Propositions,Properties and Relations: Wittgenstein's “Notes on Logic” and the Tractatus

Frege famously argued that truth is not a property or relation. In the “Notes on Logic” Wittgenstein emphasised the bi‐polarity of propositions which he called their sense. He argued that “propositions by virtue of sense cannot have predicates or relations.” This led to his fundamental thought that the logical constants do not represent predicates or relations. The idea, however, has wider ramifications than that. It is not just that propositions cannot have relations to other propositions but also that they cannot have relations to anything at all. The paper explores the consequences of this insight for the way in which we should read the Tractatus. In the “Notes on Logic” the insight led to Wittgenstein's emphasis on “facts” in any attempt to understand the nature of symbolism. This emphasis is continued in the Tractatus. It is central to his view that propositions are facts which picture facts which prevent us from construing such picturing as a relation between what pictures and what is pictured. It illuminates the importance of context principle with regard to the distinction between showing and saying to which Wittgenstein attached so much importance and it underlies the non‐relational view of psychological propositions which he advocates. Finally, if propositions by virtue of sense cannot have predicates or relations the paradox at the end of a work which consist largely of propositions about propositions becomes intelligible.     

Sense and Simplicity: Wittgenstein's Argument for Simple Objects

This paper puts forward an alternative interpretation of the argument for simple objects advanced in the 2.0s of the Tractatus. In my view, Wittgenstein derives the simplicity of objects directly from his account of possible states, complex objects and senseful propositions. The key to Wittgenstein's argument is the idea that, if there were no simple objects, possible states would not be necessarily possible. If this were the case, however, there would be no senseful language, in Wittgenstein's view. One of the subsidiary aims of this paper is to question the idea that Wittgenstein posits simples because, without them, language would be infinitely analysable. ¹ 1 I am grateful to Malcolm Budd, Jane Heal and Jim Hopkins for their help in the development of this paper.     

The Tractatus on Logical Consequence

Abstract: I discuss the account of logical consequence advanced in Wittgenstein's Tractatus. I argue that the role that elementary propositions are meant to play in this account can be used to explain two remarkable features that Wittgenstein ascribes to them: that they are logically independent from one another and that their components refer to simple objects. I end with a proposal as to how to understand Wittgenstein's claim that all propositions can be analysed as truth functions of elementary propositions.     

The Origins of Wittgenstein's Imaginary Scenarios: Something Old, Something New

The imaginary scenarios that appear in nearly every work of the later Wittgenstein – ones involving laughing cattle, disembodied eyes that see, and the like – are decidedly absent from the Tractatus. What necessitated this change in methodology? A comparison of the Tractatus with the Philosophical Remarks, Wittgenstein's first major work after his return to philosophy, reveals that these devices are the product of something old and something new. The rationale for these devices is already present in the notion of a “propositional variable,” but Wittgenstein had little use for them until he rejected the phenomenological language and laconic style of the Tractatus.     

Meaning,Use and Ostensive Definition in Wittgenstein's Philosophical Investigations

In this paper, I argue that the restricted claim in §43a of the Philosophical Investigations is that, for a large class of cases of word meanings, the meaning of a word is its use in the language. Although Wittgenstein does not provide any example of words having uses but no meaning as exceptions to the claim, he does hint at exceptions, which are names being defined, or explained, ostensively by pointing to their bearers, in §43b. Names in ostensive definitions, or explanations, are meaningful, but not being used, and are therefore exceptions to the claim that meaning is use.     

Nominalism and Realism. How Not to Read the Tractatus' Conception of a Name

This paper focuses on a central aspect of the “picture theory” in the Tractatus – the “identity requirement” – namely the idea that a proposition represents elements in reality as combined in the same way as its elements are combined. After introducing the Tractatus' views on the nature of the proposition, I engage with a “nominalist” interpretation, according to which the Tractatus holds that relations are not named in propositions. I claim that the nominalist account can only be maintained by rejecting the “identity requirement.” I then consider an opposite – “realist” – interpretation, according to which Tractarian names include names of properties and relations. I argue that, although it can accommodate the “identity requirement,” the realist interpretation falls short of providing a correct interpretation of the Tractatus' conception of a name. I conclude by presenting an alternative account (to both nominalism and realism) of the Tractatus' conception of a name.     

