The Logic of Commands

Nicholas Rescher

• Publisher: Routledge
• Year: 2019
• ISBN:
  9781000737127
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

Originally published in 1966. Professor Rescher's aim is to develop a "logic of commands" in exactly the same general way which standard logic has already developed a "logic of truth-functional statement compounds" or a "logic of quantifiers". The object is to present a tolerably accurate and precise account of the logically relevant facets of a command, to study the nature of "inference" in reasonings involving commands, and above all to establish a viable concept of validity in command inference, so that the logical relationships among commands can be studied with something of the rigour to which one is accustomed in other branches of logic.

Chapter One

INTRODUCTION

1.1. Imperatives and Commands. The aim of this book is to present the fundamentals of a logical theory of commands. In large measure it is devoted to a task preliminary to any adequate articulation of such a theory — the clarification of the basic constituent ideas required for a viable analysis of the complex concept of a command. Only when our feet have been set securely upon the firm ground of an appropriate conceptual clarification can a meaningful study of logical mechanisms get under way.

The topic which engages our attention here is frequently treated under the heading of the ‘logic of imperatives’. But this is not strictly correct. Imperatives (like indicatives) form a wide grammatical category; commands (like assertions) represent a rather narrower functional grouping. Imperatives can be used to give counsel or advice (unconditionally, as with ‘Ask your doctor about it!’, or conditionally as with ‘If you want to make sure of that, ask your attorney about it!’), to upbraid or reproach (‘Don’t ever advise me again!’), to denounce (‘Go to the devil!’), to implore aid or to request co-operation (‘Save me: I’m drowning!’), to make prayers and supplications (‘Give us this day our daily bread!’). They can even — in the case of conditional imperatives — be used to make a purely factual assertion (‘If you want to visit the tallest structure in Pittsburgh, visit the Gulf Oil Building!’ adds really nothing to ‘The Gulf Building is the tallest structure in Pittsburgh’¹). Laws of nature are sometimes formulated as hypothetical imperatives — for example ‘If you want water to freeze, cool it to 32°F!’ in place of the direct ‘Water freezes at 32°F’.

We shall here deal only with commands (construing this term broadly to include orders, directives, injunctions, instructions, and prohibitions or ‘negative’ commands²), and even this only in part. The particular way in which we are concerned with commands needs further specification in certain respects which will be indicated below. Although considerations of precision may ultimately lead us into certain departures from ‘ordinary language’, it is our purpose to develop a theory of ‘commands’ in the sense of the everyday use of the relevant concepts.

¹ For just this point about certain ‘hypothetical imperatives’ see Hare (1952), p. 34. [All references of this author-plus-date form refer to the Bibliography appended at the end of this book.]

² There are substantial analogies between the locution ‘X commands Y to do A’ on the one hand, and the locutions ‘X’s requests Y to do A’ and ‘X urges Y to do A (i.e., recommends that he do A)’ and ‘X authorizes (permits) Y to do A’, on the other. Compare Wellman (1961), pp. 230–235. Many points of the logic of commands can be carried over to the logic of requests, recommendations, and authorizations, but we shall not explore such kinships here.

1.2. The Key Problem. While a great many interesting issues arise within the rather wide area of a ‘logic of commands’, one problem above all lies at the focus of our interest here. It is this: Can one articulate appropriate concepts of inference and of validity in such a way as to legitimate the inference of a command conclusion from premisses consisting of other commands (and also possibly including assertoric statements)? This question of the prospects for ‘valid inference’ among commands is on our conception of the matter the key problem of the logical theory of commands.

The concept of validity, although it is our main objective, is not actually dealt with overtly until half-way through the book — it is broached in Chapter Seven, to be precise. The reason is simply that (as the White Rabbit explains to the King of Hearts) ‘There’s a great deal to come before that!’ The inquiry begins with a general examination of the conceptual structure of commands (in Chapter Two), and then goes on to build up (in Chapters Three through Five) the necessary terminology, symbolism, and ideographic and conceptual machinery needed for the ensuing formal discussion. Chapter Six is transitional and preparatory — it introduces the auxiliary concept of ‘coverage’ of a command by one or more others. This concept gives the paradigm of validity which serves as basis for the development of the conception of validity finally presented in Chapter Seven and developed there-after. The larger issues of a logic of commands can be dealt with in a fruitful and straightforward way only after the necessary groundwork has been prepared.

1.3. Why a ‘Logic of Commands’? Quite apart from whatever intrinsic interest a logical theory of commands may possess, it seems worthwhile from two external perspectives. Firstly, it cannot but help to shed the light of contrast upon the logical theory of purely assertoric statements. Secondly, the inquiry will possess an instrumental value for ethics, where the notion of commanding cannot but play a role. Indeed various recent writers on ethics — R. M. Hare, in particular — have tried to conjure with commands and imperatives, and have tried to base far-reaching conclusions in ethical theory upon considerations regarding them. (We shall have occasion to consider below the particularly interesting stratagem of Henri Poincare.)

