Valid Arguments
I need help with these two questions. Perhaps an example to illustrate the answer provided?
5. An invalid argument that can be made valid by the addition of a new premise? Yes.
Plenty of examples, but let me offer a more general observation. We can always
make an invalid argument valid, by adding a contradiction into the premises. For
an argument is valid if and only if it is impossible for all the premises to be true and
the conclusion false. If the premises are contradictory, then it is impossible for them
all to be true (and the conclusion false).
6. A valid argument that can be made invalid by the addition of a new premise? No.
An argument is valid if and only if it is impossible for all the premises to be true
and the conclusion false. Adding another premise will only make it harder for the
premises all to be true together.
5. An invalid argument that can be made valid by the addition of a new premise? Yes.
Plenty of examples, but let me offer a more general observation. We can always
make an invalid argument valid, by adding a contradiction into the premises. For
an argument is valid if and only if it is impossible for all the premises to be true and
the conclusion false. If the premises are contradictory, then it is impossible for them
all to be true (and the conclusion false).
6. A valid argument that can be made invalid by the addition of a new premise? No.
An argument is valid if and only if it is impossible for all the premises to be true
and the conclusion false. Adding another premise will only make it harder for the
premises all to be true together.
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