Principles of Logics

Dr. Akhlas AhmedIBT, City Campus

Jan 28th, 2017Lecture # 2

• The etymology of word logic!• Greek word• Logos…• Sometimes translated as sentence,

discourse, reason, rule and ratio. • These translations are not enough to help us

understand the more specialized meaning of "logic" as it is used today.

• What is logic?• Logic is the study of the principles of

correct reasoning. (a rough definition)

• Logic…a new definition• Logic is not the psychology of reasoning. • According to this definition, logic is concerned with the

principles of correct reasoning. • Studying the correct principles of reasoning is not the

same as studying the psychology of reasoning. • Logic is the former discipline that tells us how we ought

to reason if we want to reason correctly.• Whether people actually follow these rules of correct

reasoning is an empirical matter, something that is not the concern of logic.

• Psychology…• The psychology of reasoning is an empirical

science.

• It tells us about the actual reasoning habits of people, including their mistakes.

• A psychologist studying reasoning might be

interested in how people's ability to reason varies with age. But such empirical facts are of no concern to the logic.

• The principles of logic…• What are these principles of reasoning that

are part of logic?

• There are many such principles, but the main (not the only) thing that we study in logic are principles governing the validity of arguments - whether certain conclusions follow from some given assumptions.

• The principles of logic…• Look at the arguments… • Example # 1: • If Tom is a philosopher, then Tom is

poor.• Tom is a philosopher.• Therefore, Tom is poor. • Your opinion about argument?

• The principles of logic…• Look at the arguments… • Example # 2: • If K>10, then K>2.• K>10.• Therefore, K>2.• Your opinion about argument?

• The principles of logic…• Look at the arguments… • Example # 3: • If Tarragona is in Europe, then

Tarragona is not in China.• Tarragona is in Europe.

Therefore, Tarragona is not in China.• Your opinion about argument?

• Findings from the examples…• In all three examples, these arguments are

obviously good arguments.• Their conclusions follow from the

assumptions. If the assumptions of the argument are true, the conclusion of the argument must also be true.

• A logician will tell us that they are all cases of a particular form of argument known as "modus ponens":

• If P, then Q. P. Therefore, Q.

• Conclusion…• Logic is not just concerned with the

validity of arguments. • Logic also studies consistency, and

logical truths, and properties of logical systems such as completeness and soundness.

• Rules of reasoning in logic…• Modus ponens might be used to illustrate two

features about the rules of reasoning in logic. • First feature is its topic-neutrality. As the four

examples suggest, modus ponens can be used in reasoning about diverse topics. This is true of all the principles of reasoning in logic.

• The laws of biology might be true only of living creatures, and the laws of economics are only applicable to collections of agents that engage in financial transactions.

• But the principles of logic are universal principles which are more general than biology and economics.

• Famous definition of logic…• According to famous logician Alfred Tarski

(1901-1983)… • From his famous book ‘Introduction to logic and

to the methodology of deductive sciences, Dover, page xi.’

• [Logic is] ... the name of a discipline which analyzes the meaning of the concepts common to all the sciences, and establishes the general laws governing the concepts.

• Famous definition of logic…• According to famous logician Gottolob

Frege (1848-1925)… • From his 1956 paper "The Thought : A

Logical Inquiry" in Mind Vol. 65

• [Logic is] ...To discover truths is the task of all sciences; it falls to logic to discern the laws of truth. ... I assign to logic the task of discovering the laws of truth, not of assertion or thought.

• Concept of Necessity in Logic…• Logic is different from the empirical sciences like

physics, chemistry or biology. • Logic truths donot depend on any particular

accidental features of the world.• The principles of logic are derived using reasoning

only, and their validity doesnot depend on any contingent features of the world.

• Example, logic tells that any statement of the form "If P then P." is necessarily true. This is a principle of the second kind that logician study. This principle tells us that a statement such as "if it is raining, then it is raining" must be true. We can easily see that this is indeed the case, whether or not it is actually raining. Furthermore, even if the laws of physics or weather patterns were to change, this statement will remain true.

• Concept of Necessity in Logic…• The scientific truths are contingent. • Physics and the other empirical sciences

investigate the way the world actually is• Physicists might tell us that no signal can travel

faster than the speed of light, but if the laws of physics have been different, then perhaps this would not have been true.

• Similarly, biologists might study how dolphins communicate with each other, but if the course of evolution had been different, then perhaps dolphins might not have existed.

• So the theories in the empirical sciences are contingent in the sense that they could have been otherwise.

• What is logic?• Logic is the study of valid reasoning. • That is, logic tries to establish criteria to

decide whether some piece of reasoning is valid or invalid.

• OK, so then what do we mean by ‘valid reasoning’?

• Reasoning…• A piece of reasoning consists of a sequence of

statements, some of which are claimed to follow from previous ones. That is, some are claimed to be inferred from others.

• Example: “Either the housemaid or the butler killed Mr. X. However, if the housemaid would have done it, the alarm would have gone off, and the alarm did not go off. Therefore, the butler did it.”

• Valid Reasoning…• While in every piece of reasoning certain

statements are claimed to follow from others, this may in fact not be the case.

• Example: “If I win the lottery, then I’m happy. However, I did not win the lottery. Therefore, I am not happy.”

• A piece of reasoning is valid if the statements that are claimed to follow from previous ones do indeed follow from those. Otherwise, the reasoning is said to be invalid.

• Sound Reasoning…• Not all valid reasoning is good reasoning.• Example: “If I win the lottery, then I’ll be

poor. So, since I did win the lottery, I am poor.”

• This piece of reasoning is valid, but not very good, since it assumed an absurd claim (‘If I win the lottery, I’ll be poor.’ Huh??)

• Sound reasoning is valid reasoning based on acceptable assumptions.

• Truth and Implication…• Logic studies the validity of reasoning.• Logic does not study soundness.• Therefore, logic alone cannot tell us whether

an argument is good. Hence, logic alone is not a guide to truth.

• Instead, logic can tell us, assuming certain things to be true, what else will be true as well. Thus, logic is a guide to implication.

• Arguments, Premises and Conclusion• In logic, pieces of reasoning are analyzed using

the notion of an argument• An argument consists of any number of premises,

and one conclusion• Again, in logic, we are merely interested in

whether the conclusion follows from the premises: we are not interested in whether those premises are true or acceptable.

Quiz # 2 (28.1.2017)Q2. How is science different

from logic?

Assignment # 2 (28.1.2017)Q1. Suppose we find out that people

reason better when they are not under stress. Should this be

counted as a principle of logic?

Q2. How is mathematics different from logic?