Let us turn to the examination of the logical characteristics of the particle represented by “or” and similar words. As usual, the actual results depend only on the rules chosen and hence they are more or less independent of the motivations involved.

While it is clear that the word “or” is used in various ways, including arguably in some cases the denying of the simultaneous acceptability of the sentences connected by it, there is at least one usage or family of usages (frequently called “inclusive or”) for which admission of A commits one against denying or rejecting “A or B,” or for that matter “B or A.” We are actually inclined to believe this to be the basic meaning of “or,” but whether we are right in this or not, it is this inclusive use of “or” which provides the colloquial basis for disjunction, as we shall use the term in this and succeeding chapters.

Our first, rather minimal, system for disjunction will have only one connective, with properties sufficient to make it a normal disjunction in the sense specified in chapter 2.

Historical Notes

The purpose of this section is to satisfy the historical interests of the reader and, as far as I am able, to discharge the obligations of academic honesty.

Before entering into the details, I would like to point out that more of my ideas than I am able to trace are due to the influence of my teachers of logic: Rudolf Carnap, Evert W. Beth, Arend Heyting, and Stephen C. Kleene, to whom I must add, primarily through their writings, Alonzo Church and Alfred Tarski. The influence of these teachers on my thinking is so pervasive that the tracing of any idea of mine to one or more of them would never surprise me.

With regard to more specific indebtedness:

Chapters 1-2: The modern concept of logical calculus on which these definitions rest is primarily due to Gottlob Frege and to a lesser degree to David Hilbert, Bert rand Russell, and Charles Saunders Peirce. The formulation of structure and derivation concepts is, I believe, original in its detail, but to a considerable degree, is based on formulations by Church, Rosser, and to a lesser degree, Carnap and Gentzen.

Chapter 3: The greater portion of this chapter is based on the work of E.L Post and J.B. Rosser.

Chapter 4: With few exceptions, the systems in chapters 4 - 9 were determined by a natural architectonic. Most of them had however been independently developed earlier and the following notes indicate the earliest source I have been able to discover.

This book is a textbook on logic. It does, however, differ in a number of respects from the greater number of its sister textbooks with which the reader may be familiar, including, very probably, the one used in the reader's first course in logic. In the first place, it is not entitled “introduction to” or any of its total or partial synonyms, such as “elements,” “fundamentals,” or the like. While there are several reasons for this, the most important one is that it is not an introduction, but is written primarily with an eye to students who have already been introduced to the subject, presumably in the form of a college course in modern, or symbolic, logic (there is a sense in which it is nevertheless an introduction, but that would be hair-splitting). By and large, the main (and important) purpose of such courses, and consequently of texts appropriate to them, is to teach students how to use a certain technique, modern formal logic, in the evaluation of arguments and, while doing so, to introduce some of the concepts and theory of modern logic. In consequence, most of these books rightly devote a considerable portion of their material to, for instance, the problem of translating arguments from colloquial language into the formal system or systems used (in some cases, where the course or book is intended primarily for mathematicians, common mathematical language, which is often indeed more closely related to the formal systems, is the main object of comparison, instead of “natural” language).

In the preceding, I have attempted, and I trust generally succeeded, to present a body of information and technique concerning logical systems without grinding any philosophical axes (I suppose I have as many of these as anyone). In this final chapter, I shall discuss the bearing of some of the results and the significance of this type of study, and here I shall make no promises to restrain myself concerning philosophical implications.

At first sight it might seem quite reasonable to take the position that a subject as esoteric and mathematical as the formal study of logical systems probably has no philosophical implications at all, just as I suppose most people interested in philosophy would be inclined to say that the theory of partial differential equations or the theory of the multiple integral does not. Indeed, many philosophers, particularly of the so-called ‘ordinary language’ tradition, have taken such a position with regard to formal logic. I feel that I cannot concur, for reasons which I hope will be made clear in the succeeding pages.

There are several significant aspects to the study of formal systems. While one can examine them in other ways, I shall consider them in order of decreasing formalism.

One obvious use, actually of surprisingly general importance to many logicians, is that these systems can be interesting in themselves, that is to say as an intellectually challenging game, somewhat in the way chess and multi-dimensional tic-tac-toe are.

