1. The construction of a formal argument
Logic
The construction of a formal argument

2. Logic: the study of the correct rules of reasoning
Reason vs. Rhetoric
Propositions: declarative statements that assert a claim
They are either true or false
Analytic vs. Synthetic propositions (Kant)
analytic: predicate adds nothing to the subject
E.g =4
Deductive reasoning
Pure rationalism; no new information from the world
Synthetic: predicate adds knowledge to subject.
Conclusions come from our observation of the world
E.g. “The rose is red.”

3. Induction Drawing conclusions from observation of particular cases
Scientific method
Knowledge is always a matter of probability
We frame expectations of future events
Arguments not “valid” in formal sense; rather, “strong” or “weak”
Analogical reasoning (“if it cures cancer in mice, it should cure cancer in people”)
Occam’s Razor

4. abduction Reasoning “to the best explanation”
Seeks to add explanatory reason
“Occam’s razor”
Seek simplist explanation
Is there a God? (utilizing abductive reasib)

5. Deductive reasoning {deduce: to derive a conclusion from something known)
Syllogisms: formal arguments with premises and conclusions
Truth preserving (as in a mathematical equation)
Validity vs. soundness
A valid and sound argument should always be true
Categorical syllogism
A) Socrates is a man
B) All men are mortal
C) therefore: Socrates is mortal
(valid & sound argument)
A) Socrates is a dolphin
B) All dolphins are mortal
C) Therefore: Socrates is mortal
(valid but unsound)

6. Hypothetical Syllogism forms
Modus Ponens: (affirming the antecedent)
If P, then Q
A) If it rains the ball game will be cancelled
B) It’s raining
C) the game is cancelled
Modus Tallens (denying the consequent)
If P, then Q; Not P; not Q
B) It is not raining
C) the game is not cancelled

7. Invalid Hypothetical forms
Denying the antecedent
A) if P, then Q
B) not P
C) therefore, not Q
Example
A) If Mary is a mother, she is a woman
B) Mary is not a mother
C) Therefore, Mary is not a woman

8. Invalid Hypothetical Forms
Affirming the consequent
A) If P, then Q
B) Q
C) therefore, P
Example:
If Mary if a mother, she is a woman
Mary is a woman
Therefore, she is a mother

9. Necessary vs. Sufficient
Necessary—”A” is required for “B” result
(To earn good grades one must study diligently)
Sufficient—”A” is one cause of “B” result
(beheading is sufficient for death)
Necessary and sufficient
(For the world to be made right, Jesus must return)

10. Logical fallacies: a lifelong pursuit