The word 'may' (verbal reasoning)

Question

(As originally found http://pistonheads.com/gassing/topic.asp?h=0&f=10&t=622599&i=0).

Last night a school was vandalised by youths on motorbikes who were pulling wheelies on the football pitch. Stuart Brown owns a motorcycle.

The question:

Stuart may have been one of the youths who vandalised the school.

Answer can be (A. True) (B. False) or (C. Impossible to tell.)

Clive · Accepted Answer

Hi,
As originally found here).

Last night a school was vandalised by youths on motorbikes who were pulling wheelies on the football pitch. Stuart Brown owns a motorcycle.

The question:

Stuart may have been one of the youths who vandalised the school.

Answer can be (A. True) (B. False) or (C. Impossible to tell.)

Before I try to answer, let me first ask you to consider how you would answer in the above categories for these statements.

Stuart may be 75 years old.

Stuart may have been in jail last night.

Stuart may not know how to pull a wheelie.

Stuart may have been in a submarine under the Atlantic ocean last night.

Do you see any difference between my questions and yours?

Best wishes, Clive

Anonymous · Answer

Thanks for the reply Clive.

I would choose true for all of your statements. I'm not sure C makes much sense (e.g. is it impossible to tell if Stuart may be 75 years old?)

I can't say that I see any major differences between the original statement and any of yours?

Clive · Answer

Hi,
If 'true' means 'It is true that Stuart may have been . . . ', then I'd say the original statement and my statements are all true.

If 'true' means that 'Stuart was one of the youths who did this', then the answer is that it is impossible to tell, based on the facts as given.

In the context of a 'may' statement, I interpret C to mean the rather awkward 'It is impossible to tell if it is possible that . . . '. It's pretty hard to understand this.

In such problem statements, anything is possible, unless we are given facts that show it is not possible.

Best wishes, Clive

Anonymous · Answer

I concur. It is woefully worded with respect to option C.

Thanks.

CalifJim · Answer

Years ago, my logic teacher said, "Any statement of the form 'It may be the case that ...' is always true."

In fact, he even wrote the "truth table" on the board:

X : | true | false

It may be that X : | true | true

Thus: 'It may be that the moon is made of cheese' is true, i.e., 'The moon may be made of cheese' is true.

According to 'formal logic' then, the answer is A.

Whether the rules of 'formal logic' are the same as those of 'ordinary language logic' is an open question. It appears to me that 'matters of fact' are more important in 'ordinary language logic', so that in ordinary language 'The moon may be made of cheese' is false because we know for various reasons that the moon is not, as a matter of fact, made of cheese.

CJ

MrPedantic · Answer

I would say that the "may" statement is true for any of these 2nd statements:

1. Stuart has been on the school football pitch.
2. Stuart has vandalised a school.
3. Stuart has a motorbike.
4. Stuart is a youth.
5. Stuart exists.
6. Stuart likes coffee.
7. Stuart is reading this thread in horror.

or even:

8.

MrP

Kooyeen · Answer

CalifJimYears ago, my logic teacher said, "Any statement of the form 'It may be the case that ...' is always true."

That is interesting, and I was going to agree, but then I realized there are some faults after seeing your example "The moon may be made of cheese"... It's not made of cheese, so everyone would answer "that's false".

MAY means "possible with probability greater than 0".
The moon may be made of cheese ---> It is possible with probability greater than 0 that the moon is made of cheese:
- True if the fact "the moon is made of cheese" has been associated with a probability P greater than 0
- False if it has been associated with a probability P = 0
So it can only be true if you don't believe in science, you are suspicious anyway, or you don't know anything about the moon.

So the original question can be seen this way:
Last night a school was vandalised by youths on motorbikes who were pulling wheelies on the football pitch. Stuart Brown owns a motorcycle.
Stuart may have been one of the youths who vandalised the school. ---> It is possible he's one of those who vandalized the school
- True if we associate the fact Stuart was among them with a probability P > 0
- False if that's impossible and we associate it with P = 0
- Impossible to tell if we don't associate that event with a probability

From the information we have, we can't exclude Stuart from the list of suspects, and so we can't associate the fact with P = 0. If you think it's impossible to tell, not associating a probability would mean you are not willing to express an opinion, so it's not a sensible answer. So I guess that statement is true.
If we knew Stuart was an old man, it would have to be excluded, the associated probability would be 0, and the statement would be false.

CalifJim · Answer

KooyeenMAY means "possible with probability greater than 0".

That's one interpretation.

Or. MAY means "possible in some possible world".

But then what does "possible in some possible world" mean?

CJ

MrPedantic · Answer

In the original thread, the responses of "Elysium" are quite interesting. He opts for C ("impossible to tell"), on the basis that further information about Stuart (i.e. his age) is required, before we can even say that "Stuart may have been one of the youths". For all we know (according to Elysium), Stuart may be 75 years old; in which case, it would not be possible for Stuart to have been one of the youths. Thus we can't include S. among our suspects (A), or exclude him (B), till we know his age; which means we have to choose C.

This line of argument has quite a few subscribers on the original forum, and also seems to reflect the intentions of the test-writer, who does indeed give C as the answer (in a book of tests of "verbal reasoning").

The fallacy here seems to lie in an equivocation on "may": Elysium and the question-setter seem to think that there is a degree of uncertainty > 0 but < 1 which "may" may not express. In other words, according to E., we can only say "On the available evidence, X may have happened" when more evidence becomes available.

The invalidity of C may become clearer with fuller responses:

A. Last night youths on motorbikes vandalised a school. Stuart owns a motorbike. On the available evidence, the statement "S. may have been one of the youths" is true.

B. Last night youths on motorbikes vandalised a school. Stuart owns a motorbike. On the available evidence, the statement "S. may have been one of the youths" is false.

C. Last night youths on motorbikes vandalised a school. Stuart owns a motorbike. On the available evidence, it is impossible to tell whether the statement "S. may have been one of the youths" is true or false.

If we can dismiss A or B, we can also dismiss C. Since B is not a reasonable inference, only A is possible.

MrP

The word 'may' (verbal reasoning)

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