We shall now consider systems which extend PI by including a second connective, this time one that takes one argument. This connective is suggested by the ordinary word “not.” As in the case of ⊃, its properties in each system are precisely those given by the rules of the system; the degree to which it otherwise corresponds to the usage of “not” will not interest us in our systematic considerations. It is our intention, however, to introduce a series of systems with progressively greater specification of the connective (which we symbolize by ∼). As a first step, then, we wish to introduce the weakest plausible negation consistent with PI. Here we are helped by the relation between negation and what is sometimes referred to as “absurdity” (sometimes also as “inconsistency”). One of our strongest presystematic agreements concerning negation is that the result of simultaneously asserting a sentence A and its negation ∼ A is absurdity. In this connection, it is irrelevant as to which sentence we started from. There does appear to be a minority intuition, namely, that A and not-A is very different from B and not-B; this however appears to be correlated with a strong rejection of positive implication and we will not consider it at the present time.

I have outlined a conception of autonomy; a conception that is in various ways different from other conceptions of autonomy that have historically been developed. One way of attacking such a conception is by arguing that it does not fulfill the evaluative tasks that have traditionally been associated with the notion. In this chapter I wish to defend the conception developed in Chapter 1 against a certain attack and then to argue for the value of exercising autonomy when understood in this way.

There is a traditional view of autonomy that must view my conception as too thin to be of value because there is no specific content to the decisions an autonomous person takes. Suppose we have a person who has not been subjected to the kinds of influence – whatever they turn out to be – that interfere with procedural independence. Suppose the person wants to conduct his or her life in accordance with the following: Do whatever my mother or my buddies or my leader or my priest tells me to do. Such a person counts, in my view, as autonomous. But has not such a person clearly forfeited autonomy? Must autonomy involve a particular content, a substantive and not merely procedural independence from others?

I shall argue that the conception of autonomy that insists upon substantive independence is not one that has a claim to our respect as an ideal.

In ethics, as in the law, there is often agreement concerning what to do in a particular case, or about the importance of a moral principle, co-existing with disagreement about why we should act in a certain manner, or on the nature or basis of the moral principle. Similarly, moral theories may agree about specific cases of lying while giving different accounts of why a lie is or is not justified.

In the past few years a number of criminal prosecutions have brought to public attention the issue of entrapment: Abscam, the DeLorean cocaine trial, Operation Greylord, various sting fencing operations. The investigative techniques used in, say, Abscam, although highly elaborate, expensive, and ingenious are only one example of the range of investigative techniques with which I shall be concerned in this essay. What these techniques have in common is the use of deception to produce the performance of a criminal act under circumstances in which it can be observed by law enforcement officials. I shall use the term “pro-active enforcement” to cover such techniques and the question I shall be discussing is under what circumstances, if any, is the use of such measures legitimate.

Let me begin by saying something more about the nature of proactive law enforcement and also by giving a fairly extensive sample of the use of such techniques. The sample will not only make clearer the nature of such operations but also provide a range of cases for testing judgments about the acceptability of such techniques.

Traditionally, law enforcement in our society has left most of the burden of reporting criminal offenses to private citizens. It is left to individuals, usually victims, to come forward with a complaint of criminal action and to provide much of the evidence in identifying and prosecuting the criminal. Government's role has been limited to various patrol activities and to reaction to complaint.

The concept of autonomy has assumed increasing importance in contemporary moral theory. Appeals to the ideal of an autonomous moral agent play a role in grounding moral argument that appeals to sentiment or self-evidence or intuition played in earlier centuries. In such discussions moral judgments are often contrasted with factual or scientific judgments and claims are made about autonomy (as well as related notions such as authority and objectivity) in the moral context that are sharply distinguished from parallel claims in the scientific context. My aim in this essay is, as they say on prelims, to compare and contrast the nature of autonomy in morality and science.

In Chapter 1, I have characterized autonomy as the capacity of a person critically to reflect upon, and then attempt to accept or change, his or her preferences, desires, values, and ideals. The idea of moral autonomy is a particular case of this, and the rough idea is that persons are responsible for, and have the capacity for, determining for themselves the nature of the moral reasons, considerations, and principles on which they will act.

When I speak of autonomy I shall take this to be a property of persons and I shall only indirectly be concerned with the discussion that has proceeded under the heading of the autonomy of morality, that is, the connection or lack of connection between facts and values. I am primarily concerned with autonomy as specifying certain features of persons involved in their deliberations upon moral issues. I am concerned with moral autonomy and not the autonomy of morals.