# Validity of a simple logical argument

## Is the argument valid?

• ### The argument doesn't make sense

• Total voters
11
• Poll closed .
Or you just note that any argument using contradictory premises is valid. End of story.
Oh, sure, you could work with a non-mainstream definition of logic and arrive at a different result. But using that mainstream definition, the argument is valid. Period. Nothing more to see here. These aren't the invalid forms you're looking for. Move along. Move along.

Or you just note that any argument using contradictory premises is valid. End of story.
Oh, sure, you could work with a non-mainstream definition of logic and arrive at a different result. But using that mainstream definition, the argument is valid. Period. Nothing more to see here. These aren't the invalid forms you're looking for. Move along. Move along.
I didn't ask people to use any particular definition or method.
I asked whether the argument was valid. And as it stands, 4 voted "valid", 4 voted "not valid".
And why should anyone have to use any particular definition of validity? Just because it's "mainstream"?
So, I guess, Copernicus should have shut his mouth and go mainstream. That's a very enlightened perspective on things. Galileo, too. Einstein. Let's only do mainstream from now on! Whoa.
EB

I saw one guy produce a proof that Joe is a squid. His proof is 10 lines long but I can do it 8. He infers from his proof that the argument is valid, even though you can prove using his same method that Joe is not a squid in 3 lines. Yet, he persists. He exhibited what he thinks is a proof and that's it. His method is flawed but he doesn't know that and he certainly doesn't understand why it is flawed. Using apparently the same method, I proved correctly the argument not valid:

Proof
An elephant is not a squid..............P3
Joe is an elephant...........................P5
Therefore, Joe is a not squid..........P3, P5, R1: ((x ≠ y) ∧ (z = x) ) → (z ≠ y)

Which is basically what you said.
Formally, for the argument to be valid, since equality is not a logical symbol, you need to add a premise with the R1 rule ((x ≠ y) ∧ (z = x) ) → (z ≠ y). But it's implicit anyway.
EB
Well, explain this to me.
Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value true if both functional arguments have the same logical value, and false if they are different.
https://en.wikipedia.org/wiki/Logical_equality

I didn't ask people to use any particular definition or method.
I asked whether the argument was valid. And as it stands, 4 voted "valid", 4 voted "not valid".
And why should anyone have to use any particular definition of validity? Just because it's "mainstream"?
No - so as to be sure that it is understood consistently from person to person. If we can each choose our own definition and not tell the other people party to the discussion what our definition is, you get muddled discussion. Once you get consistency of definition, that can be more easily avoided.
So, I guess, Copernicus should have shut his mouth and go mainstream. That's a very enlightened perspective on things. Galileo, too. Einstein. Let's only do mainstream from now on! Whoa.
Ah, once again attempting to elevate yourself through false comparison. Hey ho. But if you feel your only recourse is to play the Galileo gambit, or variations thereof, then it really would appear that your well is dry.
It's one thing to propose a non-mainstream theory, and have the capability of supporting it and defending it despite widespread criticism, but it's quite another to simply ask a question (or 4, or 5, or however many of these inane threads it has been) and be utterly unable and/or unwilling to provide any semblance of meaningful defence whatsoever to your own answer of it, and then try to link yourself even in some small way to such people through simply holding a non-mainstream notion of a word. Truly remarkable egotism on your part. And so very flawed.
And to quote Sagan properly this time: "They laughed at Columbus, they laughed at Fulton, they laughed at the Wright Brothers. But they also laughed at Bozo the Clown."

I saw one guy produce a proof that Joe is a squid. His proof is 10 lines long but I can do it 8.

P1. A squid is not a giraffe
P2. A giraffe is not an elephant
P3. An elephant is not a squid
P4. Joe is either a squid or a giraffe
P5. Joe is an elephant
Conclusion: Therefore, Joe is a squid
We construct a proof by contradiction.

1. Joe is either a squid or a giraffe (P4)
2. Assume, provisionally, that Joe is a giraffe.
3. Joe is not an elephant (deduction from assumption 2 and P2).
4. But deduction 3 is in conflict with P5.
5. Therefore, assumption 2 must be wrong (deduction from steps 1-4 and the assumption that all the given premises are true). Joe is not a giraffe.
6. Therefore, Joe is a squid (deduction from step 5 and P4).

You would want to know.
Sometimes, it feels you guys just don't speak English.
To decide whether it is true that A implies B.
Sure, I hope I have understood that even before you told me. The question was obviously why use a truth table to decide whether something implies something else.
And then, why use this particular truth table?
EB

Well, explain this to me.
Sorry, I'm not a rune-reading machine. So, wake up, if you can't articulate your point, I won't do it for you.
EB

We construct a proof by contradiction.
1. Joe is either a squid or a giraffe (P4)
2. Assume, provisionally, that Joe is a giraffe.
3. Joe is not an elephant (deduction from assumption 2 and P2).
4. But deduction 3 is in conflict with P5.
5. Therefore, assumption 2 must be wrong (deduction from steps 1-4 and the assumption that all the given premises are true). Joe is not a giraffe.
6. Therefore, Joe is a squid (deduction from step 5 and P4).
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

