# POLL 4 on a very simple argument especially designed for Sarkus

## Is the argument valid?

• ### I don't know

• Total voters
6
• Poll closed .

#### Speakpigeon

Valued Senior Member
This is a poll on a very simple logical argument.

It is designed to help people understand modal logic and for some to stop the red herring of the so-called "undistributed middle", something Sarkus insistently argued, against my argument on the Conscious Mind..

You can all vote, not just Sarkus.

Here is the argument:
x may be some part of B;
y is some part of B;
Therefore, x may be y.
Is this argument valid?

Thank you to vote before posting any comment.
EB

Uh, if B is the set of natural numbers between 1 and 100. If x is the set of all even numbers between 1 and 100. And y is an even number between 1 and 100.

Sure, I guess.

:EDIT:

But x+y=1 could make it true.

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Taking polls on the validity of a logical argument, still?

Maybe if you expressed them as syllogisms, in clear language, you could get results.

As it is, you have muddled some existential concerns in vague language. Clearly if we interpret the language as allowing:
"x" is a leaf of uncertain provenance noticed in a tangle of shrubbery,
B is a nearby tree with branches extended into that shrubbery,
and y is a root of that tree,

we would have a case in which the premises were true and the conclusion false.

we would have a case in which the premises were true and the conclusion false.
But the conclusion wouldn't be false.

The conclusion is may be, not is.

So, x may be y is always going to be true. 'X may be Y' is true, regardless of whether X happens to be Y.

The only way it could be false, is if the premises directly and explicitly counterindicate it.

Unfortunately for SP's argument, it also makes it trivially true.

It can be simplified to:
There is no explicit premise that X cannot be Y.
Therefore X may be Y.

Which reduces further to
X may be Y.

But the conclusion wouldn't be false.

The conclusion is may be, not is.

So, x may be y is always going to be true. 'X may be Y' is true, regardless of whether X happens to be Y.

The only way it could be false, is if the premises directly and explicitly counterindicate it.

Unfortunately for SP's argument, it also makes it trivially true.

It can be simplified to:
There is no explicit premise that X cannot be Y.
Therefore X may be Y.

Which reduces further to
X may be Y.
So, this may not be a discussion of logic, but playing word games.

What we have here is logic which is not 2-valued, but 3-valued.
That is, we have that A is true, A is false, or A might be true or false (is indeterminate). . .

3-valued logic has been around for a while, but strangely hasn't done much of a tour of duty.

But the conclusion wouldn't be false.

The conclusion is may be, not is.
And that would be false, given the existential interpretation of the language employed.
There is no possibility of a leaf being part of a root. So there are circumstances in which the premises are true and the conclusion false.
If that interpretation of the language of the argument is allowed.
So, x may be y is always going to be true
Not if the language is interpreted existentially, as in that example.

So, this may not be a discussion of logic, but playing word games.
It's logic alright, obviously modal logic, and obviously a legitimate branch of logic.
People who think not would have to be able to articulate their point to be taken seriously.
For all I know, iceaura may not be playing word games and may be indeed dead serious with the point he is making.
He seems utterly incapable of taking the argument at face value, as worded and phrased, and therefore as a modal argument.
He can't stop himself proving the non-modal argument he has himself produced is not valid, without explaining how that fact could possibly relate to the modal argument proposed in the OP.
Beats me.
EB

What we have here is logic which is not 2-valued, but 3-valued.
That is, we have that A is true, A is false, or A might be true or false (is indeterminate). . .
3-valued logic has been around for a while, but strangely hasn't done much of a tour of duty.
It is either true or false that x may be some part of B;
It is either true or false that y is some part of B;
It is either true or false that x may be y.
EB

And that would be false, given the existential interpretation of the language employed.
There is no possibility of a leaf being part of a root. So there are circumstances in which the premises are true and the conclusion false.
Yes, but only in your own non-modal argument.
You should take a leave of absence to take the time to look into modal logic and try to understand it. It's really not that difficult. It's even entirely intuitive. But you, obviously, can't do it.
If that interpretation of the language of the argument is allowed.
Not if the language is interpreted existentially, as in that example.
I'm not sure what you're trying to say here but you don't prove a modal argument not valid by proving not valid a redacted, non-modal version of it.

You can prove that something may be the case by exhibiting an instance of it being the case: For example, "X may be a tree" is proved true by exhibiting an actual tree.
However, "X may be God" isn't falsified by exhibiting a box where God isn't.
EB

Yes, but only in your own non-modal argument.
It's your argument we're trying to make sense out of.
I'm not sure what you're trying to say here but you don't prove a modal argument not valid by proving not valid a redacted, non-modal version of it.
I "redacted" nothing. If you want to restrict the interpretations of your muddled verbiage to something that stands on its own and forms a valid argument, feel free to do us the favor.
However, "X may be God" isn't falsified by exhibiting a box where God isn't.
But "Therefore, X may be God", a conclusion drawn from premises, is often falsified just that way. The X box has been exhibited in the premises, see, and God isn't in it.

