# Validity of a simple logical argument

## Is the argument valid?

• ### The argument doesn't make sense

• Total voters
11
• Poll closed .
The problem doesn't appear to be the logic. The problem is that the one asking the question always leaves an escape route to avoid agreement.
A form of trolling that pretends sincerity to tease people into taking the posts seriously and then at the last moment, using a deliberately included ambiguity to avoid humiliation and in doing so attempt to humiliate the responder.
It's pretty much the standard behavior of those who take delight in using their "superior" intellect to make others squirm.
Pretty much nailed, it. QQ had the guts to say it out loud.

At least three relatively new members off the top of my head use this tactic prodigiously.

When asked, the teacher explained that the class had taken a vote, and preferred the first way.
One wonders what happens when these kids are confronted by a cake divided into three parts. Since 1/3 + 1/3 + 1/3 = 3/9 = 1/3, they must find it inexplicable that the three pieces apparently make a whole cake.

Yes, better still, but there is shorter:
P4. Joe is either a squid or a giraffe
H1. Joe is a giraffe................................P4
D1. Joe is not a giraffe..........................P5, P2
D2. Joe is a squid..................................P4, D1
QED
Same thing, really, just shorter.
So, yeah, Hallelujah.
If you like it, you can keep it. Cadeau.
EB
Utter nonsense.
P5. Joe is an elephant, not a squid, nor a giraffe, he is an elephant as declared in the conditions of the deductive exercise!
P4. is a logically flawed premise. It posits an impossible contradiction both ways.

The conclusion is already provided before the false deduction. The OP question may be logical in format but it contains false premises. Therefore the entire logical exercise is "unsound" and "not valid".

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The problem doesn't appear to be the logic. The problem is that the one asking the question always leaves an escape route to avoid agreement.
A form of trolling that pretends sincerity to tease people into taking the posts seriously and then at the last moment, using a deliberately included ambiguity to avoid humiliation and in doing so attempt to humiliate the responder.
It's pretty much the standard behavior of those who take delight in using their "superior" intellect to make others squirm.
Surely you have better things to do with that superior intellect than flex your perverse form of sadism... or perhaps one should seriously ask : "What do you hope to achieve here at sciforums.com Speakpigeon ?"
Derail.
EB

Only if they wanted to claim they were using "modal logic" - or some other of the known logics.
If they are not using any particular established logic, or reasoning logically in any dictionary sense of the term, then one supposes they could employ their own definitions and meanings of whatever terms they wished. They could even decide "validity" by majority vote of the spectators.
Here I'm using the 2,400-year-established logic of Aristotle. Would that be good enough, do you think?
Between Aristotle and Kant, no known major intellectual figure ever articulated any substantial disagreement with Aristotle's definition of logical validity implicit in his notion of syllogism.
So, yeah, that has to be good enough.
And, by the way, that's indeed deciding what is validity by vote.
So, I guess this just goes on to show you don't know much about what you're talking about.
Years ago I ran into a biologist who had student-taught school in Quebec, and swore this was a true account: a fellow student teacher at the school had watched their mentor teacher instructing the students in the addition of fractions, and saw that the children were being taught to add the numerators and the denominators to find the sum. That is, 5/4 + 1/3 = 6/7. Not wishing to intrude, as a rookie, but nevertheless disturbed, they took the teacher aside as soon as they could and politely informed them that the usual procedure was otherwise. They then explained that usual procedure - common denominator, all that. The teacher was amenable, and introduced this new way of doing things to the children. But a month or so later, when the student revisited that classroom to say hello, they were adding as before. When asked, the teacher explained that the class had taken a vote, and preferred the first way. The biologist swore that actually happened. At the time, I did not really believe them. These days -
Derail, but, still, that's a good story. It sure helps me understand you guys.
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So, you think there's a correct definition of validity and that's the one you use?
OK, go on, provide the definition of validity you think is correct and then what you think would be the justification given by experts as to why this definition would be the correct one.
Let's see if you know what you're talking about.
EB

Utter nonsense.
P5. Joe is an elephant, not a squid, nor a giraffe, he is an elephant as declared in the conditions of the deductive exercise!
P4. is a logically flawed premise. It posits an impossible contradiction both ways.
The conclusion is already provided before the false deduction. The OP question may be logical in format but it contains false premises. Therefore the entire logical exercise is "unsound" and "not valid".
Do you at all understand that I take the "proof" I provided to be utter tosh?!
Or are you so beside your shoes that you can't get yourself to read what you pretend to be responding to?!
So, yeah, Hallelujah?
Still, this shows again that we agree as to validity.
Little comfort, though.
EB

So, you think there's a correct definition of validity and that's the one you use?
Nope.
I have used a criterion of invalidity.
Here I'm using the 2,400-year-established logic of Aristotle.
Show, don't tell.
Derail, but, still, that's a good story.
It's not a derail.

So, the provisional results are that 5 think the argument is not valid and 5 think the argument is valid.
There are a few possible biases, here.
First, some people here just can read very well and some will cast the wrong vote. Still, same chance either way, so it shouldn't matter too much.
Second, people with even slight cognitive disorders or mental issues may be more likely to vote "not valid" and this whatever the argument. However, there will be even more likely to vote "The argument doesn't make sense", so, again, this bias shouldn't be too much of an issue.
Third, people with a training in formal logic are much more likely to be dogmatic in their assessment of this particular argument and therefore to vote valid. Here, we have at least three people like that, James R., Sarkus and Baldeee.
So, overall, I think it's fair to surmise that a substantial majority of people assessing the argument on an intuitive basis will say it is not valid.
Thank you all to have contributed to this experiment and to have contributed your own subjective evidence. Now we have the better empirical evidence of this objective result.
Thanks.
EB

Great, so you get to conclude that formal logic can seem unintuitive. What's new! This was highlighted on the first page of this thread, that the definition of validity in classical logic throws up seemingly counterintuitive examples of valid arguments. But I'm glad you are satisfied with the result of your experiment, even it is one that has been known for rather a long time.
Does that mean you'll now stop littering this forum with your threads?

