Exercise 2.6 - Answers
1 |
(i)
|
Yes
(in so far as it is acceptable to use "[j®y]" to translate "if j,
y" at all). Maybe the
first sentence implies that he was happy that Liverpool had
won; but arguably this is just a matter of implicature.
|
| |
(ii) |
No.
The first sentence means that John doesn't know whether Liverpool
won the cup. Even if we take "John doesn't know" to mean
"John does not know that Liverpool won the cup", the second
sentence does not capture what the first sentence says. It would,
for instance be true if Liverpool did not win the cup and John knows
that they did not; but the first sentence would be false.
|
| |
(iii) |
Yes.
We could equally have had "[you will succeed ®
you will try]".
|
| |
(iv)
|
No.
The first sentence would be true if trying were necessary for your
success but not sufficient, whereas the second sentence would be false.
Equally if trying were sufficient for success but not necessary, the
second sentence would be true but the first false. An acceptable translation
would be, "[you will succeed ®
you will try]"; or (equivalently), "[¬you will try ®
¬you will succeed]"; or "¬[you will succeed Ù
¬you will try]"; or "[¬you will succeed Ú you will try]".
|
| |
(v) |
Yes. Or "[you
will succeed ® you will try]"; or "¬[you will
succeed Ù ¬you will try]";
or "[¬you will succeed Ú you will try]". These are all equivalent.
|
| |
(vi)
|
No
(most likely). The original sentence means (most probably) that I
will be in the garden whether my mother telephones or not; that is,
it will be false if I shall not be in the garden. The second sentence,
however, will be true if I shall not be in the garden and my mother
does not telephone.
|
| |
(vii) |
Yes
|
| |
(viii) |
Answer.
No. Most likely the first sentence is saying something general about
eggs: any egg that has been boiled for ten minutes in hard. In that
case it will be false if some eggs boiled for ten minutes are hard
and some are not. The second sentence, however, will be true it some
egg has been boiled for ten minutes and some egg is hard (even a different
one). It would not do, either, to translate the first sentence as;
"[An
egg has been boiled for ten minutes ® it is hard]"
Assuming
that "it is hard" is (as it should be) a stand-alone sentence,
the "it" will have to refer to some specific thing, if "it
is hard" is to be true. Let us suppose that it does, and that
the thing (whatever it is) is hard. Then the second sentence will
be true, but the first could easily be false. Let us suppose instead
that the thing, whatever it is, is not hard, but that an egg has been
boiled for ten minutes. In that case the second sentence will be false,
but the first sentence could easily be true – unless, of course, the
thing that isn't hard happens to be an egg which has been boiled for
ten minutes!
|
| |
(ix) |
No.
The mere fact that the egg was not boiled at all would be enough to
make the second sentence true. But, if the egg was a hen's egg, we
can be pretty sure that the first sentence is false. |
|