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# Logic 1

## on Jun 02, 2011

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## Logic 1Presentation Transcript

• Logic
Logic is a word that means many things to different people.
Many words such as logic and logical could be replaced by expressions such as rational behavior and reasonable.
For instance, you may say that “Nicole acted quite logically in locking her door”, meaning that Nicole had good, well thought-out reasons for doing what she did.
• Logic
Definition
LOGIC deals with meanings in a language system, not with actual behavior of any sort. Logic deals most centrally with PROPOSITIONS. The term ‘logic’ and ‘logical’ do not apply directly to UTTERANCES (which are instances of behavior)
A proposition is the meaning of an utterance of a declarative sentence which describes some state of affairs.
• Logic
Exercice
Based on the definition of the term logic, what can you say about the following statements? In other words, do they satisfy the narrow sense of logic?
It’s not logical to want to kill herself yes/no
Harry is so illogical: first he says he doesn’t want to come, and then he changes his mind. Yes/no
The truth that Socrates is mortal follows logically from the fact that Socrates is a man and the fact that all men are mortal. Yes/no
Ali is not coming is logically, the negation of Ali is coming. Yes/no
• Logic
There is an important connection between logic and rational action. But it is wrong to equate the two.
Logic is just one contributing factor in rational behavior. Rational behavior involves:
Goals
Assumptions and knowledge about existing states of affairs
Calculations, based on these assumptions and knowledge, leading to ways of achieving the goals.
• Logic
Example:
Goal: To alleviate hunger
Assumptions and Knowledge:
• Hunger is alleviated by eating food
• Cheese is food
• There is a piece of cheese in front of me.
• I am able to eat this piece of cheese.
• Calculations:
• Logic
If hunger is alleviated by eating food and cheese is food, then hunger is alleviated by eating cheese.
If then hunger is alleviated by eating cheese, then my own hunger would be alleviated by eating this piece of cheese in front of me, and
Eating this piece of cheese would alleviate my hunger, and my goal is to alleviate my hunger, so therefore eating this piece of cheese would achieve my goal.
• Logic
Rational action: eating the cheese
HOWEVER,
If the word cheese is replaced by chalk, would the calculations lead to the conclusion that I should eat a piece of chalk?
Yes, the calculations would lead to the same conclusion, because logic provides rules for calculations regardless whether we think it is irrational to eat a piece of chalk.
• Logic
Analytical sentences
Are those expressing necessary truths of logic
Ex. Either John is here or John is not here.
a. John is here and John is not here
b. If someone is here, then no one is here.
• Logic
A notation for simple proposition
• A simple proposition is like a simple sentence which has one predicator. The predicator is written in CAPITAL LETTERS
The arguments of the predicator are represented by lower-case letters.
Example:
Abraham died would be represented as a DIE.
Fido is a dog by f DOG
Ted loves Alice by t LOVE a
Phil introduced Mary to Jack by p INTRODUCE m j
• Logic
Exercice: Translate the following into this simple notation:
(1) Arthur dreamed
(2) Bill Gulped
Charlie Swore
Patrick cursed
Why do we omit ‘the’, ‘a’ in forming this logic?
Answer: these do not affect the truth of the proposition
Exercice, p. 148