"This kind of X always may be God" (what you need for "therefore", above) is falsified by exhibiting a definitely not-God example of that kind of X.

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I agree with Dave.

The argument reduces to "x may be y".

The fact that y is some part of another thing, B, would appear to be irrelevant. And the first premise says nothing useful: x might be part of B, or it might not. To put it another way, it might be true that x is part of B, or it might be false. Since we aren't told which, this premise adds no information to the rest of the argument.

With premise 1 being contentless (apart from instantiating a thing labelled "x") and premise 2 being irrelevant to the conclusion (apart from instantiating a thing labelled "y"), there really is no argument here at all. It is therefore pointless to talk about its validity.

Is the assertion that any given x might be a y true? It depends, of course, on what x and y are. Is it valid to say that any given x might be a y, before assigning referrents to x and y? I suppose it is. Valid, but not an argument, and rather obvious besides.

But something is valid, at least in the modern usage, when it is impossible for the premises to be true and yet the conclusion false.
If x and y are mutually exclusive parts of B then the conclusion can surely never be true.
For example, let's assume aliens discover our language and see two symbols: X and Y, (and in terms of the argument above, our alphabet is B).
They accept two premises as true: X may be a letter of the alphabet, and Y is a letter of the alphabet.
Is it true that the letter X (x) may be Y (y)?
No.
They are distinct parts of B, and can never be the same - i.e. it is impossible for them to be the same.
Since validity requires it to be impossible for the premises to be true and yet the conclusion false, this surely suggests that this form is invalid.
Is the assertion that any given x might be a y true? It depends, of course, on what x and y are. Is it valid to say that any given x might be a y, before assigning referrents to x and y? I suppose it is. Valid, but not an argument, and rather obvious besides.
If you can assign referrents that make the argument false, even if the premises are accepted as true, then the form is surely invalid?

Validity is all about form - and a valid form means that the conclusion must follow from the premises (excepting those arguments deemed valid for contradictory premises and the like), such that it is impossible for both the acceptance of the premises as true and for the conclusion to be false, irrespective of what the referrents are.

I just don't see it in this argument by speakpigeon, for the reasons iceaura has provided, which pretty much repeat the reasons Sarkus gave in the very first thread speakpigeon raised on this type of argument (or maybe it was the second... there have been a few).
Whether it is strictly a case of undistributed middle as Sarkus suggested at the time, I don't know, but it certainly seems to be of that ilk:
The argument splits up B into parts.
It doesn't then seem to distribute all those parts across the premises through form alone.
Thus it seems to be invalid, as it allows for the possibility that the conclusion could be wrong (per the example by iceaura, and by me above).

If the argument was, say: "X may be a part of B; Y is any part of B; therefore X may be Y" then this would be valid, as the parts of B are fully distributed.
That's how I see it.

So I'm voting not valid.

So, this may not be a discussion of logic, but playing word games.
Depends on what you think of the OP.
If respectable, then he's arguing in good faith.
If not, then he's playing word games with an agenda toward another thread.

The OP tends to put contributions he does not like on Ignore, so that may also speak to good versus bad faith discussion.

Bespokepigeon said:
It is either true or false that x may be some part of B;
So, it may be true that x is part of B, and it may be true that x is not part of B?

Taking polls on the validity of a logical argument, still?
Maybe if you expressed them as syllogisms, in clear language, you could get results.
It is a syllogism.
It's clear language.
If you think not, buy yourself a dictionary.
As it is, you have muddled some existential concerns in vague language.
There's no other language I know of to express the same syllogism.
Clearly if we interpret the language as allowing:
"x" is a leaf of uncertain provenance noticed in a tangle of shrubbery,
B is a nearby tree with branches extended into that shrubbery,
and y is a root of that tree,
we would have a case in which the premises were true and the conclusion false.
That's obviously not true.
You should take the time to consider the problem more carefully.
EB

It's your argument we're trying to make sense out of.
Sorry you're failing.
I "redacted" nothing. If you want to restrict the interpretations of your muddled verbiage to something that stands on its own and forms a valid argument, feel free to do us the favor.
Of course you did. Here's your redacted version:
"x" is a leaf of uncertain provenance noticed in a tangle of shrubbery,
B is a nearby tree with branches extended into that shrubbery,
and y is a root of that tree
Therefore, x may be y.
Which is obviously invalid but has no relation to my argument.
But "Therefore, X may be God", a conclusion drawn from premises, is often falsified just that way. The X box has been exhibited in the premises, see, and God isn't in it.
"This kind of X always may be God" (what you need for "therefore", above) is falsified by exhibiting a definitely not-God example of that kind of X.
Sorry, I don't understand this mess.
EB

