Making inferences

The semantic theory developed up to Chapter 6 has concentrated mainly on the interpretation of sentences and phrases in isolation from each other, but one of the criteria for assessing the adequacy of a semantic theory set out in Chapter 1 is that it should account for the meaning relations that hold between different expressions in a language. This means, amongst other things, that the semantic theory proposed here ought to guarantee that, where reference and context are kept constant, the sentences in (1.b) and (1.c) are paraphrases of (1.a) while (1.d) and (1.e) are entailments of it and (1.f) and (1.g) are contradictions of it.

1. a. Jo stroked the cat and kicked the dog.

2. b. Jo kicked the dog and stroked the cat.

3. c. The cat was stroked by Jo and the dog was kicked by Jo.

4. d. Jo stroked the cat.

5. e. Someone kicked the dog.

6. f. The dog wasn't kicked.

7. g. No-one stroked anything.

The intuitively identified relations between the sentences in (1) derive from the interpretations of the conjunction and, the negative not and the quantifier pronouns no-one and someone. Such relations are generally referred to as logical entailments, paraphrases or contradictions. (Note that these terms are used ambiguously between the relation that holds amongst sentences, as here, and the product sentences themselves, as in the first paragraph above.)

Verb phrases and other constituents

One of the conditions of adequacy for a semantic theory set up in Chapter 1 is that it conform to the Principle of Compositionality. This principle requires the meaning of a sentence to be derived from the meaning of its parts and the way they are put together. The interpretation procedure for the grammar fragment set up in the last two chapters adheres to this principle insofar as the translations of sentences, and thereby their interpretations, are derived from the translations of their parts and the syntactic rules used to combine them. Thus, for example, the translation of the sentence Ethel kicked the student is derived from the translations of the two noun phrases Ethel and the student and the verb kicked. These are combined using the translation rule for transitive sentences to give kick'(ethel',the-student'). The truth or falsity of the resulting formula can then be directly ascertained by checking whether the ordered pair of entities denoted by the subject and object in that order is in the set of ordered pairs denoted by the predicate, kick'.

Unfortunately, in the theory of Chapters 2 and 3, compositionality is maintained only at the expense of the syntax. The ‘flat’ structure of the predicate-argument syntax of Lp and its interpretation requires a flat sentence structure in the English syntax in order to maintain a direct correspondence between syntax and translation, and thus a transparent relation between elements in the interpretation and constituents of the English sentence.

Translating English into a logical language

In this chapter and the next, we will lay the foundations on which a good deal of logical semantics is built. In accordance with the discussion in Chapter 1, we first define a logical language into which sentences of English are translated in order to circumvent the problems of ambiguity and underdeterminacy found in the object language. Having defined the translation language, and specified the procedure for translating simple English sentences into it, our attention will turn to the interpretation of these logical expressions in terms of their truth-conditions, thus providing an indirect interpretation of the corresponding English sentences.

The syntax of LP

Like all languages, natural or artificial, logical languages have a syntax, i.e. a set of rules for constructing composite expressions from simpler ones. The logical language described in this chapter, called LP, contains expressions that fall into one of four logical categories: individuals, predicates, formulae and operators (or connectives). Expressions in each of the first three categories can be further subdivided into two sorts: constants, which have a fixed interpretation, and variables, which do not. These two sorts of expression correspond, roughly, to content words (e.g. table, run, Ethel) and pronominal expressions (e.g. she, they) in natural languages, respectively. This chapter deals only with constants, but variables will become increasingly important in later chapters.

Sentences in natural languages translate into formulae in LP which have the logical category t (as sentences have the syntactic category S).

Semantics and semantic theory

In its broadest sense, semantics is the study of meaning and linguistic semantics is the study of meaning as expressed by the words, phrases and sentences of human languages. It is, however, more usual within linguistics to interpret the term more narrowly, as concerning the study of those aspects of meaning encoded in linguistic expressions that are independent of their use on particular occasions by particular individuals within a particular speech community. In other words, semantics is the study of meaning abstracted away from those aspects that are derived from the intentions of speakers, their psychological states and the socio-cultural aspects of the context in which their utterances are made. A further narrowing of the term is also commonly made in separating the study of semantics from that of pragmatics. Unfortunately, the nature of the object of inquiry of the discipline (what constitutes semantic meaning, as opposed to pragmatic meaning) and the domain of the inquiry (what aspects of meaning should be addressed by the discipline) remain difficult and controversial questions. There are, however, three central aspects of the meaning of linguistic expressions that are currently accepted by most semanticists as forming the core concern of linguistic semantics. These central concerns of semantic theory, adapted from Kempson (1977:4), are stated in (1) and may be adopted as criteria for ascertaining the adequacy of semantic theories which apply in addition to the general conditions on scientific theories of falsifiability and rigour.

Where entailments fail

In previous chapters (particularly Chapter 7), we looked at certain types of entailment relations that are guaranteed by the theory of interpretation set out in the earlier part of this book. Certain contexts exist, however, where expected entailments do not hold. Consider, for example, the inference pattern in (1).

