In its original version, before Wittgenstein decided to extend the book’s scope, the Tractatus advanced a solipsism of a decidedly etiolated sort – so etiolated, indeed, that the self which according to this solipsism claims ownership of the world ends up stripped of any substantial content. By the time it was published, however, the solipsism passage had been revised so as to gesture towards a puzzling ‘metaphysical’ subject, whose importance seems to be primarily (though no doubt not exclusively) ethical. By the time he wrote the Blue Book Wittgenstein no longer held the unitary conception of language on which his Tractarian conception of solipsism depended, but he continued to deny coherence of a substantial self.

I look at Wittgenstein’s statement, in his letter to Russell, of the “main contention” of his book. I consider also the relation between his main contention and what he describes in the book as his fundamental idea. I discuss also what he means when he says that what he calls his main contention, and his main point is the cardinal problem of philosophy.

This chapter explores Wittgenstein’s two references to the arts in 4.014. The first is his musical example of the unity of language and the world; the second his allusion to the fairytale The Gold-Children by Brothers Grimm. The chapter argues, first, that Wittgenstein’s early notion of logic incorporates forms that for Kant belong to transcendental aesthetic, namely, space and time. Second, it spells out how this commitment motivates Wittgenstein’s musical example and why it is crucial to draw a distinction between transcendental form and empirical structures made possible by that form. Finally, the chapter argues, pace Peter Sullivan, that the unity of language and the world is guaranteed by the metaphysical subject as their common origin. If the fairytale is read as a condensed illustration of Wittgenstein’s position, then this common origin is signified by a golden fish.

Truth and content are theoretically prior in Frege to the act of judgment. Wittgenstein takes the opposite view, maintaining that truth is fundamentally correctness in judgment and that a content is fundamentally something to be judged. At Tractatus 4.063, Wittgenstein gives an argument against the Fregean position. Judgment can aim internally at truth, Wittgenstein holds, only if it is internal to truth that it is correctness in judgment.

This chapter discusses Wittgenstein’s remarks on mathematics in sections 6.02–6.031 and 6.2–6.241. These remarks are limited to arithmetic, with definitions of the natural numbers (6.02) and of multiplication (6.241). In the first part, we discuss Wittgenstein’s criticism of the theory of types involved in Russell’s rival ‘logicist’ account, with specific criticisms of Russell’s axioms of infinity (5.535) and reducibility (6.1232). The second part presents Wittgenstein’s positive account of natural numbers in terms of ‘repeated applications of an operation’ (based on his remarks on operations at 5.2–5.254) and of arithmetical calculations. Limited parallels with the lambda calculus are brought to the fore, while explanations that presuppose a scheme of primitive recursion are criticized. The third section discusses related philosophical remarks about the centrality of the ‘method of substitution’ (6.24), arithmetical equations as ‘pseudo-propositions’ (6.241 & 6.2), and the claim that the identity of the two sides of an equation is merely perceived, not assertable (6.2322). Looking ahead, the fourth and final part discusses briefly Wittgenstein’s reasons for abandoning this approach in the early ‘middle period’.

Some readers of the Tractatus claim that, for Wittgenstein, the correct philosophical method is “a method of logical analysis in terms of a symbolic logical notation, whereby the logical, syntactical or formal properties of logically unclear expressions are clarified by translating them into a logically perspicuous notation” (Kuusela 2019, p. 85). This chapter aims at refuting this view, maintaining that Wittgenstein distinguishes between logical analysis and philosophical clarification. More precisely, I would like to establish that, drawing on certain features of Russellian logical practice (as illustrated for instance in On Denoting), Wittgenstein makes a distinction between logically ordered language and completely analyzed language. For him, philosophical clarification does not consist in an analysis of ordinary language but in the visible manifestation (at the level of signs) of the logical ordering of its symbols.

This Introduction provides summaries of the chapters of the book and briefly discusses some of the main obstacles we encounter when we attempt to engage with Wittgenstein’s Tractatus.

In his search for publishing the Tractatus, Wittgenstein wrote a letter to Ludwig von Ficker while trying to explain the deeper meaning of his work, which he considered to be an “Ethical one”. Whereas other philosophers would establish theories about ethical and religious matters, Wittgenstein emphasized his decision to keep silent about the sphere transcending the world of language and of science. In this chapter, I discuss the limits of language and of science, the significance of silence, the view sub specie aeternitatis, the dimension of wonder, the difference between what can be said and what can only be shown, and Wittgenstein’s mystical approach toward the ineffable.

The method proposed in the Tractatus is to find a perspicuous logic of our language. It thus seems to conform to Russell’s ideal of a scientific method in philosophy. Language, though, is for Wittgenstein essentially the language of the first person. This means that the central issues in the Tractatus, such as ‘What is a sentence?’ and ‘What is a judgement?’, have to be approached by means of a first-person method. Perhaps surprisingly, this method is less vulnerable to psychologism than Russell’s method. How are we to understand the use of the first-person indexical in the Tractatus? It is not used as a referring term: it does not stand for the author, a world-soul, or a transcendental subject. Its function is rather to engage the reader in applying the first-person method when aiming to understand the Tractatus.

Wittgenstein’s Tractatus deploys modal vocabulary, especially “possibility.” Some readers take this to signal commitment to substantive modal theories. For others, it is metaphysical nonsense to be thrown away. We steer a middle path. We uncover the central role of possibility in Wittgenstein’s philosophical development from criticism of Russell’s multiple-relation theory of judgment to the conception of propositions as pictures in the Tractatus. In this conception, modality is not the subject matter of theorizing but an ineluctable aspect of picturing of reality whose showing forth Wittgenstein aims to help us see by operationalizing the construction of propositions.

In this chapter, I interpret section 6.361 of Wittgenstein’s Tractatus – containing Wittgenstein’s second reference to Heinrich Hertz in the book – in the context of the nearby framing remarks concerning the ‘law of causality’. Attention to the relevant details of Hertz’s work sheds light on a number of Wittgenstein’s remarks about mechanics in the 6.3s and, in particular, explains Wittgenstein’s claim that ‘What can be described can happen too, and what the law of causality is meant to exclude cannot even be described’ (6.362). For Wittgenstein, to describe events in causal terms is to describe them via an appeal to temporal and spatial asymmetries. However, no alternative is available: a description that did not appeal to such asymmetries would not be a description of anything. According to the Tractatus, descriptions are recognized as causal when they are embedded in a unified theoretical framework, but causal powers, understood as relations of material necessity, do not exist.

Elizabeth Anscombe has called the part of the Tractatus dealing with the relation between the will and the world “obviously wrong.” To understand and assess this view, I look at what Wittgenstein, Schopenhauer, and Anscombe say about the will. She is right to reject the view of the will that she calls wrong, but it is possible that Wittgenstein intends his readers to reject it too. Recent work by Anne-Marie Søndergaard Christensen, Eli Friedlander, Modesto Gómez-Alonso, and Michael Kremer helps us to see this, and to understand Wittgenstein’s views on ethics as well. The will, conceived as something distinct from our actions in the world, is indeed a chimaera, as Anscombe argues. Will belongs to what we do. And it is not, as such, something that we can or should reject. If we are to reject anything in this neighbourhood, it is idle wishing that the world would change.