A nice little argument worth thinking about. The following is a valid inference.
(p → q) & (r → s), therefore (p → s) v (r → q)
But given this we can easily show that at least some cases of English indicative conditionals do not fit this scheme. Since they would if they were material conditionals, they are not material conditionals. Here's an example, taken from Graham Priest, who takes it from W. S. Cooper:
If John is in Paris he is in France & if John is in London he is in England.
From this we obviously cannot conclude
If John is in Paris he is in England or if John is in London he is France.
Another one. This is valid:
~(p → q), therefore p
But this is not:
It is not the case that if there is a good God the prayers of evil people will be answered. Therefore there is a good God.
Because, of course, it does not follow that there is a good God merely from the assumption that "if there is a good God the prayers of evil people will be answered" is false.