1. a. The Morning Star is the planet Venus.

2. b. The Evening Star is the Morning Star.

3. c. Therefore, the Evening Star is the planet Venus.

The validity of this inference pattern illustrates a general rule that holds in the extensional semantic theory developed in Chapters 2 to 6 of this book. This rule is called Leibniz's Law or the Law of Substitution and it allows the substitution of extensionally equivalent expressions for one another in a formula while maintaining the truth value of the original formula. Thus, in (1), since the Morning Star and the Evening Star denote the same entity, the latter expression may be substituted for the former in the first premiss to give the conclusion. Indeed, because all three terms in (1) have the same extension all of them may be substituted for each other salva veritate (the Latin phrase used by Leibniz meaning ‘with truth unchanged’). The Law of Substitution can be formally defined as in (2) which, in words, says that if an expression a is extensionally equivalent to another expression b, then a formula φ is truth-conditionally equivalent to the formula formed from φ by substituting an instance of b for every instance of a.

The 1877 and 1878 articles “The Fixation of Belief” and “How to Make Our Ideas Clear” are generally thought to initiate pragmatism, which Peirce would later call pragmaticism. Both are parts of a series of six papers intended for a book called “Illustrations of the Logic of Science.” They represent Peirce's concern with proposing a theory of inquiry based on his conception of experimental science. At the time they were written, Peirce regarded it as his mission to incorporate the logic of experimental methods into philosophy. An explicit expression of this aim can be found in his later writing where he aligns himself with “those few fellow-students of philosophy, who deplore the present state of that study, and who are intent upon rescuing it therefrom and bringing it to a condition like that of the natural sciences” (5.413). Thus, Peirce's discussion of the way beliefs may be fixed and of the proper criterion for clarifying ideas is a means to this longerrange goal. The consequences of realizing this goal imply the reinterpretation of traditional philosophical issues. Most of the issues so important to Peirce throughout his career will be seen to emerge within the context of his concerns in the 1877 and 1878 articles.

Before considering these articles, let me make two preliminary observations. The first is that I bypass four earlier essays, “On a New List of Categories,” “Questions Concerning Certain Faculties Claimed for Man,” “Some Consequences of Four Incapacities,” and “Grounds of Validity of the Laws of Logic.” Some key points in three of these will be taken up later in connection with semeiotic and with further consideration of Peirce's view of inquiry.

Beginning a book on the philosophy of Charles S. Peirce is something like entering a labyrinth with almost as many entrances as passages. What aspect of his thought provides the best entry? should Peirce's work be considered in chronological order? Should his ideas be traced to antecedents in the history of philosophy? Should his thought be understood as representative of a school or tradition such as empiricism, rationalism, pragmatism, Aristotelianism, orscholasticism? Should he be approached as an antimetaphysician, or should his thought be interpreted more broadly in terms of his metaphysical speculations? Are there certain topics, themes, or theses that are more basic and hence best used as organizing principles in offering an account of his philosophy? These questions reflect the fact that selection, arbitrary or purposeful, is necessary at the outset. The approach to be taken in this book has a purpose. It assumes that there are basic themes in Peirce's thought that can be used as organizing principles. These themes express the two main purposes mentioned in the Preface: to introduce Peirce to readers who have had little or no acquaintance with his ideas and to propose that there is a cohesiveness in his thought that implies an architectonic – an architectonic that has at its core a special kind of realism.

Our entry into Peirce's philosophy, then, will be made through four themes, each serving as the topic of a chapter. These themes were chosen because they are foundational ingredients of his thought as a whole.

The Nature and Function of Philosophical Categories

It should not be necessary to launch a lengthy general discussion of the nature and functions of categories in philosophy in order to give an account of what they are and the role they play in Peirce's thought. However, some comments about categories in general are necessary. Briefly, and most generally, categories in philosophy are fundamental conceptions, in the sense that they are conditions of intelligibility. Such conceptions may be regarded as the classes or types of things into which things that are and can be known can be divided. Or they may be considered to be the ways or conditions according to which things can be distinguished and accordingly known. Some things can be made intelligible because they can be located in space and time – as substances that serve as referents for subjects in sentences or propositions. These belong to the category of substance. Some things can be made intelligible because they can be determined to be contingent (Abraham Lincoln's beard, which may or may not be shaved off), whereas others are regarded as necessary (2 + 2 = 4 in a number system based on 10). These belong to the category of modality, which includes contingency, possibility, and necessity. Fundamental classes or conditions of intelligibility are not unlimited in number. They are necessary for identifying, classifying, and relating what may be an unlimited number of things in the universe (or universes of discourse) encountered in any and all domains of experience, including the domain proper to science and that which is available to common sense. However, one may distinguish what Peirce called a “long list” and a “short list” of categories. Aristotle's categories belong to the long list.

