I.(20) Determine the truth values of each of the following propositions using the appropriate symbolism and methods of translation with immediate inference. Show all steps in the transformation of statements.

Given: "P()F" is true.

1. P))F - no transformation.  On the square of opposition, undetermined.

2. non-F))non-P:  contrapositive:  P))F.  On square, undetermined.

3. non-F()P:  converse:  P()non-F; obverse P((F.  On square, undetermined.

4. non-P((non-F:  contrapositive:  F((P.  Convert the given proposition to F()P.  Compare given [F()P] to F((P.  On square, undetermined.

5. non-F)(P:  converse:  P)(non-F; obverse P))F.  On square, undetermined.

II.(20) For the arguments below, provide the symbolic expansion and determine whether they are valid or invalid using a Venn Diagram. 

1. OAE-22. AIO-3

OAE-2 expansion
P((M
S))M
S)(P

AIO-3 expansion
M))P
M()S
S((P

EAI-1 expansion
M)(P
S))M
S()P

Venn Diagrams will be done in class.
 

3. EAI-1

4. At least some non-C is B, which implies that no C is a D, since every non-B is a non-D.
    Translation problem:
        Conclusion:  C)(D
        Major Premise:  non-B))non-D
        Minor Premise:  non-C()B

            Standard order:

non-B))non-D - contrapositive:  D))B
non-C()B - converse: B()non-C; obverse:  B((C
C)(D

    Standard form and order

    D))B
    B((C
    C)(D

        Mood and figure:  AOE-4
                Invalid argument.  Venn Diagram will be done in class.

5. Flammable chemicals are always toxic, and some toxic chemicals are non-edible. It follows that some flammable chemical is non-edible.
    Translation problem:
        Conclusion:  F()non-E
        Minor Premise:  F))T
        Major Premise:  T()non-E

            Standard Order:

T()non-E - obverse:  T((E
F))T - no transformation
F()non-E - obverse:  F((E

Final transformation:
T((E
F))T
F((E

    Mood and Figure:  OAO-1
        Invalid argument.  Venn diagram will be done in class.

6. God must exist since a thing that is non-existent is imperfect, and God is perfect.
Conclusion:  (All) God is an existent thing.  = G))E
Minor Premise:  (All) God is perfect.
Major Premise:  All non-E are non-P (non-perfect)

Standard Order:

non-E))non-P --- contrapositive:  P))E
G))P - no transformation
G))E - no transformation

    Final transformation:

P))E
G))P
G))E

    Mood and Figure:  AAA-1, valid.  Venn diagram of AAA-1 already done in class.
 
 

III.(30) Provide one of the following: 1) The statement that makes the argument in question valid, or 2) the reason (considering the rules/fallacies [see the list of acceptable uses above]) that the argument cannot be rendered valid, if in fact it cannot be.
 

1.No valid argument is non-deductive, and all invalid arguments are unsound, so all sound arguments are deductive.
Translation:
Conclusion:  All S are D.
Major Premise:  No V are non-D
Minor Premise:  All non-V are non-S
    Symbolic Form:

V)(non-D
non-V))non-S
S))D
        Transformation:
V))D
S))V
S))D
    Valid.  AAA-1.

2.F((G. Therefore, L))G.
    This is a second order enthymeme (missing the minor premise).  The partial symbolic representation is:
F((G
Minor Premise Missing
L))G

    Explanation:  There is no premise you can add to make the argument valid.  As it stands, it commits the fallacy of ACFNP.  The major premise is an O form (negative) and the conclusion is an A form (affirmative).

3.AI_-2

    The partial mood and figure (expanded) is:
P))M
S()M
    Explanation:  There is nothing to add to make the argument valid.  As it stands, it commits the fallacy of undistributed middle.

IV. (30) Open Section. Choose any two of the following.

1.What is the mood and figure of an argument which: 1) commits the fallacy of illicit process of the major term, 2) commits the fallacy of illicit process of the minor term, and 3) shows the middle term appearing in the predicate position in both of its occurrences?
    Explanation:
  The middle term appearing in the predicate position in both occurrences means the argument is in 2nd figure.
        Since the argument commits IMIN and IMAJ, the conclusion must be an E form.
        From this point, there are several moods that fit the description of this argument.  You need to determine only one.

2.Is it possible for an argument having all terms distributed to be valid? Why? Explain briefly in terms of the rules and fallacies for categorical syllogisms.
No.  Explanation:  If all the terms in the argument are distributed in every one of their occurrences, you know that all the premises are E form premises.  An argument having two negative premises commits the fallacy of exclusive premise (EXP).

3. State the converse, the obverse, and the contrapositive of each of the following statements.

a. A))B
Converse:  B))A - but this is not equivalent to the original
Obverse:  A)(non-B
Contrapositive:  non-B))non-A

b. non-C()D
Converse:  D()non-C
Obverse:  non-C((non-D
Contrapositive:  non-D()C - but this is not equivalent to the original.

c. non-E)(F
Converse:  F)(non-E
Obverse:  non-E))non-F
Contrapositive:  non-F((E (by limitation).

d.A()non-B
Converse:  non-B()A
Obverse:  A((B
Contrapositive:  B()non-A, but this is not equivalent to the original.

e.L)(non-R
Converse:  non-R)(L
Obverse:  L))R
Contrapositive:  R((non-L (by limitation)

f.non-M))non-D
Converse:  non-D()non-M (by limitation)
Obverse:  non-M)(D
Contrapositive:  D))M