Improved Squid Argument

[Speakpigeon]

Here is the Squid argument again, with improved wording following the suggestion from a specialist in mathematical logic (A Toy Windmill).

No squid is a giraffe
No giraffe is an elephant
No elephant is a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Thank you to vote to say whether you think the argument is valid or not.

Thanks for your answers.

Please no comment without vote.
EB

 

[Koyaanisqatsi]

Truth versus validity in mathematical proof

 

[Speakpigeon]

This is not a thread about mathematical logic.

The argument is couched in ordinary language so that everybody can understand the meaning of the argument.

And the question is explicitly that of the validity of the argument, and not whether the premises or the conclusion are actually true.

Let posters decide for themselves whether they can arrive at a position merely from reading the argument.

People who don't feel confident they can decide on validity can reply that they don't know.
EB

 

[Koyaanisqatsi]

This is not a thread about mathematical logic.

?

Here is the Squid argument again, with improved wording following the suggestion from a specialist in mathematical logic

Regardless, the paper I linked to is not about mathematical logic either, per se. It's about "truth vs validity." You seem to have a problem conflating truth and validity or otherwise not understanding the purpose of validity.

To whit:

The argument is couched in ordinary language so that everybody can understand the meaning of the argument.

"The meaning of the argument," ironically, has nothing to do with whether or not it's valid and "ordinary language" likewise has nothing to do with whether or not the argument's form is valid.

Hence my posting a paper on the difference between "validity" and "truth."

And the question is explicitly that of the validity of the argument, and not whether the premises or the conclusion are actually true.

People who don't feel confident they can decide on validity can reply that they don't know.

And that will establish what exactly? Those who understand the concept of validity are those who understand the concept of validity. Those who do not are those who do not.

So what's the point?

 

[Speakpigeon]

Sorry, I'm not interested in your constant misrepresentations and hysteria in your comments. Just answer the poll.
EB

 

[Koyaanisqatsi]

Sorry, I'm not interested in your constant misrepresentations and hysteria in your comments.

Grow up.

 

[Speakpigeon]

Sorry, I'm not interested in your constant misrepresentations and hysteria in your comments.

Grow up.

Just answer the poll.
EB

 

[fast]

No squid is a giraffe
No giraffe is an elephant
No elephant is a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Awe, let me see if I can work this out. Gonna skip all the things starting with “no” because it just overwhelms me. All after I got used to the other way too—big meany.

So, starting with Joe is either a squid or a giraffe. Excuse me while I commit that to memory.
Joe is either a squid or giraffe.
Squid or giraffe
Squid or giraffe

I think I got it. Joe is either one or Joe is the other.
Squid or giraffe.

Gonna peek at the conclusion: Joe is a squid.
Hmmm, sounds consistent. Seems like I need to find something that disputes Joe being a giraffe.

What do I know? Scratch that. Been yelled at for that already. What’s given (that doesn’t hurt my head)?: Joe is an elephant. Great, now I just need to use that information to see if I can weed out him being a giraffe, so I’m looking for an elephant/giraffe connection.

No giraffe is an elephant! I think that works. I’m still wobbly because the turn of phrase “does that also mean no elephant is a giraffe?” Probably not, so I need to tread carefully.

Hmmm. Given “he’s an elephant,” ... ... I had to pause because somebody sprinkled disturbing premises into the mix which caused a spiral of a head exploding contradiction to sprout.

Okay, i didn’t get to it being valid the normal way, but using the contradictory potion method, I did arrive at the conclusion Joe is a bobcat (based on the idea that anything follows from a contradiction.) Since it follows (as does everything) and the conclusion is something out of everything, the argument is valid.

 

[Angra Mainyu]

No squid is a giraffe
No giraffe is an elephant
No elephant is a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Awe, let me see if I can work this out. Gonna skip all the things starting with “no” because it just overwhelms me. All after I got used to the other way too—big meany.

So, starting with Joe is either a squid or a giraffe. Excuse me while I commit that to memory.
Joe is either a squid or giraffe.
Squid or giraffe
Squid or giraffe

I think I got it. Joe is either one or Joe is the other.
Squid or giraffe.

Gonna peek at the conclusion: Joe is a squid.
Hmmm, sounds consistent. Seems like I need to find something that disputes Joe being a giraffe.

What do I know? Scratch that. Been yelled at for that already. What’s given (that doesn’t hurt my head)?: Joe is an elephant. Great, now I just need to use that information to see if I can weed out him being a giraffe, so I’m looking for an elephant/giraffe connection.

No giraffe is an elephant! I think that works. I’m still wobbly because the turn of phrase “does that also mean no elephant is a giraffe?” Probably not, so I need to tread carefully.

Hmmm. Given “he’s an elephant,” ... ... I had to pause because somebody sprinkled disturbing premises into the mix which caused a spiral of a head exploding contradiction to sprout.

Okay, i didn’t get to it being valid the normal way, but using the contradictory potion method, I did arrive at the conclusion Joe is a bobcat (based on the idea that anything follows from a contradiction.) Since it follows (as does everything) and the conclusion is something out of everything, the argument is valid.

It turns out that you did not need the contradiction.

