Possible Worlds: An introduction to Logic and Its Philosophy
Copyright © Raymond Bradley and Norman Swartz, 2010
Answers to exercises on pages 4344

Exercises on pages 4344
Part A
 possibly true and possibly false; contingent
 possibly true and possibly false; contingent
 possibly false; necessarily false
 possibly true; necessarily true
 possibly true and possibly false; contingent
 possibly false; necessarily false
 possibly true and possibly false; contingent
 possibly true and possibly false; contingent
 possibly true and possibly false; contingent
 possibly true and possibly false; contingent
Part B
 Let's take as an example the set {J, K, L}, and we'll suppose
that it is inconsistent. Now suppose that we add the proposition M, where
M is the proposition that the preceding proposition is false. The new set,
might then read: "{J, K, M, L}". Is this latter set now
consistent? Absolutely not. For if M is true, then K is false; i.e. it is
impossible for both M and K (whatever proposition K happens to be) to be
true. Indeed adding M to a set of propositions will not only fail to
create a new set that is consistent, it will create a new set that is
selfinconsistent whatever the original set had been!
 There is nothing 'special' about the sixth proposition. It no more
'induces' the inconsistency than does any one of the other propositions in
the set. If you were to remove any one proposition – either the first or
the second or the third ... or the sixth – the new set, consisting of any
five of the original propositions, will be selfconsistent.
 Here are some possible answers (among an infinity of correct
answers):
 {All Chevrolets have sixcylinder engines, Tom's one car is a Chevrolet,
Tom's car has an eightcylinder engine.}
 {Alicia loves Bradley, Bradley loves Alicia, It is false that both
Bradley and Alicia love one another.}
 {John borrowed $80 from Barbara and signed a note saying that he
would repay the loan, John has given Barbara exactly $20, John is debtfree.}
 (Again, this answer is just one among an infinite number of correct
answers.)
 {John has no sisters, John's only sister is his employer,
John's only sister has no employees}
 The definition is too restrictive: it excludes (i.e. fails to identify
correctly) certain necessarily false sets of propositions, viz. those that are
selfinconsistent but not all of whose members are themselves necessarily
false. Examples are:
 {Aziz is taller than Harry, Harry is taller than Aziz}
 {All squares have four sides, Some square has five sides}
 {Giuseppe drinks CocaCola, Giuseppe drinks Pepsi Cola, Giuseppe drinks only one
brand of cola.}

