1. Logic and Rational Behavior
(2007: 142)
Definition
 Logic deals with meanings in a language system, not with actual
behavior of any sort. Logic deals most centrally with propositions. The
terms logic and logical do not apply directly to utterances (which are
instances of behavior).
 There is an important connection between logic and rational behavior,
but it is wrong to equate the two. Logic is just one contributing factor
in rational behavior.
Rational Behavior involves:
 (a) goals
 (b) assumptions and knowledge about existing states of affairs
 (c) calculations, based on these assumptions and knowledge,
leading to ways of achieving the goals.

2. Example of Rational Behavior
(2007: 142-143)
 Goal: To alleviate my hunger.
 Assumptions and knowledge:
 Hunger is alleviated by eating food
 Fried rice is food.
 There is a portion of fried rice in front of me.
 I am able to eat this portion of fried rice.
 Calculation:
 If hunger is alleviated by eating food and fried rice is food, then hunger is
alleviated by eating fried rice.
 If hunger is alleviated by eating food, then my own hunger would be
alleviated by eating this portion of fried rice, and eating this portion of
fried rice would alleviate my hunger, and my goal is to alleviate my
hunger, so therefore eating this portion of fried rice would achieve my goal.
 Practice:
 Make your own example.

3. Logical Notation
(2007: 147)
 It is a specially developed way of representing propositions
unambiguously.
Examples:
 John and Mary are married are paraphrased as:
 John and Mary are married to each other or
 John is married to someone and Mary is married to someone.
 Ali throw the mango
 The fried rice is too hot
 The first interpretation:
 (j MARRIED TO m) & (m MARRIED TO j)
 The second interpretation:
 (Ex (j MARRIED TO x)) & (Ey (m MARRIED TO y))

4. A System of Logic
(2007:149)
 A system of logic, similar to a system of arithmetic, has two things:
 1. A notation (a definition of all possible proper formulae in the
 system).
 2. A set of rules (for calculating with the formulae in various
 ways).
 a. Valid arguments.
 1) If John bought that house, he must have got a loan from
 the bank. He did buy the house, therefore he did get a
 loan from the bank.
 2) John is a Scot, and all Scots are drunkards, so John is a
 drunkard.
 b. Invalid arguments.
 1) If John bought that house, he must have got a loan from
 the bank. He did buy that house, so therefore he didn’t
 get a loan from the bank.
 2) No one is answering the phone at Gary’s house, so he
 must be at home, because whenever Gary’s at home, he
 never answers the phone.

5. Modus Ponens
(2007: 149)
 Rule:
 Modus Ponens is a rule stating that if a proposition P entails a proposition Q, and P is true,
then Q is true.
 The diagram of Modus Ponens is:
 P  Q Premiss

 P Premiss
 _______
 Q Conclusion
 Examples:
 (1) John is married to Mary (P) entails Mary is John’s wife (Q).
 (2) Mr. SBY is our president (P) entails Mrs. SBY is the first lady (Q).
 Practice:
 Find your own examples.

6. Notation for Simple Propositions
(2007: 157)
 Each simple proposition has one predicator that must be
written in capitals. While the arguments of the predicator
must be represented by single lower-case letters.
 Examples:
 (1) Blackie is a dog : b DOG.
 (2) Romeo loved Juliet : r LOVE j.
 (3) Peter introduced Barbara to Jack :
 p INTRODUCE b j.
 Practice:
 Create your own examples.

7. Reasons for Stripping down
Names and Predicators (2007: 161)
 1. The reasons for eliminating elements such as
 forms of the verb be, articles, tense markers,
 and certain prepositions are:
 a. Partly a matter of serious principle.
 b. Partly a matter of convenience.
 2. The most serious principle involved is the
 traditional concentration of logic on truth.
 3. Articles do not effect the truth of the
 propositions expressed by simple sentences.

8. Prepositions in Logical Notations
(2007: 165)
 A. Prepositions with significant contributions are not omitted in
 logical notation (L.N).
 Examples:
 (1) The hat is on the table: h ON t
 (2) He is looking for Jack: h LOOK-FOR j
 (3) John is looking after her: j LOOK-AFTER h
 B. Prepositions without significant contributions are omitted in LN.
 Examples:
 (1) Jane is crazy about Beethoven: j CRAZY b
 (2) Jack is an uncle of Peter: j UNCLE p
 (3) Ellen is envious of Jane: e ENVIOUS j
 Practice:
 Create your own examples.

9. Logical notation for equative and non-equative sentences
(2007:156)
 A. LN for equative sentences:
 (1) Clark Kent is Superman: kc = s
 (2) Dr. Jekyll is Mr. Hyde: dj = mh
 (3) SBY is our president: s = op
 B. LN for non-equative sentences:
 (1) Clark Kent is a reporter: ck REPORTER
 (2) Dr. Jekyll was a gentleman: dj GENTLEMAN
 (3) SBY was a general: s GENERAL
 Practice:
 Create your own examples.

10. Logical Formulae
(2007: 157)
 Definition
 Every simple proposition is represented by a single predicator and a number of
arguments.
 Examples:
 (1) j LOVE m is a well-formed formula for a simple proposition with a
 two-place predicate as a predicator.
 (2) j m is not a well-formed formula, because it contains no
 predicator.
 (3) j IDOLIZE ADORE m is not a well-formed formula for a simple
 proposition, because it contains two predicators.
 (4) j and h LOVE m is not a well-formed formula for a simple
 proposition, because it contains (‘and’) which is neither a
 predicator nor a name.
 Practice:
 Create your own examples.

11. A way of representing items at all three
levels (2007: 161)
 Utterance:
 (1) ‘Indonesia is a republic’
 (2) ‘John loves Erna’
 Sentence:
 (1) Indonesia is a republic.
 (2) John is an artist.
 Proposition:
 (1) i REPUBLIC
 (2) j LOVE e
 Practice:
 Give your own examples.

12. Connective and (&)
(2007: 164 )
 Rule:
 Any number of individual well formed formulae can be placed
in a sequence with the symbol & between each adjacent pair
in the sequence: the result is a complex well formed formula.
 Example:
 c COME g : Caesar came to Gaul
 c SEE g : Caesar saw Gaul
 c CONQUER g : Caesar conquered Gaul
 They are combined into a single complex formula:
•(c COME g) & (c SEE g) & (c CONQUER g)

13. Commutativity of Conjucntion
(2007: 167)
 It is presented by using the following diagram:
 p & q (premiss)
 ______
 q & p (conclusion)
 In this diagram p and q are variables ranging over propositions, that is p and q
stand for any propositions.
 Examples:
 (1) t PUNISH b & t PUNISH j and t PUNISH j &
 t PUNISH b.
 (2) d IN b & m IN l and m IN l & d IN b
 Practice:
 Create your own examples.

14. Correct and Incorrect Rules in
Commutativity (2007: 168)
 (1) p (premiss)
 q (premiss)
 -----
 p & q (conclusion)
 (2) p & q (premiss)
 ------
 p (conclusion)
 (3) p (premiss)
 -----
 p & q (conclusion)
 (1) and (2) are correct, but (3) is incorrect.
 Illustrate with your own examples.