Let me show you why: Suppose you have the following argument:

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.​

Is that valid?

If you take a look, you will see that Argument 4 and Argument 3 have exactly the same form.

 

[fast]

It turns out that you did not need the contradiction.

Let me show you why: Suppose you have the following argument:

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?

No giraffe is an elephant. Of all the giraffes out in the world there are, none are elephants. I’m not espousing—just going with the stated premise. No giraffe is an elephant. Well, Joe is an elephant (P3). What does that tell me? A little thinking and I’ve pretty much ruled out joe being a giraffe. After all, no giraffe is an elephant and Joe is. Seems to me Joe ain’t no giraffe. Ooh, he’s either a squid or a giraffe and given that he’s not a giraffe, I’m left to conclude he’s a squid. Sure enough, that’s what the conclusion says, so the argument is valid because the information in it (and no hidden stuff to consider) leads me to just what the conclusion says.

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.​

Is that valid?

If you take a look, you will see that Argument 4 and Argument 3 have exactly the same form.

Yeah, valid.

 

[fast]

It’s not working for me on his argument.

 

[ruby sparks]

It turns out that you did not need the contradiction.

Let me show you why: Suppose you have the following argument:

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?

No giraffe is an elephant. Of all the giraffes out in the world there are, none are elephants. I’m not espousing—just going with the stated premise. No giraffe is an elephant. Well, Joe is an elephant (P3). What does that tell me? A little thinking and I’ve pretty much ruled out joe being a giraffe. After all, no giraffe is an elephant and Joe is. Seems to me Joe ain’t no giraffe. Ooh, he’s either a squid or a giraffe and given that he’s not a giraffe, I’m left to conclude he’s a squid. Sure enough, that’s what the conclusion says, so the argument is valid because the information in it (and no hidden stuff to consider) leads me to just what the conclusion says.

Just a thought. I may not be raising a valid point......

Is it confusing that argument 3 (above) and indeed the OP argument, are using categories (hope that's the right word) that are, in the real world, mutually exclusive (Joe can't in the real world be a squid and an elephant, given the definitions of what those are)?

Does it help if we use categories that aren't mutually exclusive?

P1: No tall person is a fat person.
P2: Joe is either a black person or a tall person.
P3: Joe is a fat person.
C: Therefore, Joe is a black person.​

Or am I talking shite?

All I can say is that it is easier for me to see how that's valid, I guess.

 

[fast]

It turns out that you did not need the contradiction.

Let me show you why: Suppose you have the following argument:

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?

No giraffe is an elephant. Of all the giraffes out in the world there are, none are elephants. I’m not espousing—just going with the stated premise. No giraffe is an elephant. Well, Joe is an elephant (P3). What does that tell me? A little thinking and I’ve pretty much ruled out joe being a giraffe. After all, no giraffe is an elephant and Joe is. Seems to me Joe ain’t no giraffe. Ooh, he’s either a squid or a giraffe and given that he’s not a giraffe, I’m left to conclude he’s a squid. Sure enough, that’s what the conclusion says, so the argument is valid because the information in it (and no hidden stuff to consider) leads me to just what the conclusion says.

Just a thought. I may not be raising a valid point......

Is it confusing that argument 3 (above) and indeed the OP argument, are using categories (hope that's the right word) that are, in the real world, mutually exclusive (Joe can't in the real world be a squid and an elephant, given the definitions of what those are)?

Does it help if we use categories that aren't mutually exclusive?

P1: No tall person is a fat person.
P2: Joe is either a black person or a tall person.
P3: Joe is a fat person.
C: Therefore, Joe is a black person.​

Or am I talking shite?

All I can say is that it is easier for me to see how that's valid, I guess.

I think there’s advantages and disadvantages. One advantage is that we can more easily relate and perhaps better think it through if we do as you say; however, truth (or even soundness) is often a distraction when trying to hone in specifically on validity. Another option is to use letters, but it’s easier to use words when trying to recollect how each part fits. At any rate, just try not to let the labels (that do refer to categories) get to ya.

 

[Angra Mainyu]

Also, and there is a little thing that keeps scratching at my thoughts. It’s about Q. I never comprehend when it’s equivalent to not ~P and when it’s not.

It's not, in the context of these arguments, since it stands for any proposition you want.

It turns out that you did not need the contradiction.

Let me show you why: Suppose you have the following argument:

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?

No giraffe is an elephant. Of all the giraffes out in the world there are, none are elephants. I’m not espousing—just going with the stated premise. No giraffe is an elephant. Well, Joe is an elephant (P3). What does that tell me? A little thinking and I’ve pretty much ruled out joe being a giraffe. After all, no giraffe is an elephant and Joe is. Seems to me Joe ain’t no giraffe. Ooh, he’s either a squid or a giraffe and given that he’s not a giraffe, I’m left to conclude he’s a squid. Sure enough, that’s what the conclusion says, so the argument is valid because the information in it (and no hidden stuff to consider) leads me to just what the conclusion says.

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.​

Is that valid?

If you take a look, you will see that Argument 4 and Argument 3 have exactly the same form.

Yeah, valid.

Excellent!