Wittgenstein somewhere spoke of a discussion as suffering from a deficiency disease caused by a too restricted diet of examples. The theory of commands has been the victim of a deceptive appearance of triviality because much of the literature confines itself to rather simple minded stock examples of the ‘John, close the window!’ type. The more complicated cases of the sort to be found in legal contexts (e.g., instructions to the executors of wills), in examination instructions, and in computer programs, for example, are generally neglected. Our present treatment of the subject will try to free itself of this defect, and will take its inspiration primarily from the last-named area.

In ordinary life, the instructions one is given are generally simple and straightforward — we can get by with simple ‘common sense’ and do not require anything sufficiently formal and formidable to deserve the name of a logic. And yet we do ‘reason’ from commands and sets of commands. And we would surely be prepared to say that the examination instructions:

Write the answer to every question you select on a single sheet!

Answer no fewer than three nor more than four questions!

would ‘imply’ the instruction: ‘Write no more than four sheets for the entire examination!’ Or again we would surely be prepared to class as ‘self-inconsistent’ the set of instructions consisting of the aforementioned two with the addition of: ‘Write your examination on exactly two sheets!’ Or (to take yet another intuitively plausible example) if we have an instruction manual that reads:

Whenever condition C is realized, take course of action A!

Never take course of action A unless you first do B!

we would want to say that these two instructions are ‘equivalent’ with:

Whenever condition C is realized, do B first and then take course of action A!

1.4. Historical Observations. The logical theory of commands is widely regarded as a very new and ‘non-classical’ branch of logic. We know, however, that it — like the logic of questions — occupied the attention of one of the great logical schools of antiquity, that of the Stoics. Diogenes Laertius reports in his list of the logical works of Chrysippus (280–209 B. C.) that this important Stoic logician wrote a treatise ‘On Commands’ (Peri prostagmaton) in two books³.

The founding father of the logical theory of commands in modern times is Ernst Mally. His Grundgesetze des Sollens: Elemente der Logik des Willens (Graz, 1926) is the groundbreaking work not only in the logic of commands but in deontic logic as well⁴. Its defects notwithstanding (and they are real, but easily exaggerated) Mally’s pioneering efforts represents an outstanding contribution to applied logic⁵.

More recent interest in the logic of imperatives received its initial impetus during the latter 1930’s in the wake of the logical positivists’ insistence upon the exclusive meaningfulness of factual assertions, and the consequent problem of attempting assertoric treatment of other types of prima facie non-assertoric statements such as imperatives⁶. The problem was especially acute for the positivists, because commands, far from being ‘nonsense’, can serve as basis for apparently rigorous reasonings: ‘Put all the blue boxes on the table; this box is blue: put this box on the table!’ The situation is helpfully summarized in a brief quote from a paper on ‘Imperatives and Logic’ published by Alf Ross over two decades ago (1944):

The problems of this treatise are in line with those which have, as far as I know, been first propounded by Walter Dubislaw in his treatise ‘Zur Unbegründbarkeit der Forderungssätze’ [published] in Theoria, 1937. Since then Jørgen Jørgensen, Grelling, Grue-Sørensen, Hofstadter and McKinsey, and Rose Rand have treated similar problems⁷. The problem has not been delimited in the same way by these authors, but their object has always been to elucidate whether sentences which are not descriptive [i.e., factual], but which express a demand, a wish, or the like, may be made objects of logical treatment in the same or a similar manner as the indicative sentences⁸.

³ Lives of Eminent Philosophers, 7: 191; ed. D. H. Hicks in the Loeb series, vol. 2, p. 300. Compare B. Mates, Stoic Logic (Berkeley, 1953), p. 19.

⁴ Mally even coined the word Deontik as name for the ‘Logik des Willens’ he was attempting to devise. Mally’s contribution to the logic of commands is concisely outlined in Menger (1939), pp. 57–58.

⁵ Mally’s work on commands culminates — but goes far beyond — discussions of this topic by Franz Brentano and others in his tradition, preeminently Brentano’s pupil Alexis Meinong, who was Mally’s teacher. For details see the Bibliography.

⁶ Imperatives gained special prominence because the positivists tended (under Kantian influence) to regard moral rules as imperatives. Thus Carnap maintained (Philosophy and Logical Syntax [London, 1935], p. 23) that there is only a matter of stylistic difference of formulation between ‘Killing is evil’ and ‘Do not kill!’

Although a great deal has been written on the logic of imperatives generally and of commands in particular in the years since the initial revival of the subject in the later 1930’s, it is, I think, only fair to say that there is virtually no single issue in the field upon which a settled consensus has been reached. Indeed a significant fraction of the literature consists of attempts to call into question the very possibility of the subject itself⁹.

⁷ For detailed citations see the Bibliography.

⁸ Ross (1944), p. 31.

⁹ See Williams (1963) for one recent example.

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Original Title Page
• Original Copyright Page
• Dedication
• Epigraph
• Contents
• Preface
• Chapter 1. Introduction
• Chapter 2. Facets of a Command
• Chapter 3. Terminology and Symbolism
• Chapter 4. The Representation of Commands by ‘Programs’
• Chapter 5. The Concept of Command Termination
• Chapter 6. Command Coverage and Decomposition
• Chapter 7. Validity and Invalidity
• Chapter 8. Validity in Mixed Cases
• Chapter 9. Logical Relations among Commands
• Chapter 10. Command Provisos
• Chapter 11. Conclusion
• Bibliography
• Indices