Epilogue

In the Introduction I made the bold claim that Wittgenstein transforms Frege’s and Russell’s logical and methodological ideas in a way that ‘can be justifiably described as a second revolution in philosophical methodology and the philosophy of logic, following Frege’s and Russell’s first revolution’. This claim was meant in a specific sense relating to the use of logical methods in philosophy, a discipline where we are often dealing with complex and messy concepts and phenomena, and having to clarify highly complicated and fluid uses of natural language. The situation is not quite the same in metamathematics, for example, and my claim was not intended to concern the employment of logical methods there, i.e. that Wittgenstein’s later philosophy of logic would constitute a revolution in this area too. For, while his later philosophy of logic has no difficulty explaining the possibility of the employment of calculi to clarify other calculi, in metamathematics there is perhaps no similarly pressing need for idealization as in philosophy, when we clarify complex concepts originating in ordinary language, since the targets of clarification in metamathematics are systems governed by strict rules themselves. Thus, this area of the employment of logical methods seems not as significantly affected. But I hope that my claim concerning the use of logical methods in philosophy can now be recognized as justified, or at least worth considering seriously, on the basis of what I have said about 1) the later Wittgenstein’s account of the status of logical clarificatory models, and how this explains the possibility of simple and exact logical descriptions, thus safeguarding the rigour of logic, 2) how his account of the function of logical models makes possible the recognition of the relevance of natural history for logic without compromising the non-empirical character of the discipline of logic, and 3) in the light of Wittgenstein’s introduction of new non-calculus-based logical methods for the purpose of philosophical clarification, such as his methods of grammatical rules, the method of language-games, and quasi-ethnology....

Non-Empiricist Naturalism

This chapter elucidates Wittgenstein’s later non-empiricist naturalism. This novel kind of naturalism makes it possible to recognize the relevance of natural historical considerations concerning humans and language use for logic, while retaining the traditional conception of logic as a non-empirical discipline. The justification and generality of the employment of natural history based logical models is explained, and distinguished from the justification and generality of empirical statements. The different ways in which Wittgenstein makes use of natural historical considerations in logical or grammatical clarification are discussed, and the difference of Wittgenstein’s approach from broadly Kantian philosophical anthropology clarified. The correctness or truth of logical accounts is explained and a method of multidimensional logical descriptions introduced.

The Tractatus’ Philosophy of Logic and the Logocentric Predicament

This chapter explains how Wittgenstein’s early philosophy of logic resolves problems that arise for Frege’s and Russell’s philosophies of logic, relating to the status of logic, its apriority, bindingness, and justification of inferences. Relatedly, I discuss how Wittgenstein’s modifies Russell’s account of generality in logic with the purpose of addressing problems that arise for Frege’s and Russell’s views about logic as a substantial science, and how Wittgenstein replaces their accounts of logic as a science with a view of logic as an explicatory discipline the purpose of which is to clarify what thinkers and language users already know in the capacity of thinkers and language users. The chapter shows how Wittgenstein argues from within Frege’s and Russell’s accounts of logic, resolving tensions therein, rather than arguing dogmatically from the point of view of his own picture theory of language. Against a widely assumed view in the historiography of logic, I explain how metatheoretical considerations are possible from the point of view of Wittgenstein’s universalist account of logic, and how the so-called paradox of the Tractatus is resolved.

Frege’s and Russell’s New Logic

This chapter discusses the background of Wittgenstein’s work in the logical methodologies of Frege and Russell. It outlines the dialectical context and background for the problems in the work of Frege and Russell discussed in chapters 2 and 3, and to which Wittgenstein responds in the Tractatus by developing further their philosophies of logic and logical methodologies. Key issues to be addressed are the notion of a logical language or a concept-script, the sense in which logic is not a branch of psychology, and Frege’s and Russell’s accounts of logic as a science. The final section 1.4 contextualizes the interpretation of the Tractatus proposed in subsequent chapters by situating it in the context of current scholarly disputes regarding the Tractatus, between the so-called resolute reading and traditional metaphysical interpretations that attribute ineffable nonsensical theses to the Tractatus.

The Method of Language-Games as a Method of Logic

This chapter develops an interpretation of Wittgenstein’s method of language-games as a method of logic that exhibits continuities with Frege’s, Russell’s, and the early Wittgenstein’s conceptions of logic and logical analysis as the method of philosophy. On the proposed interpretation, the method of language-games is a method for isolating and modelling aspects of the uses of linguistic expressions embedded in human activities that enables one to clarify complex uses of expressions by gradually building up the complexity of clarificatory models. Wittgenstein’s introduction of the language-game method constitutes an attempt to overcome certain limitations of calculus-based logical methods, and to extend the reach of logical methods, so as to make accessible areas of language use and thought that are not accessible by means of calculus-based methods. Rather than rejected, calculus-based methods are retained as a special case of logical methodology. The method of language-games is thus compatible with the employment of calculus-based methods in logic and philosophy, and the method of language-games involves no exclusive claim to being the correct method.

