I. Deductive arguments with one premise, those based on: A. the Square of Opposition, and

B. Those which are logical equivalences (some converses & contrapositives; all obverses) or related by limitation.

II. Deductive arguments which combine I.A & B.
 

ELEMENTS USED IN DECISION PROCESS

1. Decide whether to look first at the Square or the equivalences: For Square, the terms will be the same (no complements of original terms; no switch in places) AND there will be a change of quantity or quality or a combination. For equivalences, there can be a change of positions of terms or a substitution of one or more complements (or for "by limitation" which are not really equivalences, there will be a quantity change) or a change in quality. If there is more than one of these changes, there might be a chain of inferences.

2. For each immediate inference do the following:

(a) Recognize the logical relation between the premise and the conclusion (or intermediate conclusion).

(b) Decide if the logical relation allows a valid immediate inference

(c) If a valid inference is allowed, decide the truth value of the conclusion, given the truth value of premise.

3. Where there is more than one immediate inference--hence a chain of inferences from the given premise to the proposed (final) conclusion), you will need to trace out each intermediate conclusion, where such an intermediate conclusion then acts as the premise for the next (intermediate or final) conclusion in the chain. Do this by applying one or more of the changes that occur between the original premise and the final conclusion where this(these) changes(s) matches that for one of the types of logical relations based either on the Square or logical equivalences.
 

ARGUMENT TYPE I.A.:

If [the premise] "Some people are brave" is true, then

[the conclusion] "Some people are not brave" is ______ [supply truth value], because _____ [give logical relation name]
 

DECISION PROCESS

1. Both statements have the same subject and predicate terms, so I will look at the Square. The premise is I-form and the conclusion is O-form, which are subcontraries to one another.

2. The definition of subcontraries states that if one is known to be true, the other cannot be determined--hence no valid inference can be drawn.

3. Thus, the truth value of the conclusion is UNDETERMINED.
 

ARGUMENT TYPE I.B.:

If [the premise] "All success stories are matter for inquiry" is false,

then [the conclusion] "All matters for inquiry are success stories" is _______ [supply truth value],

because ____________[give logical relation name]
 

DECISION PROCESS

1. The two statements have the same terms in different places, so I need to look at the forms for logical equivalences. The switch of terms is the only change, and the form matches that of conversion.

2. The premise is an A statement and conversion is INVALID for As.

3. So, the truth value of the conclusion is undetermined.
 

ARGUMENT TYPE II (Mixed) Exercise will start with just (a) and (c) given.

(a) [the premise] "All nursery rhymes are myths" is true.

So, (b) [an intermed. concl.] ___________________ is ______, because:_______

And so, (c) "No nonmyths are nonnursery rhymes" is ________, because:_______
 

DECISION PROCESS: (1) Between (a) & (c) there is a change of quality, substitution of two complements, and position switch. The last two map to contrapositive & the first to Square.

(2) Generate CONTRARY of (a): (b) "No nursery rhymes are myths"

(3) Generate CONTRAPOS. of (b): "No nonmyths are nonnursery rhymes"--which is (c) above. (4) CONTRARY (b) of a true A-statement (a) is FALSE. and (5) the CONTRAPOS. (c) of an E-statement (b) is invalid, so (c) is UNDETERMINED.