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.