Reason and Argument

1
Reason and Argument

• Chapter 7 (2/2)

2
Existential Commitment

• Since existential commitment doesnt make a
  difference to most syllogisms (arguments
  constructed out of A, E, I, and O claims) we
  dont 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.

3
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

4
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.

5
Venn Diagram Method

1. Draw three circles in the appropriate way
2. Label each circle in the appropriate way
3. Diagram the premises
4. 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.

6
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

7
The Rules Method

• First, Vocab (different context than Grices
  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)

8
Distribution (se p.214)
Claim Subject Predicate
A Distributed not
E Distributed Distributed
I not not
O not Distributed
9
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.

10
Just for fun
Figure 1 Figure 2 Figure 3 Figure 4
Barbara Cesare Darapti Bramantip
Celarent Camestres Disamis Camenes
Darii Festino Datisi Dimaris
Ferio Baroco Felapton Fesapo
  Bocardo Fresison
  Ferison