Consider any absolute statement of the general form:
[ul]
[li]All X are Y[/li][li]P is always Q[/li][li]A leads invariably to B[/li][/ul]
Subsequently, exceptions are found; that is, it turns out:
[ul]
[li]Only most X are Y[/li][li]P is occasionally O[/li][li]A sometimes leads directly to Z, not B[/li][/ul]
In this case (an exception is found to a statement previously considered absolute), is the original statement completely wrong, or only partly wrong?
Poll to follow…
I voted absolutely wrong, but I can imagine ways to specify “partly wrong” which would make that the right answer. In the absence of a definition of “partly wrong,” though, I went for the default–it tunrs out not all X are Y, so the statement all X are Y is simply false.
Got any examples? I can’t imagine any that wouldn’t render the original statement completely wrong, unless the original statement included qualifiers like “all X that we currently know of are Y” or “all X in the United States are Y,” or didn’t require some fundamental disagreement on what X and Y meant.
Completely wrong, no two ways about it. The speaker has made a claim that turns out to not be true. They can make a new claim if they like (eg, some x are y) but that new claim isn’t automatically tue or even made just by proving the larger claim false.
Well, the phrase “partly wrong” suggests degrees of truth and falsity. So you could make a logic where the truth-degree of universal statements “All X are Y” reflects the proportion of X’s that are Ys.
So if no X’s are Ys, then the statement is completely wrong, while if a few are, then the statement is mostly wrong, and if half are, then it’s half right, and if most are, then it’s mostly right, etc.
It’s wrong, but I think there’s a difference in confidence levels between:
“The 8:30 train is always on time.”
and
“I personally guarantee that the 8:30 train is always, 100%, positively, absolutely on time down to the millisecond and if it isn’t, may god strike me dead and may my children die in horrible agony.”
So the second claim would be more wrong than the first. But they would both be pretty wrong.
This is a hard question, but I decided completely wrong. Whatever assumptions you made to posit the first statement, all of those underlying assumptions are now suspect.
That said, we don’t really do that in practice. If I hold an absolute political opinion, and someone points out an exception, I don’t throw out everything I assumed before, I just assume I’m mostly right.
Hmmm.
“Partly wrong” suggests that there something in these statement that is true. But nothing is.
In logical terms, completely wrong. But in the real world we deal with things where all X are Y except for some very rare exceptions, and colloguially all means almost all. In that case I would say the statement is then imprecise, not completely or partially wrong.
Standup Logician:* All X are Y is a true statement!
Audience: HOW TRUE IS IT?
N/M
I would say completely wrong if I was the type to go around making absolute pronouncements.
I agree that it is completely wrong. When you’re dealing with formal logic, there is no middle ground, it’s either true or it’s false. If we don’t hold to this, the rules break down. Consider, if we have “All X are Y” then if I can prove that w is X then I know w is also Y. If, however, I find that z is X but is not Y, I now can’t really say anything about w anymore. The thing is, all we now know is that not all X are Y. It’s possible that we don’t have any evidence that any X is a Y, or it’s possible that there’s a billion instances of X and only z is X but not Y, so I can’t even make a strong case that most X are also Y so w is probably Y.
So, we have to treat absolute statements as boolean, but this is also why they’re very easy to disprove, because they only require a single counter-example, but they’re often difficult to prove, because we have to demonstrate that they’re true for all possible cases. This is also why it’s important to avoid absolutes in arguments akin to “you always do X” and “you never do Y”.
I consider an absolute statement, of the sort listed in the OP, as having the implied condition “there are no exceptions.” So if there are, in fact, exceptions, the statement is incorrect.
Formal logic includes many-valued logics, and a many-valued logic could be designed to accomodate a “partly right” answer to this question.
The question is what that would be useful for, if anything. But as for whether it can be done, it definitely can be.
To me, the middle statement isn’t untrue.
[ul]
[li]Puppies are always Qute (P is always Q)[/li][li]Puppies are occasionally Old English Sheepdogs. (P is occasionally O)[/li][/ul]
There is nothing that states that O and Q are varieties of the same thing. It’s not like [ul]
[li]Puppies are always dogs (P is always Q)[/li][li]Puppies are occasionally cats. (P is occasionally O)[/li][/ul]
StG
You’re right, but it was just a badly-phrased question, not a trick one. Should have said ‘P is occasionally O, not Q’
Puppies, by definition, are never Old anything.
Oh… But as for the OP: Are you trying to develop a critique of Cognitive Behavioral Therapy?
No, puppies can only be young English Sheepdogs, not old ones.
I think formal logic is unhelpful in deciding this.
Let’s say I tell someone, “The wait staff at Laughing Jack’s are always friendly.” The truth value of this is not important: what’s really important to my audience is the utility value of the statement. They can take that statement to mean that, if they’d like to deal with friendly wait staff, they should consider eating at Laughing Jack’s; they can also take it to mean that, if they want to know what I consider to be friendly wait staff, they should consider what the wait staff at Laughing Jack’s are like.
Of course someone could answer, “Technically you’re totally wrong, because two years ago there was a waiter there who’d just broken up with his girlfriend and when I stiffed him on the tip he glared at me. Therefore your absolute statement is completely wrong, QED.”
But the correct response to that person isn’t to say, “You’re right, and my statement was completely wrong.” The correct response is to say, “Why are you always such a douche?”