1. For Friday, read chapter 2, sections 1-2 (pp. 12-19). As nongraded homework, do the problems on p. 19. Graded homework #1 is due at the beginning of class on Friday.

2. What is Logic? Logic is the study of methods for evaluating arguments. An argument is a set of statements, one of which is the conclusion and the rest of which (the premises) are meant to provide rational support for the conclusion. What is a statement? It’s the sort of sentence that could be true or false.

3. How do we evaluate arguments? All humans are reptiles. All reptiles live in trees. Therefore, all humans live in trees. What’s good about this argument? What’s bad?

4. We separate questions of form from questions about the truth and falsity of premises (or conclusions). About form: Does the conclusion follow from the premises? About the status of the premises: Are the data accurate? Are the assumptions correct? Are the premises true?

5. All humans are reptiles. All reptiles live in trees. Therefore, all humans live in trees. The form of this reasoning is: All As are Bs. All Bs are Cs (where C = things that live in trees) Therefore, all As are Cs.

6. In logic we address questions about form only (see Forbes’s comments about topic neutrality and independence of actual truth or falsity). So, my description of Logic should really say, “Logic is the study of methods of evaluating reasoning, i.e., the step(s) taken from the premises to the conclusion of an argument.”

7. We will be studying deductive logic, which applies to arguments the premises of which are supposed to guarantee the truth of their conclusions. In everyday life, much of our reasoning is inductive. It involves probabilities: we ask what is likely to be true based on some premises (evidence, data).

8. Validity is the central concept in the study of deductive logic An argument is valid if and only if it is necessary that if the premises are all true, then the conclusion is true. Put differently, an argument is valid if and only if it is impossible for all of the premises to be true and the conclusion false at the same time (that is, in a single situation). Any argument that is not valid is invalid.

9. Soundness If possible, we would like our arguments to be valid and to have all true premises. An argument with both characteristics (valid, with all true premises) is sound. Any argument that is not sound is unsound. An unsound argument is either invalid or has at least one false premise (or both).

10. All whales are fish. No fish live in trees. Therefore, no whales live in trees. Valid? Sound? Answer: Valid, but unsound; one false premise is enough to make the argument unsound.

11. Some fruits are green. Some fruits are apples. Therefore, some fruits are green apples. Answer: Invalid, and unsound—even though all three statements in the argument are true. A note about ‘some’: For our purposes, ‘some’ means ‘at least one’.

12. These arguments involve category relations: all humans are said to be in the category of reptiles. But for the next few weeks, we’ll be studying sentential logic; we will treat entire simple sentences as single units: If I win the lottery, then I’ll be rich. I just won the lottery. Therefore, I’m rich

13. Sentential Logic The system contains three kinds of symbol, each playing a different role: 1. The five sentential connectives: ~ (tilde), & (ampersand), v (vee), → (arrow), and ↔ (double- arrow). These connect together (or preface) symbols of the second type 2. Capital letters A-Z abbreviate simple (or atomic) statement. These are grammatically simple sentences that have no words corresponding to sentential connectives in them.

14. ‘~’ abbreviates ‘not’ and equivalent phrases, such as ‘it is not the case that’ Joanne is not tall. (J: Joanne is tall) ~ J ~ J It is not the case that Tom is a lawyer. (T: Tom is a lawyer) ~ T

15. ‘&’ abbreviates ‘and’ and equivalent terms José is a doctor and Martin is a lawyer. (J: José is a doctor; M: Martin is a lawyer) J & M Theresa is poor, even though she is a doctor. (P: Theresa is poor; D: Theresa is a doctor) P & D