Being Good and Being Logical

Philosophical Groundwork for a New Deontic Logic

James W. Forrester

• Publisher: Routledge
• Year: 2015
• Print ISBN: 9781563248795
• eBook ISBN: 9781317476085
• Topic: Politics & International Relations
• Subtopic: Politics
• Index: Politics & International Relations

This work represents an attempt to show that standard systems of deontic logic (taken as attempts to codify normal deontic reasoning) run into a number of difficulties. It also presents a new system of deontic logic and argues that it is free from the shortcomings of standard systems.

Part I

Problems of Standard Deontic Logic

Chapter 1: What Is Deontic Logic, and Why Should I Care?

In this chapter, I shall raise four basic questions about deontic logic. To the first question, I shall try to give a definitive answer. But to the other three, my answers will only be provisional; a full response can only come in the course of this book.

The four questions are:

• What is deontic logic?

• Why should anyone but specialists care about deontic logic?

• Is there any interesting way in which deontic logic diverges from ordinary logic?

• What can philosophers in general, and the author of this book in particular, hope to contribute to the study of deontic logic?

I shall take up these questions in turn.

Deontic logic, as a branch of logic, is the study of those rules and axioms which license a certain class of inferences. Because deontic logic is usually taken as a kind of deductive logic, the licensing procedure takes this form: if the premisses of an argument are true, and if the argument is in accordance with the principles of deontic logic, the conclusion of the argument must be true. And for an argument to be in accordance with a set of principles, it cannot be the case that those principles are true and the individual steps in the argument false.¹

My point in going over this well-trodden ground is that in any area of logic, the concept of truth is fundamental. A valid deductive inference is truth-preserving: the truth of the premisses guarantees the truth of the conclusion. Even if someone should suppose deontic logic to be inductive, the concept of truth would still be central; the truth of the premisses would establish a high probability that the conclusion is true.

A standard adjunct to any branch of logic is therefore a semantics — that is, a set of truth-conditions for the premisses and conclusions that make up arguments. In ordinary propositional logic, the semantics usually employed is Tarski’s Convention T: The statement ‘S is F’ is true if and only if S is F. To check on the truth of ordinary propositions, one need only check on how the world really is. At least in principle, that is easy to do.

But as David Hume observed long ago, it is not as easy as many think to derive an ‘ought’ from an ‘is’. The statements typical of deontic logic concern the acts that people ought or ought not to do, the situations that should or should not exist, the acts that people may or may not do, and the situations that are or are not permissible. If Hume was right, then it is at least difficult and perhaps impossible to come up with actual states of affairs that can serve as truth-conditions for deontic statements.² And lacking a semantics, deontic logic would be at best a formal exercise.

Of course, it is open to deontic logicians to claim that certain actual, non-deontically described states of affairs do serve as truth-conditions for deontic statements. But then, the burden of proof is on them to provide such a semantics. And the experience of philosophers has been that Hume’s skepticism seems well founded.

The objection to deontic logic that I have just sketched has a close counterpart in crude versions of ethical non-cognitivism. If moral language is no more than a sophisticated expression of people’s feelings and attitudes towards other people, actions, and objects, then moral statements are neither true nor false; and being neither true nor false, moral statements admit of no logic.

If there is to be any useful study of deontic logic, then, deontic statements must be capable of being either true or false. That, in turn, means that deontic logic must have a semantics, a set of truth-conditions, that goes beyond Tarski’s Convention T.

The development of modal semantics provided a way of escape from skepticism over the very possibility of deontic logic. For as with deontic statements, it is no easy task to come up with actual states of affairs that can serve as truth-conditions for claims about what logically must or can be true. But by allowing themselves to talk of what is the case in other possible worlds, however that talk is to be interpreted, modal logicians broke the impasse holding their subject back. The statement “Necessarily snow is white” is true if and only if snow is white in all possible worlds; the statement “Possibly snow is white” is true if and only if snow is white in some possible world; and the statement “Snow is white” is, as always, true if and only if snow is white in this possible world.

Deontic logic beats back its skeptics by employing the same device. “George ought to pay his debts” is true if and only if some state of affairs concerning various possible worlds is the case. A deontic logician will agree with Hume’s gloomy assessment of the likelihood of finding truth-conditions for deontic statements in this world; that is why deontic logicians have espoused possible world semantics for their subject.

I shall argue in Chapter 5 that possible world semantics is more than just a convenient way for a deontic logician to respond to a skeptical, Humean objection. Without a possible world semantics, I maintain, deontic logic is literally impossible. But for now, it is enough to suggest that deontic logicians have had good reason to model their subject on modal logic and semantics.

Deontic logic, then, can be set out axiomatically or semantically. If it is set out axiomatically, it consists of a set of axioms and inference-rules, from which a set of theorems can be derived. If it is set out semantically, it consists of a set of relations between deontic statements and facts concerning certain possible worlds. In particular, the facts concerning possible worlds must warrant us fully in accepting the truth of every application of the axioms and theories of the axiomatic system. Thus axiomatics and semantics are connected.

However, in constructing deontic logic along the lines of modal logic, theorists have implicitly raised a point of major philosophical concern. Modal reasoning, like all propositional reasoning, is, in Aristotle’s sense, theoretical: it is aimed at laying bare what is in fact the case. But much of deontic reasoning is rather practical: it is aimed at action, rather than at knowledge. If a form of practical reasoning can actually be construed on a model taken from theoretical reasoning, we are much further than we thought in the development of a truly practical logic.