The Tractatus’ Philosophy of Logic and Carnap

This chapter discusses the relation between the Tractatus’ and Carnap’s philosophies of logic, arguing that Carnap’s position in The Logical Syntax of Language is in certain respects much closer to the Tractatus than has been recognized. Explained in Carnapian terms, the goal of the Tractatus is to introduce, by means of quasi-syntactical sentences, logical principles and concepts of a logical language to be used in philosophical clarification in the formal mode. A distinction between the material and formal mode is therefore part of the Tractatus’ view, and contrary to Carnap’s criticism, the sentences of the Tractatus can be clearly distinguished from nonsensical metaphysical statements. Moreover, despite the Tractatus’ rejection of syntactical statements, there is a correspondence between Wittgenstein’s saying–showing distinction and Carnap’s object-language/syntax-language distinction. Both constitute ways to clarify the logical distinction between the logico-syntactical determinations concerning language and the use of language according to such determinations, a distinction absent in Frege and Russell. Wittgenstein’s distinction thus constitutes a precursor of the object-language/syntax-language distinction which the latter in a certain sense affirms. The saying–showing distinction agrees with Carnap’s position also in marking logic as something that is not true/false about either language or reality, a view that underlies Carnap’s principle of tolerance. The standard view that Carnap overcame the philosophy of logic of the Tractatus in the 1930s must therefore be regarded as problematic and misleading.

Introduction

Gottlob Frege and Bertand Russell are widely regarded as the founders of analytic philosophy. A longer list also includes G. E. Moore and Ludwig Wittgenstein. This is not because analytic philosophers subscribe to Frege’s and Russell’s views about particular philosophical matters. It is hard to think of examples of such agreed-upon views. Rather, Frege’s and Russell’s role as founders is due, before all, to certain methodological ideas which they introduced. Especially important in this regard is the idea that philosophical progress could be achieved by means of the methods of symbolic or mathematical logic to whose development both contributed in important ways. This book, in essence, is an examination of Frege’s and Russell’s methodological and logical ideas and their further development and transformation by certain other philosophers, especially Ludwig Wittgenstein, but also Rudolf Carnap and Peter Strawson. It is in this sense a book on methodology in analytic philosophy. And although the book assumes the form of the examination of the history of analytic philosophy, especially the work of Wittgenstein, it is just as much—or more—about the future of analytic philosophy. The underlying question that motivates this book is what analytic philosophy could be or become, and whether it is possible for it to redeem its original promise of progress. For it seems fair to say that progress has been less impressive than Russell promised and more controversial than he may have expected (see ...

Resolving the Dispute Between Ideal and Ordinary Language Approaches

This chapter addresses the long-standing dispute on logic and philosophical methodology between the so-called ideal and ordinary language schools of analytic philosophy, and proposes a resolution to it. While the ideal language school emphasizes the importance of the simplicity and exactness of concepts for philosophical clarity, the ordinary language school regards it as crucial to philosophy to clarify the concepts and the uses of natural language in their actual complexity, viewing emphasis on simplicity and exactness as misguided. For the ideal language school this, again, comes across as a dismissal of good scientific methodology. The proposed resolution draws on the later Wittgenstein’s account of idealization in logic, from the point of view of which the notion of relevance is crucial for understanding the completeness of philosophical accounts. This enables us to satisfy simultaneously the different requirements of the two schools for an adequate method, explaining how one can both meet the ideals of simplicity and exactness in logical clarification and acknowledge the complexity of the concepts and uses of natural language. The last section compares Wittgensteinian clarificatory models with Carnapian explications, and explains the benefits of the former over the latter.

Ideality and Reality

This chapter discusses Wittgenstein’s later account of the status of logic and logical idealization. It explains how Wittgenstein solves the problem of logic seeming to lose its rigour, consequent to the acknowledgement that the uses of language targeted for logical clarification often do not meet the ideals of logic of simplicity and exactness, and that language use therefore apparently cannot be described in the simple and exact terms of logic without falsification. This solution then makes it possible for the discipline of logic to acknowledge that thinking and language use are natural historical phenomena, not abstract ideal objects, and at the same time to retain its non-empirical character. The novel account of the status of logic developed by Wittgenstein is distinguished from the extant aprioristic, conventionalist, and empiricist accounts of logic, and Wittgenstein’s account of idealization in logic is contrasted with idealization in science. The chapter also explains how this account solves a number of problems that arise for the logical methodologies of Frege, Russell, the Tractatus and Carnap, and how logic need not involve any metaphysical claims.