Beginning,ending and remembering

Wittgenstein famously opens his Philosophical Investigations with a quotation in which Augustine recounts how he acquired language. Instead of going into the widely discussed question of how Wittgenstein relates to Augustine's picture of language, this article inquires into what else might be at stake in invoking Confessions at the very beginning of his work. At the very least, such a gesture seems to suggest that Wittgenstein wants to inscribe himself into the Augustinian legacy. More specifically, this article argues that Philosophical Investigations centres on three problems that Wittgenstein has inherited from Augustine – namely what one might call the problem of beginning, the problem of ending and finally the problem of memory. The problem of beginning not only points to the local problem of how to start writing confessional philosophy, but also what authorizes such philosophy in the first place. The problem of ending concerns the direction of such philosophy and the problematic stance of its goal, while the problem of memory turns on the task of progressing from beginning to ending.     

THE NUMBERING SYSTEM OF THE TRACTATUS

The significance of the complicated numbering of the propositions in the Tractatus has occasioned much speculation. Wittgenstein's own explanation has, following Stenius, been generally regarded as misleading. But an examination of the Prototractatus reveals that the numbering system was for Wittgenstein principally an aid in the composition of his work. It allowed him to mark out certain propositions which required further work or supplementation, without disturbing the basic structure of the treatise. But the reworking of the Prototractatus to form the Tractatus considerably changed the original order in which the ideas were connected, and thus made it more difficult to understand the Tractatus. Several specific examples make it clear that it is essential to look back at the context of the Prototractatus in order to achieve a correct interpretation of many of the propositions in the Tractatus.     

Some paradoxes in Kripke's interpretation of Wittgenstein

Kripke's skeptical interpretation of Wittgenstein's project in the Philosophical Investigations attributes to Wittgenstein a radical skepticism about the objectivity of rules and thus the meanings of words and the existence of language as well as a skepticism about the truth conditions underlying our alleged facts about the world. Kripke then contends that Wittgenstein solves this skeptical paradox by committing himself to what I shall call a Communitarian View of language. There are a number of difficulties with Kripke's interpretation of the project of the Philosophical Investigations. These include his evaluation of the notion of the rule, his interpretation of the private language arguments, his uses of the term intention, and his truncated reading of 201. In this paper I shall address and attack this interpretation of Wittgenstein as a questionable reading of the Philosophical Investigations, and I shall suggest some alternative interpretations of Wittgenstein's views which avoid both radical skepticism and a Communitarian View of language.     

From Metaphysics and Philosophical Theses to Grammar: Wittgenstein's Turn

The paper discusses the question ‘what does Wittgenstein mean by not having theses in philosophy?’ His conception of philosophy without theses, as this is articulated in his later work, is understood as a response to the problem of dogmatism in philosophy and a non‐metaphysical form of philosophy. I argue that although already the Tractatus aims at a philosophy devoid of theses, it involves a relapse back to such theses. Its conception of philosophical clarification involves a particular conception of the essence of propositions. This way the form of the activity of clarification is determined by a philosophical/metaphysical thesis. In his later philosophy Wittgenstein, however, manages to solve this problem. His solution, explained with the help of the metaphor of ‘turning our whole investigation around’, consists of a change in the comprehension of the status of philosophical statements. For instance rules (e.g. definitions) and examples are understood as what he calls ‘objects of comparison’. Such objects of comparison are something that cases of language use (to be investigated with the purpose of clarification) are to be compared with, but the philosopher is not to make the claim that such objects of comparison show what the cases of language use under examination must be. The modality (expressed by ‘must’) is a characteristic of the philosopher's mode of presentation. It should not be claimed to be a feature of his object of investigation (the uses of language to be clarified).     

La Evolucion de la filosofia de Wittgenstein

Summary The author claims that there is a basic difference between theTractatus and thePhilosophical Investigations; despite Bernstein's and O'Brien's claims to the contrary, there are, indeed, two Wittgensteins. Yet, to ascertain the difference between both we must look at Wittgenstein's conceptions of philosophy rather than at his views on logic and language. Wittgenstein's different, and even divergent, views on logic and language are grounded on his two views on philosophy and not the other way around. At the same time, Wittgenstein's views on philosophy are caused by his ways of conceiving the scope of philosophical activity in regard to language. Both in theTractatus and in thePhilosophical Investigations, Wittgenstein points out what is important in language for philosophy, but in each case he reaches very different conclusions. Now, when all is said, there remains one unifying factor in all of Wittgenstein's investigations: it is the question of the logic of language, which shifts positions from theTractatus to theInvestigations, so that what was earlier a hidden structure becomes later the grammar of its indefinitely complexe uses.     

