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

[Speakpigeon]

This is a poll on the logical validity of the following argument:

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

Is this argument logically valid?
Either way, why?
EB

 

[James Brown]

I don't see how Joe can be both an elephant (Line 5) and a squid (Line 6) especially if Line 3 says that an elephant is not a squid.

 

[Speakpigeon]

I don't see how Joe can be both an elephant (Line 5) and a squid (Line 6) especially if Line 3 says that an elephant is not a squid.

Sorry, your comment doesn't make sense.
EB

 

[James Brown]

I don't see how Joe can be both an elephant (Line 5) and a squid (Line 6) especially if Line 3 says that an elephant is not a squid.

Sorry, your comment doesn't make sense.
EB

Never mind. I withdraw my vote.

 

[Jimmy Higgins]

I don't see how Joe can be both an elephant (Line 5) and a squid (Line 6) especially if Line 3 says that an elephant is not a squid.

Sorry, your comment doesn't make sense.
EB

ROFL

Lines 1 to 3 say, A, B, and C are unique to each other.
Line 4 then says Joe is either A or B.
Line 5 then contradicts Line 4 by saying Joe is C.
Line 6, at this point failing turing test, concludes Joe is A.

 

[Speakpigeon]

Mathematical logic, as it is recognised by most mathematicians today as the standard method of logical calculus, says the argument is valid.

It doesn't say that the argument doesn't make sense.

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.

So, our three grownups here all in effect agree that mathematical logic doesn't make sense.

Unless anyone could articulate an explanation as to why it is not the case.
EB

 

[Speakpigeon]

I don't see how Joe can be both an elephant (Line 5) and a squid (Line 6) especially if Line 3 says that an elephant is not a squid.

Sorry, your comment doesn't make sense.
EB

Never mind. I withdraw my vote.

Sorry if you took it in bad part, but you're not entirely right of course. It doesn't make much sense but it does make sense, and it is because it makes sense that we sort of feel offended by the conclusion, me included.

This feeling is normally best expressed by saying that the argument is not valid.

But, your choice.
EB

 

[Speakpigeon]

Make sense
If something makes sense, you can understand it.

I would assume that all of you can in fact understand what the argument says and what the argument means, which is that the premises together somehow justify the truth of the conclusion.

The fact that you voted "doesn't make sense" is evidence of something like a cognitive dissonance somewhere.

I'm not psychiatrist so I won't try to go further than that, but your vote seem to chime with our Trumpestuous epoch.
EB

 

[Jimmy Higgins]

Mathematical logic, as it is recognised by most mathematicians today as the standard method of logical calculus, says the argument is valid.

It doesn't say that the argument doesn't make sense.

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.

So, our three grownups here all in effect agree that mathematical logic doesn't make sense.

Unless anyone could articulate an explanation as to why it is not the case.
EB

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.

 

[Bomb#20]

This is a poll on the logical validity of the following argument:

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

Is this argument logically valid?
Either way, why?
EB

Yes, it's valid, because the conclusion follows from the premises. (It's unsound, since at least one of the premises is false, but plenty of unsound arguments are valid.)

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.

Sorry if you took it in bad part, but you're not entirely right of course. It doesn't make much sense but it does make sense, and it is because it makes sense that we sort of feel offended by the conclusion, me included.

This feeling is normally best expressed by saying that the argument is not valid.

But, your choice.

It's best expressed by saying that the argument is not sound.

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.

It's valid in the sense that he has listed six sequential statements and the sixth logically follows from the first five. (Well, from the second through the fifth. Statement 1 was unnecessary. Statements 3 through 5 imply that statement 2 is false. So 3 through 5 plus 2 are mutually contradictory; and a contradiction implies anything, even that an elephant is a squid.)

 

[Jimmy Higgins]

"but plenty of unsound arguments are valid"

Okay, I fold.

 

[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)

There are other ways to invalidate this.

 

[Bronzeage]

All men are mortal.
Socrates is a man.
Therefore, all men are Socrates.

The process if elimination only yields a correct answer, if the correct answer is included in the group which is being eliminated. In the field of advanced auto mechanics, one way to be certain you are wrong is anytime you say, "That must be it, because there isn't anything else it could be."

 

[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.

 

[Wiploc]

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 word you want is sound, not valid.

A valid argument would have a true answer if the premises were true. Thus, this argument is valid:

P1: All men are mortal.
P2: Yogi Bear is a man.
C: Therefore, Yogi Bear is mortal.

The form is valid even though one of the premises is false. So we have validity without soundness.

P1: All comiq are nank.
P2: Wortl is a comiq.
C: Therefore, Wortl is nank.

That works. It's valid. It doesn't mean anything so the statements have no truth value, but the form is valid.

If a sylogism is valid, and the premises are true, then the conclusion will also be true. Such a synonym is sound.

 

[bigfield]

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 word you want is sound, not valid.

A valid argument would have a true answer if the premises were true. Thus, this argument is valid:

P1: All men are mortal.
P2: Yogi Bear is a man.
C: Therefore, Yogi Bear is mortal.

The form is valid even though one of the premises is false. So we have validity without soundness.

P1: All comiq are nank.
P2: Wortl is a comiq.
C: Therefore, Wortl is nank.

That works. It's valid. It doesn't mean anything so the statements have no truth value, but the form is valid.

If a sylogism is valid, and the premises are true, then the conclusion will also be true. Such a synonym is sound.

Neither of your examples are self-contradictory.

 

[untermensche]

Yes.

But for anything useful the premises must be not be a contradiction of known truth.

Starting with "Billy is a squid" either means he is in the navy or it is frivolous nonsense that will take you nowhere.

There is masturbatory logic (several recent threads shoot to mind) and logic with utility.

 

[Wiploc]

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 word you want is sound, not valid.

A valid argument would have a true answer if the premises were true. Thus, this argument is valid:

P1: All men are mortal.
P2: Yogi Bear is a man.
C: Therefore, Yogi Bear is mortal.

The form is valid even though one of the premises is false. So we have validity without soundness.

P1: All comiq are nank.
P2: Wortl is a comiq.
C: Therefore, Wortl is nank.

That works. It's valid. It doesn't mean anything so the statements have no truth value, but the form is valid.

If a sylogism is valid, and the premises are true, then the conclusion will also be true. Such a synonym is sound.

Neither of your examples are self-contradictory.

No, they are valid.

 

[bigfield]

Neither of your examples are self-contradictory.

No, they are valid.

I understand that, but I don't understand why an argument can be valid when the conclusion contradicts a premise.

 

[Bomb#20]

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.