# Philosophical Logic

John P. Burgess
Edition: STU - Student edition
Pages: 168
https://www.jstor.org/stable/j.ctt7s8vk

1. Front Matter
(pp. i-iv)
(pp. v-vi)
3. Preface
(pp. vii-viii)
4. Acknowledgments
(pp. ix-xii)
5. CHAPTER ONE Classical Logic
(pp. 1-12)

What is philosophical logic? For the reader who has some acquaintance with classical or textbook logic—as it is assumed that readers here do—the question admits an easy answer. Philosophical logic as understood here is the part of logic dealing with what classical leaves out, or allegedly gets wrong.

Classical logic was originally created for the purpose of analyzing mathematical arguments. It has a vastly greater range than the traditional syllogistic logic it displaced, but still there are topics of great philosophical interest that classical logic neglects because they are not important in mathematics. In mathematics the facts never...

6. CHAPTER TWO Temporal Logic
(pp. 13-39)

Consider the following argument:

(1) Publius will vote and Quintus will vote, but Publius will not vote when Quintus votes.

(2) Therefore, either Publius will vote and then Quintus, or Quintus will vote and then Publius.

The argument cannot be treated by classical sentential logic, since such a compound as “Publius will vote andthenQuintus will vote” (or the reverse), unlike the simple “Publius will vote and Quintus will vote,” is not truth-functional. The argument does not especially invite treatment by classical predicate logic, either, since it contains no overt quantification. Classical logic makes no direct provision for arguments...

7. CHAPTER THREE Modal Logic
(pp. 40-70)

As temporal logic is concerned with the relationships amongwasandisandwill be, or past and present and future, somodallogic is concerned with the relationships amongmay beandisandmust be, or possible and actual and necessary. Modal logic goes right back to the beginnings of logic, with Aristotle—and doubt and disagreement over it goes almost back to the beginning of logic as well, with Aristotle’s immediate successors Theophrastus and Eudemus, who completely revised their teacher’s theories.

On one point there has been general agreement since then: the possibility ofAis the...

8. CHAPTER FOUR Conditional Logic
(pp. 71-98)

Conditionals are instances of “ifA,B” or “B, ifA.” TheA-position is called theantecedentorprotasisposition and theB-position theconsequentorapodasisposition. Conditionals come in two types, generally distinguishable in English by the absence or presence of “would” in the consequent, the stock example of the contrast between them being the following pair:

(1) If Oswald did not shoot Kennedy, someone else did.

(2) If Oswald had not shot Kennedy, someone else would have.

The difference is easy to appreciate intuitively—almost anyone would agree to (1), but only a conspiracy theorist to (2)...

9. CHAPTER FIVE Relevantistic Logic
(pp. 99-120)

Objections have been raised against the classical treatment of logical implication or logical consequence for countingBas an implication or consequence ofA1, … ,Anin two degenerate cases: first, the case whereBis valid (ex quolibet verum), and second, the case where theAiare jointly unsatisfiable (ex falso quodlibet). Often in discussions of this issue the word “entailment” is used as a synonym for “logical implication” or “logical consequence.” The instance ofex falso quodlibetaccording to which an arbitrary conclusionBis entailed by the premise$A \wedge \neg A$(or the premisesAand...

10. CHAPTER SIX Intuitionistic Logic
(pp. 121-142)

According to classical mathematics, one can prove that there exist irrational numbersaandbsuch thatabis rational as follows. Consider${\sqrt 2 ^{\sqrt 2 }}$. Either it is rational or it is irrational. If${\sqrt 2 ^{\sqrt 2 }}$is rational, set a = b =$\sqrt 2$, which has been known to be irrational since the earliest times. If${\sqrt 2 ^{\sqrt 2 }}$is irrational, seta=${\sqrt 2 ^{\sqrt 2 }}$andb=$\sqrt 2$, and a little algebra showsab= 2, which of course is rational.

This is an example from the mathematical folklore of an existence proof of the kind callednonconstructive. It purports to prove the existence...

11. References
(pp. 143-148)
12. Index
(pp. 149-153)