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In Vienna during the 1920s there emerged a group of philosophers — the logical positivists — who wished to deny that any metaphysical questions were meaningful. Although they held much of the Tractatus in high regard, they took the parts of it which gestured towards the unsayable — especially the mystical sections near the end of the book — to embody a straightforward mistake on Wittgenstein's part. If they accepted the Tractarian conception of language, even in outline, their position thus amounted to a denial of the concept of the self. This chapter examines the extent to which the positivists' account of arithmetic, the locus classicus for which is Carnap's Logical Syntax of Language, survives their denial of metaphysics.

Wittgenstein’s doctrines of what can be said and of what cannot be said but only shown, and the paradoxical conclusion of the Tractatus that the sentences of the book are nonsensical, are outlined. Professor Cora Diamond’s interpretation of the Tractatus is sketched. It is criticized as inconsistent with the text of the Tractatus, on the one hand, and with everything that Wittgenstein said about the Tractatus, both while writing it and thereafter, on the other.

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.

The controversy between Norman Malcolm and Peter Winch over the correct interpretation of the Tractatus conception of names, naming, and the method of projection of names is discussed. Evidence in favour of Malcolm’s realist interpretation of the Tractatus doctrine is elaborated: the meaning of a Tractatus name is not exhausted by its logico-syntactical role, which determines only its form. The method of projection is meaning by a name in an elementary proposition the object that is its meaning. In an appendix, Professor Cora Diamond’s objections to this interpretation are rebutted.

This chapter focuses on two main issues: the issue of indexicality, and the extension of the notions of logic to indexical languages; and the issue of the notation itself. It begins with a discussion of logical syntax, and then turns from there to possible characterizations of the notion of consequence. It concludes with a discussion of some further semantic phenomena, which underscore the need to take context and language together.

This chapter discusses the methodology that guided logico-linguistic analysis from Gottlob Frege’s 1879 Begriffsschrift to Rudolf Carnap’s 1934 The Logical Syntax of Language. In the first four decades of this period, culminating with Bertrand Russell’s 1918–19 lectures on The Philosophy of Logical Atomism, analysis was viewed as an increasingly powerful tool employed in the service of solving traditional philosophical problems. The logicist reduction of arithmetic to what was taken to be logic was the driving force, providing the exemplar of philosophical analysis and the model for extending it beyond the philosophy of mathematics. The methodology is indicated by the role played by A2 in answering Frege’s guiding philosophical questions Q1 and Q2.

This chapter steps back and provides a general overview. It begins by discussing how each of the classic conventionalist slogans (about truth in virtue of meaning, analyticity, tautologies, and more) fares in light of my conventionalist theory. Then the chapter discuses Carnap’s Logical Syntax-era theory of logic and mathematics in detail, before turning to Giannoni’s less well-known account in Conventionalism in Logic. Finally, the chapter briefly considers how it is that the rejection of conventionalism has turned into a new dogma, not just of empiricism, but of contemporary philosophy as a whole.

This chapter synthesizes and discusses the main results of the book, namely (i) the treatment of ordinary scalar terms and their implicatures, (ii) pure NPIs (emphatic, weak, strong) (iii) NPIs that double up as FCIs (existential and universal), and (iv) intervention effects of various sorts. The data seem to bear out the claim that Polarity Sensitive Items (PSIs) are indefinites whose alternatives have become obligatorily active (a case of ‘grammaticization’). The behavior of PSIs follows under these assumptions from a general view of how alternatives are factored into meaning via a process of exhaustification. A tightly regulated system of parameters paves the way to understanding both historical and typological variation in the Polarity System. Minimality effects constitute a key piece of evidence in favor of this view and a unique window on how the Polarity System works. The crucial role that logical triviality plays in this account is also discussed along with consequences of such role on the relation between syntax and logic, on the generative paradigm, and on our understanding of human cognition.

The focus of this essay is the idea of the univocity of being, championed by Duns Scotus and given prominence more recently by Gilles Deleuze. Although one concern of the essay is with how this idea can be established, its primary concern is with something more basic: how the idea can even be properly thought. This issue is explored with the aid of some ideas about logical syntax borrowed from Wittgenstein’s Tractatus. One incidental benefit of the exercise is to indicate how there can be dialogue between analytic philosophers and those of other traditions.

This chapter explores smart contracts in their broader historical context. The use of statistics and the so-called ‘mathematization’ of law is not new: from Aristotle to Descartes to Leibniz, the common denominator was that mathematical precision should be applied across all disciplines. Currently, ‘computable contracts’—and more broadly, computable law—are making a powerful return. Contracts may be represented as computer data with terms made ‘machine-readable’ through a process of conversion. Conditions of agreements are not explained but listed as structured data records. However, despite the capacity to express contracts in a computable form, there is no means for interpretation. Rather, the interpretation of contractual obligations is perceived as irrelevant. Should digital data inscription and processing be considered a form of legal writing? If so, would it change the character of law? This chapter explores the significance of medium in contract drafting. In particular, it explores the translation of text to numbers by unpacking several formal programming languages currently proposed or used in computable contracts. In identifying the logic of these languages, it tackles methods of legal writing. By analysing the components of both legal and programming language, we can develop a richer dialogue on the sociological implications of translating law to algorithmic form. Further, it would be interesting to consider what contextual understanding may need to exist to ‘interpret’ contractual language.