want to prove that P is false. So, we assume P is true. From that assumption and some premises P1,...Pn that we know are true, we derive a contradiction (without making any logical errors). Now, note that in order to derive a contradiction from P1,...Pn and P - again without making any logical errors - the argument had to have an inconsistent set of premises. In other words, arguments with contradictory premises are very common in mathematics.

For example, common proofs of this sort are a proof that there are infinitely many primes, a proof that the square root of two is not a rational number, a the proof that there is no least positive rational number, etc. This is not to say that all of these facts can only be proven in this manner. But it is common to prove them (and many others) in this manner.

Examples:

https://www.usna.edu/Users/math/allman/_files/FamousProofs.pdf

Incidentally, also, here's a webpage that uses terminology I don't like, but apart from that, makes some nice points about the proof of the irrationality of the square root of two in intuitionistic logic:

http://math.andrej.com/2010/03/29/proof-of-negation-and-proof-by-contradiction/

 

[Speakpigeon]

First, by that criterion, many are indeed mistaken, because either those who say that they are not valid are mistaken, or those who say that are meaningless are mistaken (or both, but at least one of the two answers is mistaken, since the two answers are mutually incompatible).

Unless...

Your logic is failing you here. Both are right.

No surprise here.
EB

No, of course my logic is not failing. If some people say the argument does not make sense, and others say it is invalid, then one of them is correct, and the others are not - assuming they mean the same; of course, which you (given your assumption of a shared common understanding of "valid") do believe, so I can go with your that. In reality, they might not mean the same. But for that matter, some of those who say "invalid" might mean "unsound".

Also, keep in mind that those voting "invalid" do not believe the answer is "doesn't make sense" (otherwise, they would have voted that!), and the same goes in the other direction.

No wonder you don't understand logic.
EB

 

[Speakpigeon]

Incidentally, deductions with contradictory premises are very common in mathematics. For example, we want to prove that P is false. So, we assume P is true. From that assumption and some premises P1,...Pn that we know are true, we derive a contradiction (without making any logical errors). Now, note that in order to derive a contradiction from P1,...Pn and P - again without making any logical errors - the argument had to have an inconsistent set of premises. In other words, arguments with contradictory premises are very common in mathematics.

For example, common proofs of this sort are a proof that there are infinitely many primes, a proof that the square root of two is not a rational number, a the proof that there is no least positive rational number, etc. This is not to say that all of these facts can only be proven in this manner. But it is common to prove them (and many others) in this manner.

Examples:

https://www.usna.edu/Users/math/allman/_files/FamousProofs.pdf

Incidentally, also, here's a webpage that uses terminology I don't like, but apart from that, makes some nice points about the proof of the irrationality of the square root of two in intuitionistic logic:

http://math.andrej.com/2010/03/29/proof-of-negation-and-proof-by-contradiction/

The two links you give here are about proof by contradiction, or reductio ad absurdum.

Proof by contradiction basically says A implies not A, therefore not A.

Also possible, A implies B and not B; therefore not A.

In both cases, there are no contradictory premises.

Proof by contradiction has absolutely nothing to do with contradictory premises.

You really don't understand much about logic.
EB

 

[Speakpigeon]

Okay, I think I understand this madness.

You understand that if Joe is an elephant, and that he is a squid, and that an elephant is not squid, then Joe is necessarily squid and nothing else?! And indeed also is an elephant and nothing else... And indeed a cup of tea and nothing else. And indeed Donald Trump himself. And...

Wait.

I know Jimmy;
I don't know Jimmy;
Therefore, I know for sure that Jimmy is a Nazi and thus I can go on the Internet repeating that the conclusion that I know that Jimmy is a Nazi is valid.

Do you understand that to the point that you agree it's valid?!
EB

As long as you show your work, I’m fine with that.

Obfuscation says it all.
EB

 

[Speakpigeon]

Four "Not valid" votes and two "Doesn't make sense" votes against only one "Valid" one.
EB

 

[fast]

If A, then not A
A
Therefore, not A

Valid
Unsound

A
Not A
Therefore, A

Valid
Unsound

Those are my answers via how taught


If I adopt speak pigeons notion of “valid”, then on the first argument, I’m shouting “invalid” by the time I read through the first premise. On the second argument, it won’t be until I read the second premise.

He is okay with a claim of A even if it’s truth value is unknown (as far as validity is concerned), but as soon as a contradiction pops up, it’s full stop and the notion (his notion) of ever calling the argument valid is nonsensical.

It’s no wonder we’re gonna have more “not valid” votes. Until we’re taught to set aside what drives us to deny validity, we’re more apt to do so.

A and not A are contradictory. Remember what they say about logical possibilities. Anything is logically possible so long as it’s not a contradiction. So, any claim of “A and not A” is not only not possible, it’s indeed logically impossible.

So, we grasp instantly that the conclusion of

P1) if A, then not A
P2) A

Is going to be unsound, for it’s impossible for P1 to be true.

But awe, impossibly “true”. That’s why it’s unsound. For an argument to be unsound, it has to either have a false premise or be invalid.