I agree with Dave. The argument reduces to "x may be y". The fact that y is some part of another thing, B, would appear to be irrelevant. And the first premise says nothing useful: x might be part of B, or it might not. To put it another way, it might be true that x is part of B, or it might be false. Since we aren't told which, this premise adds no information to the rest of the argument. With premise 1 being contentless (apart from instantiating a thing labelled "x") and premise 2 being irrelevant to the conclusion (apart from instantiating a thing labelled "y"), there really is no argument here at all. It is therefore pointless to talk about its validity. Is the assertion that any given x might be a y true? It depends, of course, on what x and y are. Is it valid to say that any given x might be a y, before assigning referrents to x and y? I suppose it is. Valid, but not an argument, and rather obvious besides.
You MIGHT as well say x and y are unknown, anyway, and drop the whole of mathematics in the bin.
EB

But something is valid, at least in the modern usage, when it is impossible for the premises to be true and yet the conclusion false.
If x and y are mutually exclusive parts of B then the conclusion can surely never be true.
The premises don't imply that "x and y are mutually exclusive parts of B".
For example, let's assume aliens discover our language and see two symbols: X and Y, (and in terms of the argument above, our alphabet is B).
They accept two premises as true: X may be a letter of the alphabet, and Y is a letter of the alphabet.
Is it true that the letter X (x) may be Y (y)?
No.
They are distinct parts of B, and can never be the same - i.e. it is impossible for them to be the same.
The premises don't imply that "x and y are mutually exclusive parts of B".
All you've demonstrated is that x and y may be different parts of B, not that x and y may not be the same part of B.
Since validity requires it to be impossible for the premises to be true and yet the conclusion false, this surely suggests that this form is invalid.
If you can assign referrents that make the argument false, even if the premises are accepted as true, then the form is surely invalid?
Suppose there are two parts, B1 and B2. Premise 1 "x may be some part of B" means x may be B1 or B2. Premise 2 "y is some part of B", say, B2. Do the maths.
Validity is all about form - and a valid form means that the conclusion must follow from the premises (excepting those arguments deemed valid for contradictory premises and the like), such that it is impossible for both the acceptance of the premises as true and for the conclusion to be false, irrespective of what the referrents are.
Yes and the argument is valid according to that.
The premises don't imply that "x and y are mutually exclusive parts of B".
I just don't see it in this argument by speakpigeon, for the reasons iceaura has provided, which pretty much repeat the reasons Sarkus gave in the very first thread speakpigeon raised on this type of argument (or maybe it was the second... there have been a few).
Whether it is strictly a case of undistributed middle as Sarkus suggested at the time, I don't know, but it certainly seems to be of that ilk:
The argument splits up B into parts.
It doesn't then seem to distribute all those parts across the premises through form alone.
The premises don't imply that "x and y are mutually exclusive parts of B".
Thus it seems to be invalid, as it allows for the possibility that the conclusion could be wrong (per the example by iceaura, and by me above).
No. You would need to show that x may not be y. Or, equivalently, that Necessarily, x is not y.
The negation of "x may be y" is "necessarily x is not y".
You haven't shown that. You only have shown possibility: "x may not be y". Not necessity.
If the argument was, say: "X may be a part of B; Y is any part of B; therefore X may be Y" then this would be valid, as the parts of B are fully distributed.
But this is what the argument means. For premise 2, "y is any part of B" means exactly the same as "y is some part of B", unless you could articulate where would be the difference.
EB

The premises don't imply that "x and y are mutually exclusive parts of B".
They don't need to imply it, nor have I said they do.
But they possibly could be.
And in the case where they are, the conclusion is false.
Thus it is possible for the premises to be true and the conclusion nonetheless to be false.
This makes the form invalid.
The premises don't imply that "x and y are mutually exclusive parts of B".
All you've demonstrated is that x and y may be different parts of B, not that x and y may not be the same part of B.
The premises don't need to imply that they are, but when they are the conclusion is false even though the premises true.
Thus invalid.
Suppose there are two parts, B1 and B2. Premise 1 "x may be some part of B" means x may be B1 or B2. Premise 2 "y is some part of B", say, B2. Do the maths.
If x is B1 then no matter how hard you try, x is not y, nor can x ever be y.
You would have to add in an epistemological qualifier to get it to work, I think.
Yes and the argument is valid according to that.
Doesn't deem to be.
The premises don't imply that "x and y are mutually exclusive parts of B".
The premises don't need to imply it, but to be valid the form of your argument must hold for the scenario when they are.
Currently it does not?seem to.
The premises don't imply that "x and y are mutually exclusive parts of B".
They don't need to, but your argument still needs to account for that scenario.
Currently it does not seem to.
No. You would need to show that x may not be y. Or, equivalently, that Necessarily, x is not y.
The negation of "x may be y" is "necessarily x is not y".
If x and y are mutually exclusive, the premises can be true, the conclusion false.
In such cases x can not be y.
You haven't shown that. You only have shown possibility: "x may not be y". Not necessity.
No, I merely need to show that there are examples using the form such that true premises lead to a false conclusion.
That is all it takes for the argument to be considered not valid.
But this is what the argument means. For premise 2, "y is any part of B" means exactly the same as "y is some part of B", unless you could articulate where would be the difference.
1. The engine is some part of a car.
2. The engine is any part of a car.
Do you see a difference between these two statements?