Philomathy!
Professor Phil O’Mathy was always pleased to give recommendations for his former students, even those who had abandoned mathematics for less rigorous studies, like particle physics, or even less understandably gone into trade. He returned once more to filling out the form that had arrived in the morning mail.
5. If applicant is known to use alcohol or drugs, has it affected his or her performance?
? Yes ? No
O’Mathy couldn’t recall ever having seen Stuyvesant drink so much as a can of beer, and his calm, even demeanor suggested no acquaintance with any stronger intoxicants. He carefully checked “Yes” and went on to question 6.
You nerds and your precise understanding of material implication!Report
Clearly you’ve had to deal with a logician before.
Obligatory:
https://www.youtube.com/watch?v=MSifxC_L9F0Report
Perhaps I am slow today, but I’m not seeing it. The “If” condition is not met, so the “then” results are unknown. The stated reasoning is pure unsupported speculation.
That being said, badly written standardized questionnaires are a bete noir of mine. In the instant example, the information being sought after is whether or not the candidate’s performance has ever been affected by drugs or alcohol. The introductory throat-clearing merely confuses it. The humor in this anecdote is that the professor has ended up giving the opposite of what was really wanted, but still…
I frequently find myself in the position of trying to figure out what the intended question was, which often is quite different from the question as stated. Usually this is merely incompetent writing. The worst offenders, though, are psychology tests, where they simply don’t care. I am asked, for example, to rate on a scale from one to five how strongly I agree or disagree with a statement such as “I enjoy going to parties.” Perhaps I imagine a frat kegger and shudder, and strongly disagree. Or perhaps I imagine a small group of friends sharing conversation over food and drink, and strongly agree. Or (and this is what tends to actually happen) I imagine both scenarios, can’t decide which one is operative, and I mark the middle choice. Then I end up doing this on most of the questions, because so many of them run along these lines, and the psychologist who scores the damn thing complains that I am being evasive.
This greatly mystified me until I read up on the theory behind such tests and realized that to the test designer, the questions hold no semantic content. They are merely stimuli to evoke responses, which are then analyzed for statistically significant patterns. If enough test-takers respond to any given question in a predictable way, then it is a good question. The guy who imagines a frat kegger and is enthusiastic and the guy who imagines that kegger and is horrified are equally good fodder. The guy who thinks about the question and notices the ambiguity? Not so much. But so long as such people are rare, they don’t matter to whether or not the question is judged to be good.Report
In mathematical logic, the truth of “if p then q” depends only on the truth of p and q; it’s true if p is false, or q is true, or both. So the question as stated is true unless the applicant is a high-functioning partyer.Report
This is the truth table for if p then q.Report
I’ll set my Liberal Arts shod foot into Schilling’s Math trap.
If he is known to use x, and x impairs actions, then yes?Report
But do we know that Q is true? Many people drink and/or use drunks without it affecting their work performance.Report
Kazzy, the whole “problem” arises by thinking that colloquial English is an expression of a formal language: mathematical logic. It isn’t.
Formally, if the antecedent is false, the conditional is true. Think of it this way: if the question were asked on the LSAT (amazing as that might be!) the Prof got the answer right. If it were asked on a job application (as we’re supposed to believe), he got it wrong wrong wrong. The guy is so smart he’s stupid.Report
Got it.Report
Actually, I think the problem is that the mathematician has confused ‘Yes’ and ‘No’ with ‘true’ and ‘false’.
Those…are not the same things. The question is not whether or not the statement is true or false, because if that was the question, a *lot* of people would be wondering how to answer ‘Not applicable’.
But the application is *not* asking that. The options are not True/False, they are Yes/No.
The application is asking the question is ‘has [alcohol or drugs use] affected his or her performance?'(1), and the first part of it is merely to indicate that the question only applies if you know he’s used them,and how you should answer otherwise. That’s how yes/no questions with a conditional *work*.
Professor Phil O’Mathy doesn’t know the difference between ‘yes’ and ‘true’, which makes him both a bad mathematician and a pretty incompetent speaker-to-humans also.
I await someone asking him a question about the future, like ‘Are you going to the store tomorrow?’, and watching his *head explode* as he attempts to ascribe a truth value to that.
1) Incidentally, there is a slight grammarical weirdness in that sentence. The question should be ‘If applicant is known to use alcohol or drugs, have *they* affected his or her performance?’. Or, alternately, ‘If applicant is known to use alcohol or drugs, has their use affected his or her performance?’
The ‘it’ in the original question is referring to ‘their use [of drugs]’, which would be fine, except that’s not a noun phrase that appears in the sentence so probably should not have a pronounce referring to it! Readers have to mentally construct what ‘it’ must be, when there’s a perfectly good ‘they’ already there!
That’s not *incorrect* grammar, though…just a bit odd.Report
In fact, that question isn’t even in the *right format* to be a statement in formal logic.
It would be something like ‘If applicant is known to use alcohol or drugs, then *it has* affected his or her performance.’.
So the professor converted the question *into* a statement of formal logic instead of what it actually was, and then he converted the answers in the two possible attributes of that statement, instead of what they actually were. And then he answered *that*…well, technically, ‘answered’ is the wrong word, because it’s not a question. He checked the truth of the statement that he had just made up.
I’m pretty certain the joke here is *supposed* to be ‘the professor answered the question technically correct, instead of what it trying to ask’. Aka, another the ‘Where are you?/You’re in a hot air balloon.’ or ‘How do you get to Carnegie Hall?/Practice.’ joke.
This joke, sadly, completely falls apart when you realize that…no. No, he did not answer correctly. The professor is just a complete nutcase.Report