The Philosopher's Baedeker: Wittgenstein's Tractatus as Guidebook

The Wittgenstein of the Tractatus is committed to four central and interlocking claims: a limit to sense and nonsense can be drawn in logic; a limit to meaningful and meaningless language – to meaningful and meaningless nonsense – cannot be drawn in logic; whether nonsense is meaningful is shown in its use rather than its form; the Tractatus consists largely of meaningful nonsense. Undergirding these commitments is an account of language‐to‐world picturing in which shared “mathematical multiplicities” play a key role. Picturing as a global phenomenon – language‐to‐world, rather than proposition‐to‐fact – has not been well understood. The Tractatus is not a textbook. No doctrines are developed in it. No problems solved. Instead, it is a kind of Baedeker, a guidebook for those who want “to see the world aright.”     

Truth in the Investigations

According to a widespread interpretation, in the Investigations Wittgenstein adopted a deflationary or redundancy theory of truth. On this view, Wittgenstein’s pronouncements about truth should be understood in the light of his invocation of the equivalences ‘p’ is true = p and ‘p’ is false = not p. This paper shows that this interpretation does not do justice to Wittgenstein’s thoughts. I will be claiming that, in fact, in his second book Wittgenstein is returning to the pre-Tractarian notion of bipolarity, and that his new development of this notion in the Investigations excludes the redundancy-deflationary reading. Wittgenstein’s thoughts about truth are instead compatible with another interpretative option: Wittgenstein remains faithful to his methodological pronouncements, and he merely presents us with (grammatical) platitudes about the notions of “true” and “false”.

     

Categorial Indeterminacy,Generality and Logical Form in Wittgenstein's Tractatus

Many commentators have attempted to say, more clearly than Wittgenstein did in his Tractatus logico‐philosophicus, what sort of things the ‘simple objects’ spoken of in that book are. A minority approach, but in my view the correct one, is to reject all such attempts as misplaced. The Tractarian notion of an object is categorially indeterminate: in contrast with both Frege's and Russell's practice, it is not the logician's task to give a specific categorial account of the internal structure of elementary propositions or atomic facts, nor, correlatively, to give an account of the forms of simple objects. The few commentators who have hitherto maintained this view have mainly devoted themselves to establishing that this was Wittgenstein's intention, and do not much address the question why Wittgenstein held that it is not the logician's business to say what the objects are. The present paper means to fill this lacuna by placing this view in the context of the Tractatus's treatment of logic generally, and in particular by connecting it with Wittgenstein's treatment of generality and with his reaction to Russell's approach to logical form.     

The architecture of modern mathematics: Essays in history and philosophy

It is a little understood fact that the system of formal logic presented in Wittgenstein’s Tractatusprovides the basis for an alternative general semantics for a predicate calculus that is consistent and coherent, essentially independent of the metaphysics of logical atomism, and philosophically illuminating in its own right. The purpose of this paper is threefold: to describe the general characteristics of a Tractarian-style semantics, to defend the Tractatus system against the charge of expressive incompleteness as levelled by Robert Fogelin, and to give a semantics for a formal language that is the Tractarian equivalent of a first-order predicate calculus. Of note in regard to the latter is the fact that a Tractatusstyle truth-definition makes no appeal to the technical trick of defining truth in terms of the satisfaction of predicates by infinite sequences of objects, yet is materially equivalent to the usual Tarski-style truth-definitions     

Solving the Color Incompatibility Problem

It is commonly held that Wittgenstein abandoned the Tractatus largely because of a problem concerning color incompatibility. In this paper, I solve the color incompatibility problem and argue that the central program of the Tractatus can in fact be accomplished.     

The importance of being in earnest

Certain remarks in the Tractatus, taken together with a passage in a letter Wittgenstein wrote to Russell, suggest that at one time Wittgenstein inclined toward a psychologistic theory of language. But textual considerations with regard to the former and a special interpretation of the latter allow us to interpret these statements in a way that is consistent with Wittgenstein's later views.     

Contingentism versus Necessitism: The Tractatus Standpoint

The paper provides an interpretation of section 2.013 of the Tractatus which casts light on the strategic role that that section plays in the early Wittgenstein’s version of the ontology of logical atomism. The far‐reaching consequences that the proposed interpretation has on the issue of the metaphysical nature of objects are spelled out, and the identification of Tractatus objects with phenomenal qualities, that is with phenomenal abstract universals, is shown to be fully consistent with those consequences. As a by‐product of the analysis, the standpoint of the Tractatus with respect to both contingentism and necessitism is clarified.