Reason and Argument
Chapter 7 (2/2)
Existential Commitment
• Since existential commitment doesn’t
make a difference to most syllogisms
(arguments constructed out of A, E, I, and
O claims) we don’t have to make a
decision at all in most cases. Where a
decision is required, assume that people
DO make existential commitments.
Otherwise, our Venn diagram system will
be an incomplete system.
Syllogism
• A syllogism is made up entirely of categorical
claims
• There are 2 and only 2 premises and one
conclusion
– Major premise: contains the predicate term
– Minor premise: contains the subject term
• There are 3 and only 3 terms in a syllogism.
– Predicate term: predicate of the conclusion
– Subject term: subject of the conclusion
– Middle term: term that is not in the conclusion, but is
in each premise
Validity for Syllogisms
• Validity means the same thing it always has. IF
the premises are true, then the conclusion must
be.
• To determine if a syllogism is valid, we make a
Venn Diagram with three circles and then
diagram the premises. If the information given
by the conclusion is represented by
diagramming the premises, then the premises
guarantee the conclusion, and the argument is
valid.
Venn Diagram Method:
1.
2.
3.
4.
Draw three circles in the appropriate way
Label each circle in the appropriate way
Diagram the premises
If any area is the only un-shaded area of its
circle, put a * in it. (existential commitment)
After this, put your pen/pencil down.
5. Check if the information given by the
conclusion is or is not represented on the
diagram. If it is, the argument is valid, if not,
the argument is not valid.
Note about the *
• When the * could go in one of two areas
on a three-circle Venn Diagram, it must go
on the line between them to indicate that
the * is in one of the two areas, but that
the premises do not specify which.
• The information that this conveys is NOT
that there is a * in both areas, nor neither.
• See p.193-194
The Rules Method
• First, Vocab: (different context than Grice’s
rules)
– Quality: as before, is the claim affirmative or
negative?
– Quantity: Is the claim universal or particular?
– Distribution: Whether the whole of a term is
being discussed. (more on this next slide)
Distribution (se p.214)
Claim
Subject
Predicate
A
Distributed
not
E
Distributed
Distributed
I
not
not
O
not
Distributed
The Rules:
• Quality:
– 1. Nothing follows from two negative premises
– 2. If one premise is negative, then the conclusion must also be
negative. (classical theory also maintained that if the conclusion
is negative, one premise must be negative)
• Distribution:
– 3. The middle term must be distributed at least once.
– 4. The subject term may not be distributed in the conclusion if it
is not distributed in the premises.
– 5. The predicate term may not be distributed in the conclusion if
it is not distributed in the premises.
• Quantity:
– 6. Nothing follows from two particular premises.
Just for fun…
Figure 1 Figure 2
Figure 3
Figure 4
Barbara Cesare
Darapti
Bramantip
Celarent Camestres
Darii
Festino
Ferio
Baroco
Disamis
Datisi
Felapton
Camenes
Dimaris
Fesapo
Bocardo
Fresison
Ferison