Is minus 7 prime?

[jack]

My name:
Yes. Obviously the domain in question is the ring of integers, and the definition of prime for non-natural-number rings includes -7 in the integers.
No. Unless epxlicitely specified, the domain is always the natural numbers, and negative numbers and fractions are no more prime than american presidents or colours.
Moofle. Mu. Your question is malformed. Without specifying the domain, you can't correctly say either.
Even in the integers, -7 isn't prime, even though most mathematicians use that definition.
Even in the integers, -7 isn't prime, and everyone knows that.
Other. I will explain in comments.

This question actually came up in an online multiple choice test. However, another option was a positive prime, so it was clear what they meant. (Foruntately there wasn't an "other" option. Have another vote for "tests where you might know everything about the subject and popular conceptions and misconceptions thereof, but you have to second-guess the level of sophistication of the examiner to get full marks suck!" :))

But mathematical pedantry aside, it illustrates how much context can be important to the meaning of a sentence. This seems about perfectly balanced about what context you assume, but there's a continuum. At one end, the sentence is without context, you interpret it literally.

At the other, you have something like:

Q. Were you telling the truth?
A. Yes!

Where "yes" isn't the answer to *that* question, but a delayed answer to something someone else asked the other day. I think everyone could agree that's a lie. But there are intermediate stages.

If you say a sentence which would be literally true out of context, but in response to a question in a situation where it sounds like a natural reply meaning one way, when the opposite is true, and you intended that, I think that's a lie. But some people think lying is always wrong, but this doesn't count as lying.

OTOH, if you have some reason not to tell the whole truth, and don't volunteer something important, that can be acceptible. It can be misleading, and may or may not be wrong, but isn't necessarily lying.

It seems like people have seized on an overly restrictive notion of the meaning of language, and don't accept how we actually use it.

Comments

[ewx.livejournal.com]

On reflection I find myself believing both "-7 is prime", and "if someone says this works for all primes they only mean positive ones" are reasonable things to claim as true in the absence of context.

-7 plainly isn't composite, for instance. If you believe it is then I suspect you risk ending up talking yourself into -1 being prime which is plainly ridiculuous. From another angle, it is a non-unit that satisfies p|ab => p|a or p|b.

Still, if people talk about all primes, they generally do mean the +ve ones.

Obviously what's going on is that the implicit context induced by the two statements is different.

Obviously what's going on is that the implicit context induced by the two statements is different.

[cartesiandaemon.livejournal.com]

Exactly! Thank you.

Without context, primes refer to the normal, positive integer primes.

With context that is nonsense if you don't allow negative numbers, you use the obvious field.

But here, it could be either, the context is ambiguous between the two.

Re: Obviously what's going on is that the implicit context induced by the two statements is differen

[ewx.livejournal.com]

Not a field. Fields don't have primes, because everything but 0 is a unit, and 0 doesn't divide anything l-)

Re: Obviously what's going on is that the implicit context induced by the two statements is differen

[cartesiandaemon.livejournal.com]

Ring! Ring! Sorry.