Introduction

A theme central to the discussion in this book has been the expression of the belief that Peirce's philosophy presupposes an architectonic founded primarily on a form of realism. There are reasons for resisting this interpretation, however, as I have already suggested. It has been claimed that Peirce was fundamentally an idealist. This difference is understandable, for there is a sense in which he was an idealist and a sense in which he was a realist. Hence it may be claimed that he was a kind of metaphysical idealist and, at the same time, an epistemological realist. On this view, he was an idealist metaphysically in the sense that the final object of thought in general, the final aim of investigation, is regarded as not only completely thought-dependent but also mental in nature. He was a realist epistemologically, then, in the sense that in the context of any theoretical investigation, what investigation is about is independent of that investigation, but what is independent is thought or theory that is not exhausted by the particular theoretical framework at the time. I think this is a misleading suggestion. My purpose in the first section, then, will be to show why it is misleading and to propose that Peirce's conception of the constraints of an extrasemeiotic or extraepistemic condition has a fundamental function that aligns him with a special form of metaphysical realism – what I have called evolutionary realism.

The proposal that his is an evolutionary realism will, I hope, make clear that I believe Peirce wanted and managed to push beyond the traditional labels idealism and realism.

This book has two major objectives: first, to offer an introduction for persons beginning the study of Peirce and, second, to address some of the more complex issues and problematic aspects of his thought on the assumption that these issues can be understood in terms of an overarching, coherent philosophical view – what Peirce aimed at as an architectonic. I am not concerned with criticizing Peirce's ideas, although occasionally my comments raise questions that could be pursued in terms of possible criticisms and suggested answers. I refrain from criticism primarily because I do not think this task is appropriate in an interpretive account. In addition, Peirce's way of presenting his thought seems to have been more hypothetical than categorical, continually exhibiting a commitment to fallibilism. Criticism would be proper only if one were intent on moving beyond his thought, perhaps in order to launch one's own hypotheses. There is a sense in which this latter kind of consideration may enter into what I attempt in this book. To some extent my interpretation of Peirce's aims, particularly with respect to his metaphysics, inevitably flows from certain conceptions I have about what he ought to have meant in the context of his broader, long-range perspectives.

The specific interpretations I offer were initiated more than ten years ago while I was conducting seminars on Peirce. After reflecting on the conclusions I had drawn in trying to help students read and discuss Peirce intelligently, I felt the urge to bring my conclusions and the reasons behind them into a single, sustained discussion. This concern was related to my hope to suggest to students a coherent picture of Peirce's complex and sometimes apparently conflicting views.

The following discussion of Peirce's pragmaticism and semeiotic will focus on five main topics. First, it will be helpful to sketch the way in which pragmaticism implies semeiotic. Second, the anticipation of semeiotic in the early series of articles, “Certain Faculties Claimed for Man” and “Some Consequences of Four Incapacities,” will be considered in order to indicate the way in which Peirce's development of his anti-Cartesianism and his departure from Kant served as a basis for his semeiotic. Third, we shall see how the keys to pragmaticism point us toward Peirce's conception of the three conditions of sign action, or what Peirce refers to by the term semeiosis. These conditions will then be discussed. Fourth, it will be found that one of the conditions of semeiosis, the object, is presemeiotic, or preinterpreted, and at the same time semeiotic. A distinction Peirce makes between two kinds of object, the immediate and the dynamical, will then be considered briefly. Finally, Peirce's classification of signs will be outlined.

Thoughts Are Signs

The implications of pragmaticism for semeiotic should be clear. Pragmaticism is a theory of meaning. The meanings of general concepts or terms, it will be recalled, are dispositions, habits, or laws that can be formulated in linguistic expressions. Insofar as these meanings are indeterminate with respect not only to vagueness but also to generality, they remain to be interpreted with respect to the particular consequences that follow from acting in accord with them. They must be interpreted with reference to the patterns of consequences that they represent.

The conception of Peirce's envisaged architectonic can be projected beyond the context of the late nineteenth and early twentieth centuries. The projection with which I am concerned springs from two architectonic conceptions dealt with in the earlier chapters: semeiotic and evolutionary realism. These conceptions may be applied to current interconnected controversies over the possibility of deciding between metaphysical antirealism and realism and between relativism and antirelativism in interpretation theory, which for Peirce falls under the domain of semeiotic.

Our main responsibility will be to see how Peirce's philosophical outlook avoids some of the consequences of recent attacks on the possibility of affirming realism. These considerations, in turn, have a bearing on the question of whether interpretation (in art criticism as well as in theoretical investigation) has a grounding outside texts and theories.

In the following remarks I shall respond from a Peircean perspective to the challenge that metaphysical assumptions about reality or extralinguistic objects and systematic speculation about all actual and possible experience are nonsensical, futile, or at least outdated. Philosophies that have dominated Western thought until the early twentieth century – and, indeed, have persisted in some circles in this century – presuppose a metaphysical or epistemological realism or an objective idealism (whether they are set forth in terms of these labels or appear as integral to rationalisms, empiricisms, and philosophies that suppose that there are noumenal or extraexperiential conditions of thought). These views share the assumption that there is something sufficiently objective to serve as a foundation that warrants rational argument and possible conclusions about which single perspective on experience or the world is more intelligible than another.