Chapter 1: Getting Started
This text is an introduction to symbolic logic, but that may not tell you much. The word
"logic" covers a lot of territory.
Sometimes when people think about learning logic, they say things like "Oh! I'm not very
Chapter 12: Constructing Proofs with Quantifiers
We now have all the rules we need to construct proofs in the monadic predicate calculus.
In this chapter, we explore proofs further, and also look at techniques for showing the arguments
with quantified sen
Chapter 11: Proofs With Quantifiers The Rules
By now you now should be well-practiced at putting English sentences into predicate
calculus, and you should also have a good grasp of the basic semantics of predicate calculus of
the meanings of sentences in
Chapter 10: English to Symbols with Quantifiers
You now should have a good sense of what the quantifiers mean, but learning to take
complex English sentences and turn them into symbols takes practice. That will be our task in this
First recall wh
Chapter 9: Quantification Theory
Weve developed a proof system that deals with truth-functional arguments, but there are
some simple, familiar examples of reasoning that our system isnt up to dealing with. Consider:
Socrates is human.
All humans are morta
Chapter 8: Indirect Proof (Proofs within proofs part 2)
We have almost everything we need to complete our sentence logic proof system. In this
chapter, we provide the missing piece.
The idea of indirect proof sounds a little odd at first. W
Chapter 7: Conditional Proof (Proofs within proofs part 1)
So far, weve used only rules that take you from one or more lines to another by a step of
inference. But consider this bit of reasoning:
Robbie is either a chess player or a backgammon player. Fur
Chapter 6: Using the Rules
Recognizing Rules: First a review of the rules.
Addition (Add) Disjunctive Syllogism (DS):
Modus Ponens (MP)
Chapter 5: Proofs
Rules and Proofs
So far, we've used truth tables to decide when arguments are valid and to show that
certain sentences are laws of logic (tautologies in the case of sentential logic.) We now turn to a
different approach: proofs that proc
Chapter 4: Truth Tables Continued
You should be comfortable using symbols to see the structure of English compound
sentences and you should be able to answer basic questions using truth tables. In this chapter, we
expand what we can do with truth tables.
Chapter 3: Truth Tables
We've introduced the basic elements of the sentential calculus and learned how to
translate from English to symbols. In this chapter, we'll study the meanings of the connectives.
Our connectives have a simple but usef
Chapter 2: Translations Continued
Conditionals and Translations
The connectives "&," " and " are symmetrical. Reversing the order of the parts
doesn't change the truth value of the whole sentence. Not so for "."
If John is in Boston, then he is
Chapter 13: Truth and Counterexamples
In this chapter, we turn from proofs back to semantics. To ease our way into the
discussion, we start with a connection between logic and arithmetic.
Suppose that you have two predicate letters to work with