A lecture on "Logic"...

1. WHAT IS LOGIC

2. Definition
 Logic is the study of methods and
principles used to distinguish good
(correct) from bad (incorrect) reasoning.
 Logic is the study of the principles of valid
inference and demonstration
 Logic is a branch of philosophy

3. Reasoning
 Logic is the science of laws of thought
 BUT not all thought is the object of study
for the logician
 All reasoning is thinking, but not all
thinking is reasoning
 Logic is the science of Reasoning

4. INFERENCE
PREMISES AND CONCLUSION
 Inference is the process by which one proposition
is arrived at and affirmed on the basis of one or
more propositions
 Propositions are either true or false
 Not all sentences are propositions
Conclusion of an argument is the proposition that is
affirmed on the basis of the other propositions

5. Conclusion-indicators
 Therefore
 Hence
 Thus
 So
 Accordingly
 In consequence
 Consequently
 Proves that
 As a result
 For this reason

6. Premiss-indicators
 Since
 Because
 For as follows from
 As shown by
 Inasmuch as

7. Types of reasoning
 Deduction
 Induction

8. Deductive Arguments
 Conclusion claims to follow from
premises with necessity
 Valid or invalid: all-or-nothing
 If the conclusion does follow necessarily,
the argument cannot be improved by
adding more premises

9. Deductive Argument
Here’s an example of a deductive
argument:
All men are rational.
John is a man.
Therefore, John is rational.

10. Inductive Arguments
 Conclusion follows with a greater or
lesser degree of probability
 Always a matter of degree
 Can always be made better (stronger) by
adding more premises

11. Inductive Argument
Here’s an example of an inductive
argument:
 Seattle has had over 30” of rain each year
for the past ten years
 Therefore, Seattle will probably have at
least 30” of rain this year.

12. Terms of Evaluation
 Deductive: Valid or Invalid
 Inductive: Strong or Weak

13. Evaluating Deductive
Arguments
 Two Questions:
Is the argument valid, i.e., does the
conclusion follow necessarily?
Are the premises true?
 If “Yes” to both questions, then it is a
sound argument
 If “No” to either or both questions, then
argument is unsound.

14. Evaluating Inductive
Arguments
 Two Questions:
 Is the argument strong, i.e., does the conclusion
follow with a high degree of probability?
 Are the premises true, complete and relevant?
 If “Yes” to both questions, then it is a cogent
argument
 If “No” to either or both questions, then
argument is non-cogent

15. Comparison
Deductive Inductive
Strength of
Reasoning:
Valid/
Invalid
Strong/
Weak
Premises: True/False True/False
Complete
Relevant
Overall: Sound/
Unsound
Cogent/
Uncogent

16. Properties of logical systems
 Among the valuable properties that logical systems can
have are:
 Consistency, which means that none of the theorems of
the system contradict one another.
 Soundness, which means that the system's rules of proof
will never allow a false inference from a true premise. If a
system is sound and its axioms are true then its theorems
are also guaranteed to be true.
 Completeness, which means that there are no true
sentences in the system that cannot, at least in principle,
be proved in the system.