Table of Contents of Benzen's thesis

Normative Sentences and Logic _________________________________________________ 4

PART I _____________________________________________________________________ 5

A HISTORICAL OVERVIEW OF NORMATIVE LOGICS FROM ERNST MALLY TO
DEFEASIBLE DEONTIC LOGIC ______________________________________________ 5

Principles of the Historical overview_____________________________________________ 6

A Few Historical Points About Normative Logic Before 1926 ________________________ 7

Mally __________________________________________________________________ 8


Jørgensen _____________________________________________________________ 9

Ross ____________________________________________________________________ 10

Ross´ Disjunctive Paradox____________________________________________________ 12
Ross´ Conditional Fallacy ____________________________________________________ 12

THE OTHER Ross (The Scots)
__________________________________________________________________ 14

Hare´s The Language of Morals ___________________________________________ 14
Hypothetical imperatives _____________________________________________________ 16

Rescher´s Logic of Commands _________________________________________ 17

Wright´s Monadic Deontic Logic _______________________________ 21

Modal Negation Equivalences for Deontic Sentences_______________________________ 24
Square of Opposition for Deontic Sentences ______________________________________ 24
Standard Deontic Logic_______________________________________________________ 25
The Relational Semantics of Standard Deontic Logic _______________________________ 27

Formal Language ___________________________________________________________ 28

Definition of Frame _________________________________________________________ 28
Definition of Model _________________________________________________________ 28
Definition of Truth in a Model_________________________________________________ 29
Validity Defined____________________________________________________________ 29

An analytic tableau proof system for SDL________________________________________ 31
Rules for Propositional SDL __________________________________________________ 32
Basic Rules________________________________________________________________ 32
Deontic Rules______________________________________________________________ 33
Completeness and Soundness _________________________________________________ 34
Proofs, Trees and Deontic Paradoxes ___________________________________________ 34

Ross´ Disjunctive Paradox____________________________________________________ 35

Prior´s Paradox of Derived Obligation and Ross´ Conditional Fallacy__________________ 36

Ross´ Conditional Fallacy ____________________________________________________ 37

Chisholm´s Contrary-to-Duty Imperatives _______________________________________ 39

Other Paradoxes ____________________________________________________________ 41

Alternative Deontic Logics ____________________________________________________ 41
Dyadic Deontic Logic _______________________________________________________ 42

Temporal Deontic Logic _____________________________________________________ 42

The Gentle Murder Paradox___________________________________________________ 43
Deontic Preference Logics ____________________________________________________ 44

Hector-Neri Castañeda´s Logic_________________________________________________ 45
The Fence Paradox__________________________________________________________ 46

Hintikka´s Quantified Deontic Logic _____________________________________ 47
Deontic Consequence and Logical Consequence __________________________________ 48
Quantified Standard Deontic Logic _____________________________________________ 49

First-order Language ________________________________________________________ 50
First-order Atomic Formula ___________________________________________________ 51
First-order Deontic Formula __________________________________________________ 51

Castañeda and Hintikka on Quantified Deontic English _____________________________ 51
Critical Commentary ________________________________________________________ 53

Formal Semantics___________________________________________________________ 53

Truth in a First-order Model __________________________________________________ 54
Scapegoat Example _________________________________________________________ 55
Analytic Tableau Rules for Quantifiers __________________________________________ 56
Santa Claus Example ________________________________________________________ 57
Defeasible Deontic Logic ______________________________________________________ 58
Evaluation of the Historical Survey _____________________________________________ 60
Force and Fulfilment ________________________________________________________ 60

PART II____________________________________________________________________ 62
A NEW SYSTEM____________________________________________________________ 62

A: A THEORY OF MEANING FOR IMPERATIVES ____________________________ 62

Background: Propositions and Context-Free Declarative Sentences____________________ 62

Imperatives and Propositions __________________________________________________ 64

Imperatives and Deontic Sentences _____________________________________________ 66

Decisions Made by an Agent and for an Addressee ________________________________ 68

Context-free Imperatives _____________________________________________________ 69

Sentential Connectives_______________________________________________________ 70

Imperatives in Force_________________________________________________________ 71

Imperatives Fulfilled ________________________________________________________ 73

B: A LOGIC OF MANDATES (LM) _________________________________________ 74
Mandates and Imperative Force Value __________________________________________ 74
Mandates and Fulfilment Value________________________________________________ 75
Language of LM____________________________________________________________ 77
Corresponding Proposition Defined_____________________________________________ 78
Formal Semantics of LM_____________________________________________________ 79
Valuation _________________________________________________________________ 79
Validity in LM _____________________________________________________________ 80
Consequence in LM_________________________________________________________ 80
Fulfilment and Violation of Mandates in LM _____________________________________ 80
Logical Value Tables for LM__________________________________________________ 81
Analytic Tableau Rules for LM________________________________________________ 82
Basic Rules________________________________________________________________ 82
Rule for Corresponding Proposition ____________________________________________ 83
Fulfilment Rules____________________________________________________________ 83
Violation Rules ____________________________________________________________ 83

Paradoxes __________________________________________________________________ 84
Conditional Paradoxes _______________________________________________________ 84
Arthur Prior´s Paradox of Derived Obligation_____________________________________ 84
Chisholm´s Contrary-to-Duty Imperatives _______________________________________ 85
Gentle Murder Paradox ______________________________________________________ 85
Ross´ Conditional Fallacy ____________________________________________________ 86
Ross´ Disjunctive paradox ____________________________________________________ 87
Moral Dilemmas_____________________________________________________________ 89
Cave Dilemma _____________________________________________________________ 90
Contradictions of Mandates ___________________________________________________ 92
Limitations of LM and Further Research_________________________________________ 94
Summary _________________________________________________________________ 95
References ________________________________________________________________ 97
Appendix 1: Soundness of LM _______________________________________________