The Rejection of Modality

This chapter examines how Russell came to reject modality on the basis of his rejection of idealism. Russell’s anti-modal views rest on the Moore-Russell theory of propositions, not on Russell’s attack on internal relations. This theory derives from Moore’s criticisms of Bradley’s theory of judgment. Unlike most readers of Moore, who find these criticisms mostly unpersuasive, I show that, in fact, they present a substantial challenge to Bradley. Moore uses the theory of propositions that he adopts to remedy the defects of Bradley’s theory of judgment to argue, against Kant, that all true propositions are necessarily true. For Russell, Moore’s argument demonstrates that there is no distinction between truth and necessary truth, nor between truth and possible truth, which is to say, amodalism.

The Nature of Logic

How does Frege conceive of logic, if not in modal terms? For Frege, logic is a system of truths that divides into primitive truths, which are axioms or basic laws, and logical truths justified by primitive logical truths. Frege appears to hold that what makes a thought a primitive logical truth is that it provides its own justification. However, Frege appears also to give arguments for the basic laws of Frege’s systems of logic. I argue that these arguments cannot be understood as non-question-begging demonstrations that the basic laws are self-justifying. Knowledge of self-justification results from the exercise of a perception-like capacity, and Frege’s “arguments” are intended to provide his readers with the occasion to exercise this capacity with respect to the thoughts expressed by his basic logical laws.

The Truth in Modalism

This chapter takes up two further issues about Frege’s attitude towards modality. First, Frege doesn’t simply reject the relativization of truth. He gives amodalist explanations of linguistic phenomena that seem to show that truth is relative to time, and of talk of truth in various circumstances. Second, Frege’s truth-absolutism is not incompatible with two analyses of modality prominent in the history of philosophy: in terms of a priori knowledge and in terms of analytic truth. But Frege construes apriority and analyticity in logical terms. Thus, ultimately, Frege’s view is that if there are any modal distinctions, they amount to nothing more than logical distinctions. An interesting consequence of Frege’s accounts of apriority, analyticity, and modality is that they allow not only for synthetic a priori truths, but also necessary a posteriori and contingent a priori truths.

Amodalism

This chapter provides the first part of a specification of Frege’s grounds for holding that modal distinctions are not features of logical structure. If necessity and possibility are genuine properties, then they are properties of judgeable contents or thoughts, and, the possession of any of these properties is determined by the truth and falsity of a content or thought in actual and non-actual circumstances. But truth and falsity are absolute: thoughts and judgments are true or false, period; they are not true or false at a time, or at a place, or in a circumstance. Frege’s position I call amodalism, and it implies that necessity and possibility are not genuine properties of judgeable contents or thoughts.

Postscript

This chapter provides a brief comparison of a prominent contemporary conception of the criticism and justification of modal concepts with the arguments of Frege and Russell. The contemporary conception pins criticism of modality on the logical positivists’ verificationist criterion of cognitive significance. It also rests on the assumption that there is a pervasive, non-collusive intuitive agreement on the application of modal concepts, so, without the positivists’ philosophical worries, there is no ground for questioning these notions. The early analytic objections to modality have nothing to do with verificationism and pose a challenge to the basic assumption of the contemporary conception. I conclude with a reason for thinking that this assumption fails, so that there is not yet a compelling contemporary answer to the early analytic critique of modality.

The Modalities of Judgment

This chapter is an exposition of Frege’s theory of modality before adopting the sense/reference distinction. The background for understanding this theory is Kant’s conception of judgment and of the classification of judgments in the Table of Judgments. Frege agrees with Kant that modality is not an aspect of content. However, Frege’s discovery of modern quantificational logic leads him to reject Kant’s theory of logically significant structure. Moreover, Frege insists on a sharp distinction between judging and assuming, which leads him to reject Kant’s position that modalities mark distinct types of judgment. As a result, modality has no logical significance. Frege takes discourse in which we seem to ascribe necessity or possibility to contents to effect various sorts of implicature, and his accounts of these implicatures provides a reductionist and epistemic conception of modality.

From Idealism to Logicism

This chapter concerns three phases of Russell’s views of necessity and logic in his idealist period, influenced by F. H. Bradley’s theory of necessity. First, Russell defended a Kantian theory of geometry based on transcendental arguments justifying the apriority and necessity of geometry. Second, Russell begins to move away from this Kantian position when he comes to think that transcendental arguments cannot ultimately demonstrate the necessity of any judgment. Third, Russell began to contemplate a weak modal form of logicism. This chapter ends with a substantial difficulty uncovered by Russell’s exploration of this logicism: unless the axioms of logic are true but not necessary, they do not entail theorems about classes that are intuitively correct.

From Judgment to Amodalism

This chapter shows that Frege’s commitment to the absoluteness of truth rests on commitments central to his later philosophy, after he adopts the sense/reference distinction. For Frege, a thought represents something to be the case, and a judgment is fundamentally the recognition that what a thought represents obtains. Truth is that property of thoughts which one recognizes in virtue of recognizing the obtaining of what thoughts represent. The primary function of a thought is to be a step to the acquisition of knowledge, which is to say, to judgment. If the truth or falsity of a purported thought is relative, then it fails to provide what is required for judgment and is no more than an apparent thought. The truth and falsity of genuine thoughts, by grasping which we can make judgments and acquire knowledge, are absolute.

Introduction

This chapter presents the principal philosophical issue of the book: is the nature of logic specified by the concepts of necessity and possibility? According to Gottlob Frege and Bertrand Russell, the answer is no, because these concepts of modality are empty: there are no genuine distinctions among the necessary, the possible and the actual. The upshot for Frege and Russell is that logic is fundamental, and modality is to be reconstructed from logical notions. This chapter continues with a brief outline of Volume II of this work: how C. I. Lewis and Ludwig Wittgenstein argued against the anti-modal stance of Frege and Russell. I conclude with a note on the significance of this aspect of early analytic philosophy for contemporary philosophy of logic and modality.

The Continuing Banishment of Modality

This chapter concerns a development of Russell’s view of modality. It occurs in “Necessity and Possibility,” in which Russell formulates a new argument against modality. The argument begins with a survey of intuitions about modality. Russell proceeds to make these intuitions more precise, in terms of notions of logic. The resulting accounts, however, provide evidence that we have no coherent single intuitive conception of necessity and possibility. Hence nothing would be lost to logic and philosophy if we simply replaced modal concepts with one or the other of the accounts of modal intuitions in logical terms. This new argument enables Russell to retain his anti-modal position after he rejects Moore-Russell propositions. The chapter concludes by showing Russell’s continuing adherence to the rejection of modality.