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No - so as to be sure that it is understood consistently from person to person. If we can each choose our own definition and not tell the other people party to the discussion what our definition is, you get muddled discussion. Once you get consistency of definition, that can be more easily avoided.
And again, I didn't ask people to use any particular definition or method.
I asked whether the argument was valid. And as it stands, 4 voted "valid", 4 voted "not valid".
And why should anyone have to use any arbitrary definition of validity?
I then asked people to justify their assessment of validity. Not their method. I asked them to justify their assessment.
To continue your analogy that logical validity is like vocabulary, I agree it would help to know what definition the other guy is using if what he says doesn't make sense to you. But most people don't use any definition. They just know what they mean and speak from there. You don't like it, change planet. Second, it may well be that you don't understand what the other guy is saying because you are using the wrong definition. Happens a lot. So, again, look at your own assumptions.
So, you use a particular definition. Good for you but then justify that the method implicit in your definition is the correct method to assess validity. And you can't do that.
Ah, once again attempting to elevate yourself through false comparison. Hey ho. But if you feel your only recourse is to play the Galileo gambit, or variations thereof, then it really would appear that your well is dry.
It's one thing to propose a non-mainstream theory, and have the capability of supporting it and defending it despite widespread criticism, but it's quite another to simply ask a question (or 4, or 5, or however many of these inane threads it has been) and be utterly unable and/or unwilling to provide any semblance of meaningful defence whatsoever to your own answer of it, and then try to link yourself even in some small way to such people through simply holding a non-mainstream notion of a word. Truly remarkable egotism on your part. And so very flawed.
And to quote Sagan properly this time: "They laughed at Columbus, they laughed at Fulton, they laughed at the Wright Brothers. But they also laughed at Bozo the Clown."
Wrong assumption.
My heroes are Descartes, Copernicus, Aristotle and Archimedes. Archimedes was in his bath. I was in the loo.
EB

And again, I didn't ask people to use any particular definition or method.
I asked whether the argument was valid. And as it stands, 4 voted "valid", 4 voted "not valid".
And why should anyone have to use any arbitrary definition of validity?
As stated above, using a single definition avoids confusion and ensures consistency of perspective. It also avoids future dishonesty with someone claiming to use a different definition when their answer is shown to be wrong under the assumption of the mainstream definition.
I then asked people to justify their assessment of validity. Not their method. I asked them to justify their assessment.
To continue your analogy that logical validity is like vocabulary, I agree it would help to know what definition the other guy is using if what he says doesn't make sense to you. But most people don't use any definition. They just know what they mean and speak from there.
If you say they know what they mean then they must have a definition they are working from. If you don't have a working definition of a word then you can not use it sensibly.
You don't like it, change planet. Second, it may well be that you don't understand what the other guy is saying because you are using the wrong definition. Happens a lot.
I can rather easily imagine it does to you.
So, again, look at your own assumptions.
No need - they are adequately articulated, even for you.
So, you use a particular definition. Good for you but then justify that the method implicit in your definition is the correct method to assess validity. And you can't do that.
I need to do nothing other than point to it being the mainstream definition of validity within classical logic. The rest is for other people to assert their alternative is acceptable. You want to use a non-standard logic, you justify it. You want to go with just intuition, you go for it.
Wrong assumption.
My heroes are Descartes, Copernicus, Aristotle and Archimedes. Archimedes was in his bath. I was in the loo.
And where exactly have I mentioned or implied anyone being your heroes? You do like your strawmen, don't you.

If you say they know what they mean then they must have a definition they are working from. If you don't have a working definition of a word then you can not use it sensibly.
BS.
EB

There seems to be another consideration apart from validity, that of "soundness".
Validity and Soundness
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

A deductive argument is sound if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound.
All toasters are items made of gold.
All items made of gold are time-travel devices.
Therefore, all toasters are time-travel devices.
Obviously, the premises in this argument are not true. It may be hard to imagine these premises being true, but it is not hard to see that if they were true, their truth would logically guarantee the conclusion's truth.
It is easy to see that the previous example is not an example of a completely good argument. A valid argument may still have a false conclusion. When we construct our arguments, we must aim to construct one that is not only valid, but sound. A sound argument is one that is not only valid, but begins with premises that are actually true. The example given about toasters is valid, but not sound. However, the following argument is both valid and sound:
In some states, no felons are eligible voters, that is, eligible to vote.
In those states, some professional athletes are felons.
Therefore, in some states, some professional athletes are not eligible voters.
Here, not only do the premises provide the right sort of support for the conclusion, but the premises are actually true. Therefore, so is the conclusion.
Although it is not part of the definition of a sound argument, because sound arguments both start out with true premises and have a form that guarantees that the conclusion must be true, if the premises are sound arguments always end with true conclusions.
https://www.iep.utm.edu/val-snd/

Sorry, I'm not a rune-reading machine. So, wake up, if you can't articulate your point, I won't do it for you.
EB
I quoted the "point".
Logical equality is a logical operator that corresponds to equality in Boolean
algebra and to the logical biconditional in propositional calculus. It gives the functional value true if both functional arguments have the same logical value, and false if they are different.
Are you telling me the quoted logical argument is "invalid"?

I quoted the "point".
Are you telling me the quoted logical argument is "invalid"?
I still don't know what your point is. You need to articulate your point.
EB

I didn't ask people to use any particular definition or method.
That comports quite well with you not using a particular definition or method. So we're all on the same blank page here!
Good for you but then justify that the method implicit in your definition is the correct method to assess validity. And you can't do that.
OMG . . .

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That comports quite well with you not using a particular definition or method. So we're all on the same blank page here!
OMG . . .
OMG, yes you can't.
Please note that smarter people have tried and couldn't do it.
It's a notorious problem in logic but if you're interested there's definitely a Nobel Prize for you if you do it.
EB

This smart person is going to turn off the bullshit tap now. You can have all the fun.

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 ?"

And why should anyone have to use any particular definition of validity? Just because it's "mainstream"?
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.

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 -