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SUBJECT: ARGUMENT TERMINOLOGY
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I am grading your PP2s. Many of you (even most of you!) are still
having problems with logical terminology, which is making it confusing
for me to evaluate your papers.
Please remember for PP3 (and beyond):
SENTENCES can only be TRUE or FALSE
(or you can agree or disagree with them)
ARGUMENTS (which are sequences of sentences)
can be VALID or INVALID
(they can be SOUND or UNSOUND, too)
CONCLUSIONS of arguments can *FOLLOW VALIDLY*
or *NOT FOLLOW VALIDLY* from the premises of the argument
Therefore:
SENTENCES (including premises and conclusions)
canNOT be valid or invalid, or sound or unsound
ARGUMENTS canNOT be true or false
Also:
An argument is valid iff it is IMPOSSIBLE for its conclusion to be false
while all of its premises are true.
The premises of a valid argument CAN all be false.
The conclusion of a valid argument CAN also be false.
Therefore:
An argument is INvalid iff it is POSSIBLE for all of its
premises to be true AND its conclusion to be false.
The premises of an invalid argument CAN all be true.
The conclusion of an invalid argument CAN also be true.
In other words, validity has nothing to do with the ACTUAL truth or
falsity of the premises or conclusion.
It only has to do with the RELATIONSHIP of the conclusion to the
premises.
An argument is sound iff it is valid AND all of its premises ARE true.
Therefore:
An argument is UNsound iff EITHER it is INvalid
OR at least one premise is false
(OR both)
An UNsound argument CAN be valid!
If you'd like more examples of any of these possibilities, please ask.