Transcript Introduction to Sentential Logic

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