“Introduction to Logic” Ateneo de Manila High School English IV Mr. Galinato

OBJECTIVES Define LOGIC Define an ARGUMENT Define a PROPOSITION Define and identify PREMISE(S) and CONCLUSION(S) in an argument Identify INDICATORS for arguments, premises, and conclusions At the end of the lesson, the students should be able to…

Determine and differentiate GOOD from BAD arguments Determine and differentiate DEDUCTIVE from INDUCTIVE reasoning in arguments Determine whether a proposition is TRUE or FALSE Determine and differentiate a VALID argument from a SOUND argument OBJECTIVES At the end of the lesson, the students should be able to…

What is Logic? Logic differs from other academic disciplines in that it studies the forms of thought, whereas the other disciplines study their own fields of study. Examples: –S–Sociology studies human society. –E–Economics studies the economic relations in society.

Logic studies the question how to distinguish between good and bad arguments. Thus, LOGIC is a “normative” discipline (as opposed to a “descriptive / empirical” discipline) – it tries to separate the “GOOD” from the “BAD.” In Logic, we are concerned with the following: What is there in a good argument that makes it good? In other words, what makes it so compelling and forceful that it is not possible not to believe it? What is Logic?

What is an Argument? We have seen that Logic studies how good arguments differ from bad ones. But then, what is an Argument? In order to answer this, let us look at some examples: Suppose someone says to you: “The weather today is terrible.” He is stating a fact.

But if he says to you: “Classes should be suspended because of the terrible weather,” what is he trying to do? He is trying to persuade you to believe what he wants you to believe. This is the essence of an ARGUMENT. Arguments are sets of sentences designed to persuade the listener or the reader to believe their conclusions. What is an Argument?

Thus, to simply say that the weather is terrible is not an argument. When you say this to your friend, you are not trying to change his or her mind. But if you say, “Classes should be suspended because of the terrible weather,” you are ARGUING. You are not merely stating a fact.

Identify whether the following are arguments or not: –T–The blackboard is made of wood. –A–All blackboards are actually green. –E–Everyone in this class is male. –E–Everyone in this class should do well in English. –O–Our country has a democratic type of government. –D–Democracy may not be best for the Philippines.

Arguments are composed of PROPOSITIONS. Propositions are statements that are either TRUE or FALSE. Examples: –T–The earth is flat. –V–Vampires exist. –A–All Ateneo High School students are male. –K–Kobe Bryant is currently the best basketball player in the NBA. Form of Argument

Arguments have two (2) parts: One part states what the listener should believe – the point of the argument. We call this the CONCLUSION of the argument. The other part concerns the reasons supporting why the conclusion should be accepted. We call this the PREMISE of the argument. Form of Argument

Thus, in the argument: “Classes should be suspended because of the terrible weather,” the CONCLUSION is “Classes should be suspended,” and the PREMISE is “the terrible weather.”

Another example: Suppose someone says: “All Ateneo High School students are male. Girlie is a student from the Ateneo High School. Therefore, Girlie is male.” This is also an argument. What is the CONCLUSION of the argument? What are the PREMISES of the argument?

Indicators ARGUMENTPREMISECONCLUSION mustasso oughtforthus shouldbuthence necessarilysincetherefore becauseaccordingly howeverconsequently this is whyit follows that neverthelessone may infer assuming thatwhich means that in as much aswhich implies that for the reason thatone can conclude that

Good & Bad Arguments Let’s look at this argument again: –A–All Ateneo High School students are male. –G–Girlie is a student from the Ateneo High School. –T–Therefore, Girlie is male. Question: If the premises are true, can the conclusion be anything but true?

Let’s look at another argument: –J–Josef is an Ateneo High School student. –S–Some students from the Ateneo High School love math. –H–Hence, Josef loves math. The premises are all true, but are you compelled to accept that Josef MUST love math because of what the premises say? Good & Bad Arguments

Now we say that Logic seeks to establish the criteria for good arguments. In other words, Logic tries to distinguish between “good” and “bad” arguments. A GOOD argument is one whose premise establishes its conclusion. On the other hand, a BAD argument weakly establishes its conclusion or not at all. We are compelled to accept the conclusions of good arguments, but we are not compelled to accept the conclusions of bad ones.

Deductive & Inductive Arguments Look at this argument: –A–All Ateneo High School students have to study English. –T–Therefore, fourth-year Ateneo High School students have to study English. Apart from the question whether this argument is good or bad, there is another aspect of this argument. It is a DEDUCTIVE one.

Another example: –O–One-third of the students in this room love math. –C–Consequently, one-third of the students in the Ateneo High School love math. This is a totally different kind of argument from what we have been working on. This is an INDUCTIVE argument. Deductive & Inductive Arguments

In a DEDUCTIVE argument, the content of the conclusion lies entirely within the domain or the content of the premises. Going back to the example: –A–All Ateneo High School students have to study English. –T–Therefore, fourth-year Ateneo High School students have to study English.

