Chapter 7: Conditionals
We next turn to the logic of conditional, or if then, sentences. We will be treating if then as a
truth-functional connective in the sense defined in chapter 3: the truth value of a compound sentence
formed with such a connective i
Chapter 12: Methods of Proof for Quantifiers
12.1 Valid quantifier steps
The two simplest rules are the elimination rule for the universal quantifier and the introduction rule
for the existential quantifier.
This rule is sometimes c
Chapter 6: Formal Proofs and Boolean Logic
The Fitch program, like the system F, uses introduction and elimination rules. The ones weve
seen so far deal with the logical symbol =. The next group of rules deals with the Boolean connectives
, , and .
Chapter 10: The Logic of Quantifiers
The system of quantificational logic that we are studying is called first-order logic because of a
restriction in what we can quantify over. Our language, FOL, contains both individual constants
Properties of Relations and Infinite Domains
For our final topic, we will cover a few points that are not fully covered in LPL, but that are important
in two ways. First, they are important for understanding the logic of arguments involving binary
Chapter 9: Introduction to Quantification
9.1 Variables and atomic wffs
Variables behave syntactically like namesthey appear in sentences in the same places that
names appear. So all of the following count as correct atomic expressions of FOL:
Antecedent: The antecedent of a conditional is its first component clause (the if clause). In P Q, P is
the antecedent and Q is the consequent.
Antisymmetric: a binary relation R is antisymmetric iff no two things ever bear R to one another, i.e.