Dialogue Education Update 4 CRITICAL THINKING PART 1

Dialogue Education Update 4 CRITICAL THINKING– PART 1 THIS CD HAS BEEN PRODUCED FOR TEACHERS TO USE IN THE CLASSROOM. IT IS A CONDITION OF THE USE OF THIS CD THAT IT BE USED ONLY BY THE PEOPLE FROM SCHOOLS THAT HAVE PURCHASED THE CD ROM FROM DIALOGUE EDUCATION. (THIS DOES NOT PROHIBIT ITS USE ON A SCHOOL’S 1

KAHOOT- CRITICAL THINKING 2

CONTENTS Page 4 - Video - Monty Python sketch Page 5 to 7 - What is an argument? Page 7 - Factual and Inferential Claims Pages 8 to 31 - How to analyse an argument. Pages 32 to 43 - A second example. Page 45 - Bibliography 3

CLICK ON THE IMAGE BELOW FOR YOU TUBE PRESENTATION ON BAD REASONING You will need to be connected to the internet to view this presentation. Enlarge to full screen 4

AN ARGUMENT IS a group, series, or set of STATEMENTS in which one of the statements, known as the CONCLUSION, is claimed by the arguer to follow logically (by way of INFERENCE) from the other statements in the argument, which are known as PREMISES (and which the arguer claims to be 5

All arguments have the same basic structure or format: 1. Premise 2. Premise 3. Premise 4. Conclusion Factual Claim (premises are true) Inference Inferential Claim - that the truth of the conclusion follows logically (by way of inference) from the ASSUMED truth of the premises 6

FACTUAL CLAIM & INFERENTIAL CLAIM The factual claim in an argument is the claim, made by the arguer, that all of the premises in the argument are true (as opposed to false or unconvinc-ing). The inferential claim in an argument is the claim, made by the arguer, that the conclusion of the argument follows logically from its premises, assuming that the premises are true. 7

EXAMPLE OF DEDUCTIVE REASONING 1. All humans are mortal. 2. Socrates is human. therefore (inference) 3. Socrates is mortal 8

How to (1) analyze and (2) evaluate an argument 9

First, we need to find an argument to analyze and evaluate. 10

Suppose someone were to argue something really silly, like 11

“All dogs have two heads because all dogs are bananas, and all bananas have two heads. ” 12

The argument must be subjected to a 6 step analysis & evaluation. Step 1. Identify the conclusion. Step 2. Identify the premises. Step 3. Set the argument up in “standard form. ” These three steps constitute an “argument analysis. ” An “argument evaluation” consists of the next three steps, which are: 13

Step 4. Evaluate the factual claim. Are the premises true, false, or unconvincing? Step 5. Evaluate the inferential claim. Does the conclusion follow logically from the premises (assuming that they are true)? Step 6. Evaluate the argument as a whole. Is it sound or unsound? 14

LET’S APPLY THE SIX-STEP METHOD TO OUR SAMPLE ARGUMENT ABOUT BANANAS AND DOGS. (1) All dogs have two heads because (2) all dogs are bananas and (3) all bananas have two heads. Step 1. What’s the conclusion ? 15

Step 1: Can you see that the conclusion of the argument is “All dogs have two heads” 16

and that the premises are Step 2: “All dogs are bananas” and “All bananas have two heads”? 17

STEP 3: Thus, the logical (or “standard”) form of the argument is 1. All bananas have two heads. 2. All dogs are bananas. 3. All dogs have two heads. 18

Or to put it more abstractly, 1. All B is T. 2. All D is B. 3. All D is T. 19

and even more abstractly, Twoheaded Bananas things dogs 20

WE HAVE NOW (1) identified the conclusion of the argument, (2) identified the premises of the argument, and (3) represented the argument in STANDARD FORM. That is what is meant by an ARGUMENT ANALYSIS. 21

Now we need an ARGUMENT EVALUATION. Is the argument successful (“sound”)? 22

FOR THE ARGUMENT TO BE “SOUND, ” the premises of the argument must be true (as opposed to false or unconvincing) and the conclusion of the argument must follow logically from the premises (assuming that they are true). 23

Step 4: Are the premises of the argument true, or false, or unconvincing? Premise 1: Is it true or are you convinced that “all bananas have two heads”? Premise 2: Is it true or are you convinced that “all dogs are bananas”? 24

This step is easy (in this case). It is obvious to anyone in his (or her) right mind that both premises in this argument are FALSE. 25

Another point about Step 4: We need to explain WHY we think the premises are true, false, or unconvincing. 26

STEP 5: BUT WHAT ABOUT THE INFERENCE (OR INFERENTIAL CLAIM) IN THIS ARGUMENT? Does the conclusion follow logically from the premises (assuming that they are true)? In other words, IF all bananas were two-headed, and IF all dogs were bananas, would it follow logically that all dogs have two heads? 27

It would, wouldn’t it? The inference (reasoning) in the argument is “good. ” The conclusion does follow logically from the premises (on the assumption that the premises are true, which is an assumption we always make at Step 5). 28

STEP 6: IS THE ARGUMENT AS A WHOLE “SOUND”? Well, at Step 5 we saw that the inference (reasoning) in the argument is good, but at Step 4 we found that both premises in the argument are false. 29

For an argument to be sound, all of its premises must be true (i. e. , the “factual claim” in the argument must be justified) (Step 4), and the inference in the argument must be good (i. e. , the “inferential claim” in the argument must be justified) (Step 5). 30

The argument we have been considering is UNSOUND because, although it contains good reasoning, at least one of its premises is not true. 31

FOR AN ARGUMENT TO BE SOUND AS OPPOSED TO UNSOUND, both the factual claim and the inferential claim in the argument must be justified. If the factual claim is not justified (i. e. , if at least one premise is false or unconvincing), then the argument is unsound. If the inferential claim is not justified (i. e. , if the conclusion does not follow logically from the premises, assuming that they are true), then the argument is unsound. 32

AND, OF COURSE, if NEITHER the factual claim NOR the inferential claim is justified (i. e. , if the argument fails on both counts), then the argument is unsound. 33

Let’s now apply the six-step method of argument analysis and evaluation to a few simple (and unrealistic) arguments, beginning with this one: All cats are animals, and all tigers are cats. Therefore, all tigers must be animals. The argument contains three statements, right? Which one of them is the conclusion (Step 1)? 34

All cats are animals, and all tigers are cats. Therefore, all tigers must be animals. Step 2: What are the premises of this argument? Step 3: What is the logical (“standard”) form of the argument? (See next slide) 35

This is it, right? 1. All cats are animals. 2. All tigers are cats. 3. All tigers must be (are) animals. 36

Argument Evaluation 1. All cats are animals. 2. All tigers are cats. 3. All tigers are animals. Step 4: Is the factual claim justified? That is, are both premises true (as opposed to false or unconvincing)? 37

Step 5: Does the conclusion follow logically from the premises? 1. All cats are animals. 2. All tigers are cats. 3. All tigers are animals. That is, if all cats are animals, and if all tigers are cats, does it follow that all tigers are animals? 38

IF ALL CATS ARE ANIMALS, Animals 39

AND IF ALL TIGERS ARE CATS, Animals Cats Tigers it looks like all tigers must be animals, right? 40

Step 6: Is the argument as a whole sound or unsound? 1. All cats are animals. 2. All tigers are cats. 3. All tigers are animals. That is, are the factual claim and the inferential claim both justified? Are the premises true (Step 4), and does the conclusion follow logically from the premises (assuming that they are true) (Step 5)? 41

WHAT ABOUT THE FOLLOWING ARGUMENT? Tigers must be cats because all cats are animals and all tigers are also animals. Class Participation Exercise: Write a six-step analysis & evaluation of this argument. 42

Here’s the STANDARD FORM of the argument: 1. All cats are animals. 2. All tigers are animals. 3. All tigers are cats. 43

To prove that an argument is unsound is not to prove that its conclusion is false. A POSSIBLE MISCONCEPTION AT STEP 6 44

Six Steps to Analysing Clarifying and Evaluating Arguments Step 1. Identify the conclusion. Step 2. Identify the premises. Step 3. Set the argument up in “standard form. ” Step 4. Evaluate the factual claim. Are the premises true, false, or unconvincing? Step 5. Evaluate the inferential claim. Does the conclusion follow logically from the premises (assuming that they are true)? Step 6. Evaluate the argument as a whole. Is it sound or unsound? ARGUMENT- ALL WITCHES HAVE LONG POINTY NOSES. THERE ARE TWO STUDENTS AND ONE TEACHER IN OUR CLASS WITH POINTY NOSES. THEY MUST BE WITCHES. 45

BIBLIOGRAPHY Copeland, Jack. 1993. Artificial Intelligence : a philosophical introduction. Oxford: Blackwell. Furley, David. 2003. 'Rationality among the Greeks and Romans'. In The Gale Group, Dictionary of the history of ideas. University of Virginia Library. Jeffrey, Richard. 1991. Formal logic: its scope and limits, (3 rd ed. ). New York: Mc. Graw-Hill. Kirwin, Christopher. 1995. 'Reasoning'. In Ted Honderich (ed. ), The Oxford Companion to Philosophy. Oxford: Oxford University Press. Manktelow, K. I. 1999. Reasoning and Thinking (Cognitive Psychology: Modular Course. ). Hove, Sussex: Psychology Press Mc. Carty, L. Thorne. 1977. 'Reflections on TAXMAN: An Experiment on Artificial Intelligence and Legal Reasoning'. Harvard Law Review. Vol. 90, No. 5. Scriven, Michael. 1976. Reasoning. New York: Mc. Graw-Hill. ISBN 0 -07055882 -5 Wikipedia-Reasoning-http: //en. wikipedia. org/wiki/Reasoning 46