In an INDUCTIVE argument, the content of the conclusion lies at least partially outside the content of the premises. Going back to the example: –O–One-third of the students in this room love math. –C–Consequently, one-third of the students in the Ateneo High School love math.

DEDUCTIVE INDUCTIVE Premise(s) Conclusion Premise(s) Conclusion

With INDUCTIVE reasoning, we add one piece of information to another until we have enough evidence to draw a conclusion. With DEDUCTIVE reasoning, we use earlier conclusions, reached inductively by ourselves or others, to answer new questions about material.

Here is another example: –A–All the mangoes I have tasted in the basket are sweet. –O–One may infer that all the mangoes in the basket are sweet. Which is the premise of the argument? Which is the conclusion? Is it Deductive or Inductive?

Yet another example: –I–If it rains, the road will be wet. –I–It is not raining right now. –I–It follows that the road is dry. Which is the conclusion of the argument? Which are the premises? Is it Deductive or Inductive? Is it a good or a bad argument? Why?

Validity, Truth, & Soundness Look at this argument: –A–All human beings have four eyes. –C–Cyclops is a human being. –I–It follows that Cyclops has four eyes. Question: If we accept the premises as true, then are we compelled to accept the conclusion? If the answer is yes, then we have to accept that this argument is valid.

Thus, a VALID argument is one whose premises, if taken as true, are able to establish their conclusion. The premises do not have to be really true. The point is that, if they were true, then the conclusion would also be true. However in Logic, we do not want our system to simply distinguish valid from invalid arguments. We want the system to give us a TRUE conclusion, which merely valid arguments cannot guarantee. Validity, Truth, & Soundness

So we introduce another criteria: An argument is SOUND if and only if it is valid and contains all true premises. Look at the following argument: –K–Kim is an Ateneo High School student. –A–All Ateneo High School students are female. –O–One can conclude that Kim is female. Which are the premises of the argument? Which is the conclusion? Is this a valid argument or an invalid one? Why? Is it a sound argument? Why?

Look at the following argument: –A–All 4E, 4H, and 4L students belong to the Ateneo High School. –G–Gabs is from 4E. –I–It follows that Gabs is a student from the Ateneo High School. Which is the conclusion of the argument? Which are the premises? Is this a valid argument or an invalid one? Why? Is it a sound argument? Why?

SUMMARY LOGIC studies the forms of thought. It is not an empirical study. Logic studies criteria for distinguishing GOOD from BAD arguments. Good arguments are those whose PREMISES establish their CONCLUSION.

INDUCTIVE arguments are those the content of whose conclusion exceeds that of the premises. Vice versa for DEDUCTIVE arguments. An argument is VALID if there is no possibility for the conclusion to be false if the premises are true. An argument is SOUND if it is both valid and contains all true premises. SUMMARY

“Exercises on Logic”

Exercises on Logic 1.What is LOGIC? 2.What is an ARGUMENT? 3.What is a PROPOSITION? 4.What is the difference between a GOOD argument and a BAD one?

5.When do we say that an argument is VALID or INVALID? 6.Is there such a thing as a TRUE or FALSE argument? How about a VALID or INVALID proposition? 7.When is a proposition TRUE? 8.What are the conditions of a SOUND argument? Exercises on Logic

Look at the following argument: –I–I think we can assume that all male teachers from the English Department are handsome since Mr. G., who is from the English Department, is such a very good-looking teacher. 9.Identify the premise(s). 10.Identify the conclusion. 11.Is the argument deductive or inductive? 12.If it is deductive, turn it into an inductive argument, and vice versa. Exercises on Logic

Look at the following argument: –A–All two-legged creatures are humans. –C–Chickens are two-legged creatures. –C–Consequently, chickens are humans. 13.Is the argument valid or invalid? 14.Are the propositions true or false? 15.Is the argument sound? Exercises on Logic

“Points for Reflection”

Points for Reflection “We may not be aware of it but we are surrounded by ARGUMENTS. We are bombarded with statements from media and other people, trying to PERSUADE us into believing what they want us to believe. The challenge is for us to be sensitive to these PROPOSITIONS and identify which are TRUE or FALSE. We must be vigilant; we must constantly watch out for arguments which may be VALID but actually hold false PREMISES. We must be extra cautious in simply taking in any information. We must constantly practice the value of learning to think for ourselves.”

“Homework”

Homework 1.Review the concepts of logical reasoning as discussed in class a)LOGIC b)ARGUMENT c)PROPOSITIONS d)PREMISE / CONCLUSION e)GOOD / BAD argument

Homework 1.Review the concepts of logical reasoning as discussed in class f)DEDUCTIVE / INDUCTIVE reasoning g)VALID / INVALID argument h)TRUE / FALSE proposition i)SOUND argument

2.Try to jumble and mix up these concepts. For example: a)Can an INVALID argument contain TRUE propositions? b)Is a GOOD argument necessarily a VALID one? c)Etc. Homework

3.Read “Induction and Deduction,” pp , AIE. Pay special attention to SYLLOGISMS. 4.Read “The Importance of Not Being Smith” by Bob Bagnall, pp , AIE. Homework

“Thank you and goodbye class!”