Logic and Reasoning QRII. Introduction

Transcription

1 Logic and Reasoning QRII Introduction

2 A Note About Textbooks Here is an example of a standard textbook for a course like this one.

3 A Note About Textbooks It is a pretty good basic introduction to logic.

4 A Note About Textbooks It is a pretty good basic introduction to logic. A new copy costs $95 on Amazon.

5 A Note About Textbooks Textbooks are ridiculously expensive. And that is morally outrageous. In order to save my students some money, I wrote a textbook that I make available in electronic form for free. I will be updating the text this week.

6 A Note About Textbooks In the lectures, I try not to simply repeat the things I say in the textbook. But still, you may find that you want to hear someone else s voice or see another approach to logic.

7 A Note About Textbooks

8 A Note About Textbooks

9 And Now Let s start thinking about logic!

10 What is Logic? Richard Whately ( ) was the author of a very influential textbook on logic at the beginning of the nineteenth century. His textbook was one cause of the revival of interest in logic among English-speaking people. Richard Whately

11 What is Logic? Logic may be considered as the Science, and also as the Art, of Reasoning. It investigates the principles on which argumentation is conducted, and furnishes rules to secure the mind from error in its deductions. Richard Whately

12 What is Logic? J.S. Mill ( ) was a very prolific and influential British economist and philosopher. His enormous System of Logic continues to be an important text today. J.S. Mill

13 What is Logic? Logic is not the science of Belief, but the science of Proof, or Evidence. In so far as belief professes to be founded on proof, the office of logic is to supply a test for ascertaining whether or not the belief is well grounded. J.S. Mill

14 What is Logic? Gottlob Frege ( ) was a German philosopher and mathematician famous today as the discoverer of first-order logic. Gottlob Frege

15 What is Logic? To discover truths is the task of all sciences; it falls to logic to discern the laws of truth. Gottlob Frege

16 What is Logic? Susan Haack (1945-) is a British- American philosopher of logic. Susan Haack

17 What is Logic? The claim of a formal system to be a logic depends upon its aspiring to embody canons of valid argument. Susan Haack

18 What is Logic? Graham Priest (1948-) is a British- Australian philosopher and logician famous for his work on paraconsistent logics and his defense of dialetheism. Graham Priest

19 What is Logic? We all reason. We try to figure out what is so, reasoning on the basis of what we already know. We try to persuade others that something is so by giving them reasons. Graham Priest

20 What is Logic? Logic is the study of what counts as a good reason for what, and why. Graham Priest

21 What is Logic? I claim that logic has (at least) these two features: Logic is a study of reasoning. Logic is prescriptive, not descriptive.

22 Arguments Instead of looking at reasoning directly, logicians look at representations of reasoning: arguments. By studying what makes arguments good or bad, logicians hope to understand what makes reasoning good or bad.

23 Arguments Instead of looking at reasoning directly, logicians look at representations of reasoning: arguments. By studying what makes arguments good or bad, logicians hope to understand what makes reasoning good or bad. What is an argument?

24 Arguments For our purposes, an argument is a collection of sentences taken to evidentially support some other sentence, which is called the conclusion of the argument. The sentences that are supposed to support the conclusion are called the premisses.

25 Arguments For our purposes, an argument is a collection of sentences taken to evidentially support some other sentence, which is called the conclusion of the argument. The sentences that are supposed to support the conclusion are called the premisses. What weaknesses can you see in this definition?

26 Arguments PREMISSES CONCLUSION

27 Arguments PREMISSES Evidential Support Relation CONCLUSION

28 Arguments What is evidential support? What does it mean for some premisses to evidentially support a conclusion?

29 Arguments When an argument is good, its premisses evidentially support its conclusion. Since we only care about the relation of evidential support, we do not care whether the premisses of an argument are true or false!

30 Arguments Example #1. The argument sketch is a Monty Python sketch. Every Monty Python sketch is funny. The argument sketch is funny.

31 Arguments Example #2. If it is possible that God exists, then God exists. It is possible that God exists. God exists.

32 Arguments In the previous examples, if the premisses are true, then the conclusion is guaranteed to be true as well. Of course, if the premisses are not true, then the conclusion might be false. So, one way of rejecting the conclusion of an argument is to reject its premisses.

33 Arguments When the conclusion of an argument is guaranteed to be true under the condition that the premisses are true, the premisses clearly evidentially support the conclusion. But the premisses of an argument may evidentially support its conclusion without guaranteeing that the conclusion is true.

34 Arguments Example #3. Ten students were chosen at random from a group of 100. Nine of those students were history majors. More than half of the students in the group are history majors.

35 Arguments Example #3. Ten students were chosen at random from a group of 100. Nine of those students were history majors. More than half of the students in the group are history majors.

36 Arguments Example #4. The sun has risen every morning that I can remember. The sun will rise tomorrow.

37 Arguments Arguments like the first two examples are called deductive or non-ampliative arguments. The conclusions of such arguments do not amplify the premisses. They take no risks.

38 Arguments Arguments like the third and fourth examples are called inductive or ampliative. The conclusions of such arguments amplify the premisses. They assume some inductive risk.

39 Arguments If the premisses of an argument do not evidentially support its conclusion, then it is a bad argument. Completely worthless arguments are very rare in actual conversations.

40 Arguments Example #5. Every squirrel likes to eat nuts. Marmaduke once chased a squirrel. Therefore, Marmaduke likes to eat nuts.

41 Arguments Can you think of some other examples of good arguments? How about really bad arguments?

42 Next Time We ll start building a formal language in order to help us better understand the evidential support relation.