Wittgenstein and the naming relation

The thesis of this paper is that the Tractatus and the Investigations can be related as follows. Wittgenstein attempted in the Tractatus to avoid the conceptual realism of Frege and Russell with respect to propositions. He solved his problem by developing the picture‐theory of language. This solution assumed that the units of language are words which arc names of simple objects. Because of this assumption the solution has the undesirable consequence that examples oi genuine names, atomic facts and atomic propositions cannot be given although their existence is logically required by the solution. Wittgenstein had, therefore, eventually to examine the idea of a name. Thus the Philosophical Investigations in which this examination is conducted.     

The Visual Field in Russell and Wittgenstein

Bertrand Russell developed a conception of the nature of the visual field, and of other sensory fields, as part of his project of explaining the construction of the external world. Wittgenstein's remarks on the visual field in the Tractatus are in part a response to Russell. Wittgenstein, against Russell, analyses the visual field in terms of facts rather than objects. Further, his conception of the field is, in a distinctive sense, depsychologised.     

The truth and nothing but the truth,yet never the whole truth: Frege,Russell and the analysis of unities

It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there is only one ultimate ontological category. This, combined with Russell's reification of propositions, ensures that he must hold concepts and objects to be of the same logical and ontological type. In this paper I argue that, while Frege's treatment of the unity of the proposition has immediate advantages over Russell's, a deeper consideration of the philosophical underpinnings and metaphysical consequences of the two approaches reveals that Frege's supposed solution is, in fact, far from satisfactory. Russell's repudiation of the Fregean position in the Principles is, I contend, convincing and Russell's own position, despite its problems, conforms to a greater extent than Frege's with common sense and, furthermore, with certain ideas which are central to our understanding of the origins of the analytical tradition.     

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 Unity of a Tractarian Fact

It is not immediately clear from Wittgenstein’s Tractatus how to connect his idea there of an object with the logical ontologies of Frege and Russell. Toward clarification on this matter, this paper compares Russell’s and Wittgenstein’s versions of the thesis of an atomic fact that it is a complex composition. The claim arrived at is that whilst Russell (at times at least) has one particular of the elements of a fact – the relation – responsible for the unity of the whole, for Wittgenstein the unity of a fact is the product of copulative powers inherent in all its elements. All kinds of constituents of Tractarian facts – all kinds (forms) of object – are, to use Fregean terminology, unsaturated.     

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).     

Kant,wittgenstein and the limits of logic

This paper has two purposes. (1) To justify the claim that there is an important distinction underlying the saying/showing distinction of the Tractatus; the distinction which Kant characterises as that between historical and rational knowledge. (2) To argue that it is because the Tractatus accepts Frege/Russell logic as a complete representation of all thought according to laws, that what is shown cannot be recognised as knowledge. This is done by interpolating Frege's logical innovations between the views of Kant and Wittgenstein on logic and mathematics.     

The power and the limits of Wittgenstein's N operator

The power of Wittgenstein's N operator described in the Tractatus is that every proposition which can be expressed in the Russellian variant of the predicate calculus familiar to him has an equivalent proposition in an extended variant of his N operator notation. This remains true if the bound variables are understood in the usual inclusive sense or in Wittgenstein's restrictive exclusive sense. The problematic limit of Wittgenstein's N operator comes from his claim that symbols alone reveal the logical status of propositions. This would require knowledge of the size of the Tractarian domain of unchangeable, simple objects, and this, Wittgenstein maintained, cannot be known.     

Wittgenstein and logic

In his Tractatus Logico-Philosophicus Ludwig Wittgenstein (1889–1951) presents the concept of order in terms of a notational iteration that is completely logical but not part of logic. Logic for him is not the foundation of mathematical concepts but rather a purely formal way of reflecting the world that at the minimum adds absolutely no content. Order for him is not based on the concepts of logic but is instead revealed through an ideal notational series. He states that logic is “transcendental”. As such it requires an ideal that his philosophical method eventually forces him to reject. I argue that Wittgenstein’s philosophy is more dialectical than transcendental.     

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”.

     

Beltrami's model and the independence of the parallel postulate

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell's Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege's extant logical system, if Frege's system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege's logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therin. therein.     

The Emergence of Logical Formalization in the Philosophy of Religion: Genesis,Crisis, and Rehabilitation

The paper offers a historical survey of the emergence of logical formalization in twentieth-century analytically oriented philosophy of religion. This development is taken to have passed through three main ‘stages’: a pioneering stage in the late nineteenth and early twentieth centuries (led by Frege and Russell), a stage of crisis in the 1920s and early 1930s (occasioned by Wittgenstein, logical positivists such as Carnap, and neo-Thomists such as Maritain), and a stage of rehabilitation in the 1930s, 1940s, and 1950s (led by the Cracow Circle and Quine).     

The philosophy of logical wholism

The present paper is one installment in a lengthy task, the replacement of atomistic interpretations of Wittgenstein's Tractatus by a wholistic interpretation on which the world-in-logical-space is not constructed out of objects but objects are abstracted from out of that space. Here, general arguments against atomism are directed toward a specific target, the four aspects of the atomistic reading of Tractatus given in the Hintikkas' Investigating Wittgenstein (Hintikka & Hintikka 1986). The aspects in question are called the semantical, metaphysical, epistemological and formal.What follows a précis of the Hintikkas' rendering of Wittgenstein's perspective is a characterization of the wholistic interpretation, comparing Wittgenstein's world and the transcendental conditions it sets upon possible notation to a blank page and the conditions it sets upon what is about to be written there. There will not be occasion to bring arguments against each plank in the atomist's platform or in support of each facet of wholism. But there is an extended treatment of the first two aspects — the semantical and metaphysical — which takes off from Wittgenstein's determination that, in his hands, logic must take care of itself.The second half of the paper contains a negative assessment of the support the atomistic reading can glean from the texts of Tractatus and Notebooks. From a detailed look into a range of relevant textual and translational issues, we find little there to encourage that interpretation and much to discourage it.The paper closes on a preliminary consideration of one segment of the formal aspect of the Hintikkas' atomism, the idea that the analysis of Tractatus is the analysis of Russell or is, at worst, a near relative. Examination shows that Wittgenstein would have little reason to model his analysis on that of Russell. The fundamentally wholistic vision expressed in Tractatus requires a distinctively non-Russellian, decompositional version of analysis.Words are like a film on deep water Ludwig Wittgenstein Notebooks 1914–1916 A highly condensed version of the ideas here presented will appear in the article Hintikka's Tractatus in Proceedings of the XIVth International Wittgenstein Symposium, Wittgenstein Centenary Celebration, 1991.     

Information about the logical structure of a category affects generalization

This paper considers whether information about the logical structure of a category affects how people generalize. We carried out three experiments with the following structure: participants were first presented with a set of training items, and were subsequently asked to decide whether new items belonged to the same category as the training items. Each experiment had two conditions that differed only in terms of the category label provided for the training items; different category labels conveyed different information about the logical structure of the category to which the training items were supposed to belong. In all cases, participants' generalization was greatly affected by such information. Our results suggest that people make the default assumption that category labels correspond to groupings of highly similar objects.     

Peter Winch on ‘Aristotelian’ and ‘Socratic’ Reasoning

Peter Winch often returned to questions about the nature of logic. In the context of his work on Wittgenstein and political philosophy in the 1990s, Winch described a contrast between ