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Comment by ecaradec | Hacker News Reader

I think it's more that people are not familiar with the formal presentation of the problem. I doubt many people would have difficulty understanding a less abstract statement:

dog => mammal (dog implies mammal )

What can we say about not a dog ? (can be a cat, or a chair... ) What can we say about not a mammal ? (can be a chair, building... )

It's more intuitive because we as human understand the groups.

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It surprises me that more of the folks he interviewed didn't try to figure out the contours of the formal presentation of the problem by plugging in concrete examples; isn't that the default "brute force" attempt you'd expect from someone trying to work out problems like this? It's the same thing you'd expect from someone solving Leetcode problems; you don't attack the general case immediately unless you've memorized the problem before, you usually try to play around with concrete examples until you've got enough of a handle on it to try and code up something a little more general.

> I got a few vague and wordy excursions into things that are true and things that are false, but never the clear, straightforward answer. Not once.

Sounds like he made a point to shut down that line of reasoning.

What part of this quote gives you that impression?

I don't think I've ever used the word 'implies' in that context, which may be the problem with the question. It still doesn't quite make sense in my thought process. Does a dog 'imply' a mammal? I wouldn't think so, a dog guarantees a mammal.

'Implies' to me suggests a possible underlying interpretation. If someone tells me he wants to eat, it implies that he is hungry. However he might not be hungry, he might be strict about eating at 8pm for other reasons. An 'implication' is perhaps the most likely association, but not necessarily the correct one.

'Implies' is a term with a formal meaning in logic. You don't get to question a domain simply because one of its pieces of jargon has other interpretations in the vernacular.

From the title

> What Everyone Knows

I don't believe everyone knows of the formal meaning in logic, even among candidates for a Master's program. He doesn't seem to want to consider that there's a flaw in his question, rather than a failure on our academic institutions.

> and What No One Knows

The question certainly has some flaws in phrasing (discussed elsewhere in this thread). Its use of the word "implies" is not a flaw. If intro-level formal logic is a valid requirement, then there is no problem using "implies" in that context. If intro-level formal logic is not a valid requirement, then the whole question is bunk, but not the use of "implies".

It's perhaps plausible that someone might assume the colloquial definition, but if a candidate for a master's program doesn't know of the formal logic definition in the first place, that is a failure of our academic institutions.

Except that it also depends on the definition you're using for "implies," so the normal use of English breaks things if you're really asking about logic. For example, dog implies "likes dogfood" is a reasonable thing to say, but "doesn't like dogfood" certainly includes dog outliers who only eat, say, kitchen scraps, and refuse dogfood. So no, a implies b doesn't let you say not a implies not b, given the normal definition of "implies."

I suspect though that this is the kind of quibbling that will quickly pass the interview test; you say something about dogfood and colloquial use of _implies_, the interviewer says "oh no, we're talking about formal logic where implies means..." and you go on from there. And frankly, that's the kind of interview question that's useful, since if you assume that marketing people use the logic definition of "implies" you're going to be in all sorts of pain in real-world meetings about developing software.

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