by Domenic Marbaniang Formal Logic: Deductive Reasoning. Valid and Invalid Forms

1. LOGIC
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Domenic Marbaniang
LOGIC – Science of Correct Reasoning
Reasoning: Inductive and Deductive
Inductive: Inference from specific to general (Leads to
generalization; but, should not be hasty generalization).
Open to verification. Probable Conclusion. Experience &
Observation. Empirical evidence.
E.g. Sampling research..
I pick up 5 books in a shelf of 50 books and find them
to be books on psychology. I conclude that it is a
Psychology shelf.
Deductive: Inference from general to specific (Leads to
particular conclusion). Formal Logic (Relates to validity of
form). Valid or Invalid. Conclusion is necessary.
Argument from Premises.
E.g. All men are mortal
Aristotle is a man
Therefore, Aristotle is mortal
Syllogism: An argument made of two premises and one
conclusion, that contain three terms.

2. LOGIC
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Domenic Marbaniang
Premises: Major (Universal Assertion); Minor (Second
Premise).
E.g. All men are mortal (Major Premise)
Aristotle is a man (Minor Premise)
Therefore, Aristotle is mortal (Conclusion)
Term: (a) Major Term – Present in Major Premise and
Conclusion (b) Minor Term – Present in Minor Premise
and Conclusion (c) Middle Term – Present in Premises;
absent from Conclusion
E.g All men (MiddleT) are mortal (Maj)
Aristotle (Min) is a man (MiddleT)
Therefore, Aristotle(Min) is mortal (Maj)
Types of Deductive Argument: 1. Categorical 2.
Hypothetical 3. Disjunctive
1. Categorical Argument: Made up of categorical
statements. A categorical statement is a statement in
which relation is stated between terms in a categorical
manner. E.g. All men are mortal (All entities in the
category called “Man” belong to the category called
“mortal”)
E.g.

3. LOGIC
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Domenic Marbaniang
All men (MiddleT) are mortal (Maj)
Aristotle (Min) is a man (MiddleT)
Therefore, Aristotle(Min) is mortal (Maj)
Rules of a Valid Categorical Argument
1. The syllogism must only have 3 terms.
2. The Middle Term must not appear in the conclusion.
3. The Middle Term must be distributed at least once in
the premises.
4. Both premises should not be negative.
5. If one premise is particular, then the conclusion must
also be particular.
6. If one premise is negative, then the conclusion must also
be negative.
7. No conclusion can be drawn from two particular
premises.
8. If a term is not distributed in the premises, it cannot be
distributed in the conclusion.
2. Hypothetical Argument – is made up of an hypothetical
statement and an affirmation or negation of a part of the
statement.
E.g. If it is raining, then the ground is wet
The ground is not wet
Therefore, it is not raining.

4. LOGIC
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Domenic Marbaniang
Hypothetical statement is made up of two clauses: the
antecedent and the consequent.
E.g. If it is raining (antecedent), then the ground is
wet (consequent)
Rule: The second premise should affirm the antecedent
and the conclusion must affirm the consequent; or the
second premise should deny the consequent and the
conclusion must deny the antecedent. (AA-DC)
Only 2 Valid Forms
1. If x, then y
x
Therefore, y
2. If x, then y
Not y
Therefore, not x
Invalid Forms
If x, then y
Not x

5. LOGIC
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Domenic Marbaniang
Therefore, not y
If x, then y
Y
Therefore, x
If x, then y
X
Therefore, not y
3. Disjunctive Argument. Made up of a disjunctive
statement and the denial or affirmation of one of the
disjuncts. A disjunctive statement is made up of two
disjuncts.
E.g. Either he is sleeping or he is writing
Disjunct 1: He is sleeping; Disjunct 2: He is writing
Note: both of the disjuncts can be true, or one of them can
be false
Rule: The second premise should always only be the
denial of one of the disjuncts, and the conclusion the
affirmation of the other.

6. LOGIC
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Domenic Marbaniang
2 Valid Forms
Either x or y
Not x
Therefore, y
Either x or y
Not y
Therefore, x
Exclusive Cases (Where the law of Excluded Middle
Applies): Affirmation can apply.
E.g.
Either he is sleeping or he is not sleeping (analytic
statement)
He is sleeping
Therefore, it is not that he is not sleeping