Introduction to Sentential Logic Syntax and Semantics PHIL
- Slides: 9
Introduction to Sentential Logic: Syntax and Semantics PHIL 121: Methods of Reasoning March 8, 2013 Instructor: Karin Howe Binghamton University
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
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.
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 truthfunctional 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)
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
• 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
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)
• 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
