16/4/94
This island consists of a Northern and a Southern Division; but I am not sure where the boundary-line is.
The Northern Division is Brown’s estate: the Southern is mine.
Brown is selling his estate to me; but I do not know whether the sale is completed.
The following propositions are true.
I. If this field is Brown’s, it must be in the Northern Division (for otherwise it would be part of my estate).
II. If the sale is completed, then, if this field is Brown’s, it cannot be in the Northern Division (for otherwise it would be mine by purchase).
Now let “A is true” = “this field is Brown’s”
“B is true” = “this field is in the Northern Division”
“C is true” = “the sale is completed”
Then Propositions I, II, are equivalent to (i), (ii), and the question “can C be true?” is equivalent to “is it possible that the sale is completed?”
Here the 2 Propositions, “if A is true B is true” and “if A is true B is not true,” both of them contain a logical sequence. Also they are compatible; their combined effect being “A is not true.”
Hence, if C is true, A is not true; and vice versâ, if A is true, C is not true: i. e. A and C cannot be true together.
But there is nothing to prevent C alone being true; i. e. it is possible, consistently with I and II, that the sale may have been completed.