Why the hell isnt it valid?
If A, then B
If A
Therefore B

It’s valid until what, I tell you B is A in sheep’s clothing.

We are urged to refrain from allowing the truth of premises to have an impact on our perception of an arguments validity.

A
B
Therefore C

Has no stepping stones

Well, unless there’s a lot of wool :/)

 

[Jimmy Higgins]

1) Speakpigeon’s squid argument is not valid.
2) Speakpigeon’s squid argument is valid.
C) Speakpigeon’s squid argument is valid.

 

[fast]

1) Speakpigeon’s squid argument is not valid.
2) Speakpigeon’s squid argument is valid.
C) Speakpigeon’s squid argument is valid.

Your argument is valid

 

[A Toy Windmill]

If A, then not A
A
Therefore, not A

Valid
Unsound

If I adopt speak pigeons notion of “valid”, then on the first argument, I’m shouting “invalid” by the time I read through the first premise.

Speakpigeon also wrote:

Proof by contradiction basically says A implies not A, therefore not A.

Proof by contradiction has absolutely nothing to do with contradictory premises.

So maybe even if you adopt Speakpigeon's notion of "valid", then on the first argument, the first premise is fine, and it's only when you get to the second that you have a contradiction.

But I think it's best not to assume there is anything consistent going on in Speakpigeon's mind.

 

[fast]

Speakpigeon also wrote:

Proof by contradiction basically says A implies not A, therefore not A.

Proof by contradiction has absolutely nothing to do with contradictory premises.

So maybe even if you adopt Speakpigeon's notion of "valid", then on the first argument, the first premise is fine, and it's only when you get to the second that you have a contradiction.

But I think it's best not to assume there is anything consistent going on in Speakpigeon's mind.

I recall reading that. I wasn’t quite sure what to make of it, as I’m not really sure what a proof is. I’ve heard of them; I just don’t have a good grasp of how they interrelate like I am with validity and soundness.

I just assumed he was making a distinction between a contradiction and the proof of one. I’m guessing there can be a contradiction without there also being ‘a’ proof of one—not to say a contradiction would not be proof (or evidence) of itself, so I’m speculating there’s a difference between proof and ‘a’ proof—as if it’s some thing that can be written and recognized as such.

Also, it’s interrelatedness escapes me. Tell a kid we’re going to the ice-cream shop (like telling an adult an argument is valid) (or like telling a husband that the wife went with a friend so the car is in the yard). All necessary but insufficient for the guarentee of happiness. The kid is all excited—until he learns it’s 3:00am and the ice-cream shop is closed. The adult is thrilled to learn the argument is valid—but then let down to learn it’s unsound because a premise is false, etc. the husband is excited that he has a vehicle in case he needs to go somewhere—until he goes to crank it and learns there’s absolutely no gas in it.

Hence, i don’t know the kind of happiness having a proof brings, even if I did know what it was and looked like. For all I know, it might be like telling me we’re going to the ice-cream shop, that an argument is definitely valid, or that a vehicle is there for me to get in anytime I want.

 

[Angra Mainyu]

Incidentally, deductions with contradictory premises are very common in mathematics. For example, we want to prove that P is false. So, we assume P is true. From that assumption and some premises P1,...Pn that we know are true, we derive a contradiction (without making any logical errors). Now, note that in order to derive a contradiction from P1,...Pn and P - again without making any logical errors - the argument had to have an inconsistent set of premises. In other words, arguments with contradictory premises are very common in mathematics.

For example, common proofs of this sort are a proof that there are infinitely many primes, a proof that the square root of two is not a rational number, a the proof that there is no least positive rational number, etc. This is not to say that all of these facts can only be proven in this manner. But it is common to prove them (and many others) in this manner.

Examples:

https://www.usna.edu/Users/math/allman/_files/FamousProofs.pdf

Incidentally, also, here's a webpage that uses terminology I don't like, but apart from that, makes some nice points about the proof of the irrationality of the square root of two in intuitionistic logic:

http://math.andrej.com/2010/03/29/proof-of-negation-and-proof-by-contradiction/

The two links you give here are about proof by contradiction, or reductio ad absurdum.

Proof by contradiction basically says A implies not A, therefore not A.

Also possible, A implies B and not B; therefore not A.

In both cases, there are no contradictory premises.

Proof by contradiction has absolutely nothing to do with contradictory premises.

You really don't understand much about logic.
EB

No, you do not understand what you are saying. At all. Take a look at the links. In order to prove that the square root of two is not a quotient of integers, they assume it is, and from that assumption and other (known) premises, they derive a contradiction. Obviously, the premises together were contradictory premises, otherwise they could not have derived a contradiction! I gave an argument with contradictory premises in another thread, for example. It's a standard argument. Even if you do not realize that, your claims imply it's invalid.

There is a difference between assuming P to prove ¬P, and assuming ¬P to prove P (a difference that matters in intuitionistic but not in classical mathematical logic). But in any event, those are all instances of deductions with contradictory premises.