Lecture 7 June 4, 2012
Why isn’t it enough to know, say, that an argument is valid in order to know whether you should
accept its conclusion?
How do you know whether an argument that would use predicate logic is intended to be valid or
• If each of its premises and its conclusion can be written in one of the four standard forms
for categorical statements, it is intended to be valid.
• Four standard forms: All A are B, no A are B, some A are B, some A or not B.
- Can “most A are B” be translated into one of these? No, it cannot, so the Four
Rule Method cannot be used to test for cogency.
- It is saying more than “some A are B”. (“some” means “at least one”)
- It is not saying that some A are not B, since “most A are B” would be true even if
“all A are B” were true.
Ie. “Most of the students in this room are under 50”. – This isn’t false if all
the students in this room are under 50.
Can these claims fit into one of the four standard forms?
• Every A is a B. = All A are B.
• Only A are B. = All B are A.
Consider the following two claims:
1. Dr. Mc owns a van.
2. Dr. Mc does not own a van.
Could they be true at the same time? No.
They are “in conflict” or inconsistent.
They cannot both be false at the same time.
1. Dr. Mc’s one and only van is all orange.
2. Dr. Mc’s one and only van is all green.
In conflict? (Ask – Could they both be true at the same time?) Yes, they cannot
be true at the same time and there are in conflict.
Could the both be false at the same time? Yes. They could be neither green nor
• If a pair of propositions could not both be true, but could both be false, they are
• In the first example? – If a pair of propositions could not both be true, but they also could
not both be false, they are contradictories.
1. Dr. Mc has a dog.
2. Dr. Mc has a cat.
They are not in conflict.
How do we test for validity?
• In sentential, we display the pattern and compare it to our tables.
• Or we c