Logic & Proofs
Sentential Logic
Indirect Rules
Contents:
Negation Introduction
Negation Elimination
Putting Negation Into the Big Picture
Ex Falso Quodlibet and Double Negation
Finding Contradictions
Studying this chapter will enable you to:
1.
2.
3.
Appl
Logic & Proofs
Eliminating Existential Quantifiers
Movie
Eliminating Existential Quantifiers
We begin the derivation knowing that the existential quantifiers of the first two
premises will need to be dealt with prior to the universal quantifiers of the th
Logic & Proofs
Negation Introduction
Movie
Negation Introduction
Indirect arguments are, as we saw already in the introduction, very powerful and
have an intricate internal structure. Here we will discuss an example in detail.
We are given these premises
Logic & Proofs
Strategies in Action
Movie
Strategies in Action
We saw that some sentential connectives can be equivalently expressed using other
connectives. Here we want to prove that the conditional (PQ) is interderivable
with the disjunction (PQ).
We'l
Logic & Proofs
Introducing Universal Quantifiers
Movie
Introducing Universal Quantifiers
The conclusion is not a strictly positive subformula of the premises. Can we proceed
by inversion? Yes: The conclusion is a conjunction of two universally quantified
Logic & Proofs
Eliminating Universal Quantifiers
Movie
Eliminating Universal Quantifiers
To construct proofs in predicate logic, we employ strategies similar to those we used
in sentential logic: extraction, inversion, refutation or indirect argumentation
Logic & Proofs
Indirect Rules
Movie
Indirect Rules
In the last chapter we began to construct derivations, the formal analogues of proofs
and logical arguments.
So far we have studied and applied the introduction and elimination rules for the
three binary
Logic & Proofs
Strategies and Derived Rules
Movie
Strategies and Derived Rules
In the last two chapters we constructed derivations using the basic introduction and
elimination rules for the three binary connectives: conjunction, disjunction, and the
condi
Logic & Proofs
Derivations
Movie
Derivations
In sentential logic, we can use the truth-table method to decide the validity or
invalidity of any argument. That was already perfectly well known at the beginning
of the 20th century, and it was also perfectly