1. Introduction to Sentential Logic: Syntax and Semantics PHIL 121: Methods of Reasoning March 8, 2013 Instructor:Karin Howe Binghamton University

2. Issues from Part I and II that are still highly relevant statement or proposition arguments, specifically deductive arguments validity/invalidity (no, these things never go away)  consistency/inconsistency  logically equivalent statements  contradictory statements

3. Most importantly … We will be looking at the logic of statements like these: –If kangaroos had wings then they could fly. –I like apples and bananas. –You may get either a puppy or a guppy. –You may not get a tiger for a pet. –You may go to the movies if and only if you clean your room.

4. Why is it called sentential logic? It is called sentential logic because it is the logic of sentences; namely, the logic of atomic (declarative) statements, that we can then join together in different ways, using different truth- functional connectors e.g. the atomic statements "it is raining" and "the streets are wet" can be combined in a number of different ways: –If it is raining then the streets are wet. –It is raining and the streets are wet. –It is not raining. Also called propositional logic (the logic of propositions)

5. Brief overview of new things we will be learning in Part III How to translate statements into sentential logic (symbolic forms) How to determine if a symbolic sentence in symbolic logic is a WFF (well-formed formula) How to prove that arguments are valid/invalid using truth tables How to prove arguments are valid/invalid using the "short method" for proving validity/invalidity

6. How to prove arguments are valid/invalid using truth trees How to prove statements are contradictions, logical truths (tautologies) or contingent statements using truth tables How to prove that two statements are logically equivalent or contradictory using truth tables How to prove that a set of statements are consistent/inconsistent using truth tables. More stuff, depending on time

7. Logic & Proofs We will be using the online class called Logic & Proofs from Carnegie Mellon as out textbook. Signing up for Logic & Proofs: –Using the same account as the one you used to register for the Argument Diagramming course, sign up for Logic & Proofs using the course key socrates. This will cost you $35. –Important: do NOT sign up for the Free & Open Logic & Proofs!! (or you will miss out on important content, and will not be able to get credit for some of the homework exercises)

8. Introduction to Logic & Proofs As you can see, Logic & Proofs is a very interactive experience, giving you numerous ways to check your understanding as you go along. Other advantages: –Highly readable –Abbreviated rule set (basic rule set only has ten rules!) –Truth Lab and Proof Lab