So, from the premises P1: No giraffe is an elephant, P2: Joe is either a squid or a giraffe, and P3: Joe is an elephant, you can validly conclude that Joe is a squid. Great!
Now, take a look at the argument in the OP. It turns out it contains all of those three premises!. Now, it also contains more premises, but even without those extra premises (and without the contradiction stuff), just using P1, P2 and P3, you can conclude validly that Joe is a squid. You should change your vote to "valid".

(or do you think that it's possible that from some premises P1,..,Pn you validly deduce Q, but if you add more premises, then you no longer can validly deduce Q?)

 

[Cheerful Charlie]

Here is the Squid argument again, with improved wording following the suggestion from a specialist in mathematical logic (A Toy Windmill).

No squid is a giraffe
No giraffe is an elephant
No elephant is a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Thank you to vote to say whether you think the argument is valid or not.

Thanks for your answers.

Please no comment without vote.
EB

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.

 

[Angra Mainyu]

Here is the Squid argument again, with improved wording following the suggestion from a specialist in mathematical logic (A Toy Windmill).

No squid is a giraffe
No giraffe is an elephant
No elephant is a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Thank you to vote to say whether you think the argument is valid or not.

Thanks for your answers.

Please no comment without vote.
EB

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).

 

[fast]

It's not, in the context of these arguments, since it stands for any proposition you want.

No giraffe is an elephant. Of all the giraffes out in the world there are, none are elephants. I’m not espousing—just going with the stated premise. No giraffe is an elephant. Well, Joe is an elephant (P3). What does that tell me? A little thinking and I’ve pretty much ruled out joe being a giraffe. After all, no giraffe is an elephant and Joe is. Seems to me Joe ain’t no giraffe. Ooh, he’s either a squid or a giraffe and given that he’s not a giraffe, I’m left to conclude he’s a squid. Sure enough, that’s what the conclusion says, so the argument is valid because the information in it (and no hidden stuff to consider) leads me to just what the conclusion says.

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.​

Is that valid?

If you take a look, you will see that Argument 4 and Argument 3 have exactly the same form.

Yeah, valid.

Excellent!

So, from the premises P1: No giraffe is an elephant, P2: Joe is either a squid or a giraffe, and P3: Joe is an elephant, you can validly conclude that Joe is a squid. Great!
Now, take a look at the argument in the OP. It turns out it contains all of those three premises!. Now, it also contains more premises, but even without those extra premises (and without the contradiction stuff), just using P1, P2 and P3, you can conclude validly that Joe is a squid. You should change your vote to "valid".

(or do you think that it's possible that from some premises P1,..,Pn you validly deduce Q, but if you add more premises, then you no longer can validly deduce Q?)

I must have been growing weary!! Yes, I see.

 

[fast]

No squid is a giraffe
No giraffe is an elephant
No elephant is a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Validity is about finding a path to the finish line where the conclusion is the final destination.

Each premise is like a path. Consider all the paths. Each premise bolded above (if followed) will lead us to the end.

 

[fast]

Here is the Squid argument again, with improved wording following the suggestion from a specialist in mathematical logic (A Toy Windmill).

No squid is a giraffe
No giraffe is an elephant
No elephant is a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Thank you to vote to say whether you think the argument is valid or not.

Thanks for your answers.

Please no comment without vote.
EB

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.

Of course it’s flawed. It’s unsound. That is the great warning sign we should look out for with deductive arguments (whether it’s sound or unsound,) but there are some other things about arguments we can point out. For instance, whether a proposition (either in a premise or conclusion) is true. Another thing we can look at is validity. What that is exactly is in dispute. Do we go by dictionaries that explain how it’s ordinarily used, or do we use it as a technical term? When used as a technical term, we need to be careful about what it is and what it isn’t. We can have a perfectly valid argument and it still be unsound.

A) If Kansas is in the ocean, then Kansas is a squirrel.
B) Kansas is in the ocean.
Therefore C) Kansas is a squirrel

That’s valid because those two taken together leads to the conclusion.

A) If Kansas is in the ocean, then Kansas is a squirrel.
B) Kansas is in the ocean.
C) Bobby has an upset stomach
Therefore D) Kansas is a squirrel

That’s still valid. It’s like a math problem where information that is given is irrelevant. Just ignore it.

A) If Kansas is in the ocean, then Kansas is a squirrel.
B) Kansas is in the ocean.
C) Bobby has an upset stomach
D) Kansas is in space
Therefore E) Kansas is a squirrel

Obviously, if Kansas is in the ocean, then it’s not in space, but forget that. Just look to see there’s enough of the right premises to get to the conclusion —ignoring all others that merely serve to distract. A and B gets us to E, so it’s valid.

Now here’s a fun one:
A) Bobby has an upset stomach
B) bobby doesn’t have an upset stomach
Therefore C) Kansas is a squirrel.

That too is valid. Gotta love it.

You might be wondering what kind of logic allows that, as it might not always accord with what a dictionary has to say. But, it’s in the tool belt of the logician and well respected the world over. It just takes a little getting used to.

 

[fromderinside]

Gotta say it. The panda in the room. Its actually an Octopussy.