Suppose that I reason as follows: “I ought to go to the store today; to get there, I can either walk or drive; but for reasons of health I ought not to drive; so I ought to walk to the store today.” In this somewhat stilted but surely intelligible piece of reasoning, how should we understand the conclusion? It is an ‘ought’ statement, like the first premiss, and presumably we could give truth-conditions for it. But it seems more than a statement of fact. It expresses my intention to act in a certain way. I might have concluded equally well, “So I’ll walk to the store today.”

Likewise, if I reason in the same manner that you ought to walk to the store, my conclusion is generally more than just a statement that something is the case. Rather, it has an imperative flavor to it: if you are legally under my command, it would be a bad mistake for you not to walk to the store!

Not every case of deontic reasoning is practical, to be sure. We might reason about what ought to be the case, without any suggestion that you or I or anybody else should act in a certain way. Or we might reason about what people should do or should have done, even though we have no way whatsoever of influencing their actions. Hector, in Shakespeare’s Troilus and Cressida, argues cogently that the Trojans should give up Helen; then, after announcing that this is in truth Hector’s opinion, he advises them not to give her up.

But although not every case of deontic reasoning is practical, many are. Deontic reasoning seems to have a foot in both camps: the theoretical and the practical. And this dual role makes it possible for deontic logic to prove of great philosophical importance, by helping us understand practical reasoning.

We have passed to the second of the four questions with which this chapter began: Why should anyone but specialists care about deontic logic? My answer is that deontic logic gives us our best — in fact, I think, our only — chance of constructing a logic of practical reasoning. In the final chapter of this book, I shall defend this answer against some major objections.

As most philosophers know, Aristotle called attention not only to the theoretical syllogism but to what he called the practical syllogism. Whereas the conclusion of a theoretical syllogism is a statement, Aristotle claimed that the conclusion of a practical syllogism is an action.

Now clearly Aristotle was on to something: people do deliberate what they and others are to do. From our deliberation we reach decisions, form intentions, take action, issue orders. If there are rules to distinguish valid practical arguments from invalid, they would clearly be worth knowing.

Much practical reasoning seems to use counterparts of valid principles of theoretical reasoning. For example:

I must choose either plan of action A or plan of action B.

On balance, B is not as good a plan as A.

Therefore, I choose plan A.

My subordinate, Smith, can work on either the A file or the B project.

Smith’s time will be worse spent working on the B project.

Smith, work on the A file.

These are clearly of a kin with examples of the valid theoretical principle:

Either p or q.

Not q.

p.

Hence, these two practical arguments and others like them themselves seem valid. We might generalize that a valid practical argument is one which has a valid theoretical counterpart.

But many of Aristotle’s own examples of practical syllogisms lack this whiff of validity (slightly tangier than the odor of sanctity). For example:

I need a cloak.

What I need I can make.

Straightway, I make a cloak.

If this is parallel to any theoretical argument, it is to the invalid argument known as affirming the consequent.³ And yet, as a practical argument, it does not seem that bad. Even worse, some highly dubious practical arguments seem parallel to valid theoretical arguments. It is this fact that puts the sting in the various deontic paradoxes. For example:

If you murder Sheila, you should murder her gently.

But you do, in fact, murder Sheila.

Therefore, you should murder Sheila gently.

Obviously, we cannot make the parallel to valid theoretical arguments our criterion of validity in practical arguments.

But finding the criterion of validity in practical arguments is a comparatively minor difficulty. A greater obstacle to finding principles of practical reasoning is that the job of any logic is to preserve truths from premisses to conclusion. If the conclusion of a piece of practical reasoning is an intention, a decision, an order, an entreaty, or an action, the notion of truth is inapplicable to such a conclusion. An action is not a statement, so it cannot be true or false. An order or an entreaty is an imperative statement, again neither true nor false. Statements of one’s intention or decision are performatives: to respond “That is true” when someone says “I will drive into the city tomorrow” is to treat the person’s statement as a prediction of his own actions, not as a statement of his intention. None of these outcomes of practical reasoning can be either true or false; none, therefore, can be truth-preserving. Hence, practical reasoning cannot be valid, at least not in the same way theoretical reasoning can. And since logic is built on the notion of validity, a logic of practical reasoning seems impossible on its face.

But deontic statements offer a way out of the difficulties. “I ought to give her money” and “You may go now” seem, like statements of intention and imperatives, to be prescriptive.⁴ As such, they can serve as conclusions of practical arguments. One can easily amend my examples of practical arguments to end in deontic conclusions. However, unlike statements of intention and imperatives, deontic statements appear on their face to be capable of being true or false. “Please go now” cannot be true or false, but a speaker might long-windedly replace “You ought to go now” by “It is true that you ought to go now.”

It seems, then, that ordinary deductive validity applies to deontic arguments, even though much deontic reasoning is practical. If, then, we can develop a valid deontic logic, its principles will cover a large part of practical reasoning. And perhaps we will have a method, or at least a model, for understanding the rest of practical reasoning.

In the final chapter of this book, I shall look at some difficulties in the argument I have just given. Bu...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Introduction
• Part I: Problems of Standard Deontic Logic
• Part II: A New Deontic Logic
• Part III: Deontic Logic and Practical Reasoning
• Appendix 1: The Systems SDL and NDL
• Appendix 2: A Note on Quantification
• Notes
• Bibliography
• Index