So, overall, I think it's fair to surmise that a substantial majority of people assessing the argument on an intuitive basis will say it is not valid.
People assessing it on an intuitive basis are unlikely to be overly concerned about the distinction between validity and soundness. Everybody agrees it isn't sound.

Any conclusion, C, validly follows from contradictory premises. For example:

Formal argument:
P1: P
P2: not P
Conclusion: Therefore C.

An example of this in practice:
P1: John is an elephant.
P2: John is a squid.
P3: A squid is not an elephant.
Conclusion: Donald Trump is America's greatest ever President.
----

Proof that the formal argument is valid:
1. P. (from P1)
2. P or C. (necessarily true because P is true - from step 1)
3. not P. (From P2)
4. Therefore C. (true because either P or C must be true (step 2) and we know that P is false (step 3)).

Application of the formal proof to the example:
1. John is an elephant. (P1)
2. Either John is an elephant or Trump is the greatest President, or both. (True because John is an elephant (step 1).)
3. John is not an elephant. (because a squid is not an elephant (P2) and John is a squid (P3).)
4. Therefore Trump is the greatest President. (Deduced because we have shown that John is not an elephant (step 3), but, as we have shown previously, one or both of "John is an elephant" or "Trump is the greatest President" must be true (step 2).)

That is, the example is a valid proof that Donald Trump is America's greatest ever President.

People assessing it on an intuitive basis are unlikely to be overly concerned about the distinction between validity and soundness. Everybody agrees it isn't sound.
Easy to say. Now prove it. Go, on, provide quotes of people here who seemed to have voted "not valid" because they found the argument unsound.
People who assess an argument as not valid on the basis of their intuition will find the argument absurd, and this will usually shows in the way they report their position, and this even though that understand ship about formal logic.
EB

Any conclusion, C, validly follows from contradictory premises. For example:

Formal argument:
P1: P
P2: not P
Conclusion: Therefore C.

An example of this in practice:
P1: John is an elephant.
P2: John is a squid.
P3: A squid is not an elephant.
Conclusion: Donald Trump is America's greatest ever President.
----

Proof that the formal argument is valid:
1. P. (from P1)
2. P or C. (necessarily true because P is true - from step 1)
3. not P. (From P2)
4. Therefore C. (true because either P or C must be true (step 2) and we know that P is false (step 3)).

Application of the formal proof to the example:
1. John is an elephant. (P1)
2. Either John is an elephant or Trump is the greatest President, or both. (True because John is an elephant (step 1).)
3. John is not an elephant. (because a squid is not an elephant (P2) and John is a squid (P3).)
4. Therefore Trump is the greatest President. (Deduced because we have shown that John is not an elephant (step 3), but, as we have shown previously, one or both of "John is an elephant" or "Trump is the greatest President" must be true (step 2).)

That is, the example is a valid proof that Donald Trump is America's greatest ever President.
The way you do it, this argument is only valid in reference to the definition of validity you accept. If the definition you use is not correct, your "validity" here is shit.
So what is the justification that the definition of validity you use here is correct?
Is it arbitrary? If it is arbitrary, why are people here insisting I'm wrong. The question was,"Is the argument valid", and not "Is the argument valid according to mathematicians".
And if you think it's not arbitrary, then surely you should be able to explain why you think so, unless it's just a case of deferring to what you perceive as "the authority"? Is your argument here, i.e. you, Sarkus, Baldeee, an argument from authority?!
So, please explain what is the justification given by mathematicians, logicians, philosophers etc. that the definition of validity you use here is correct.
I'll be waiting anxiously not.
EB

Great, so you get to conclude that formal logic can seem unintuitive. What's new! This was highlighted on the first page of this thread, that the definition of validity in classical logic throws up seemingly counterintuitive examples of valid arguments. But I'm glad you are satisfied with the result of your experiment, even it is one that has been known for rather a long time.
Does that mean you'll now stop littering this forum with your threads?
Please explain what is the justification given by mathematicians, logicians, philosophers etc. that the definition of validity you use here is correct.
EB

Nope.
I have used a criterion of invalidity.
Show, don't tell.
It's not a derail.
Please explain what is the justification given by mathematicians, logicians, philosophers etc. that the definition of validity you use here is correct.
EB

That comports quite well with you not using a particular definition or method. So we're all on the same blank page here!
OMG . . .
Please explain what is the justification given by mathematicians, logicians, philosophers etc. that the definition of validity you use here is correct.
EB

Please explain what is the justification given by mathematicians, logicians, philosophers etc. that the definition of validity you use here is correct.
Once again:
I don't use a definition of validity here.

"I don't use a definition of validity here."
LOL.
Perhaps, as I tried to forestall above, you have both
1) confused my posting here with that of some other thread, and
2) confused a criterion for invalidity with a definition of validity.
That would explain your insistent rhetoric.
As would mental incapability on your part - losing track of your own argument. You do have several different posters to deal with, not a simple task.

The way you do it, this argument is only valid in reference to the definition of validity you accept.
How do you know?

Can you give me a workable definition of validity in which the argument I gave is not valid?

Recall that what you're comparing to is this:
"An argument is valid if the truth of the premises guarantees the truth of the conclusion."

or, equivalently:

"An argument is valid if it is impossible for the premises to all be true and for the conclusion to be false, at the same time."