Exercise 3.3
1.
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Formalise
the following arguments as faithfully as you can as correct syntactic
sequents. |
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(i)
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Aston,
I fear, are going to be relegated. The problem is that to avoid this
fate they must beat not only Sutton but also Weston. But they won't
beat Weston, surely, unless Weston lose to Sutton – and even then
they are not certain of beating them. But in any case Sutton will
beat Weston only if they are the better side and, what is more, are
at least as good as Aston. But in that case they won't lose to Aston. |
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(ii) |
Since
John doesn't know very much about gardening, he will succeed in growing
carrots only if Mary helps him. After all, to grow them to maturity
he will have to get the seeds to germinate and will have to protect
the plants from the carrot fly. And, though he might succeed in the
former by good fortune, without Mary's help, he is bound to fail in
the latter. |
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(iii)
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Without
a change in conductor, there will not be any improvement in the orchestra's
standards. A new conductor is unthinkable, though, with the present
procedure for selecting orchestral managers; but replacing that involves
a major administrative exercise, and any such exercise is bound to
require an injection of new funds. If a new source of funding is required,
then there will have to be a substantial grant from central government.
Therefore a substantial governmental grant is essential if there is
to be any improvement in orchestral standards. |
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(iv)
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Unless
the Prime Minister intervenes, the Chancellor will cut taxes before
the General Election. If he does, there will either be a run on the
pound or the Government will increase the national debt. But the Prime
Minister will not intervene. So, unless the Government increase the
national debt, there will be a run on the pound. |
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(v)
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There
will be no fight at the club tonight, because there will be one only
if John and Henry are both at the club. But John will not be allowed
into the club unless accompanied by Jenny, and if Jenny goes with
John she will not go with Henry. I know, however, that Henry won't
go unless he goes with Jenny. |
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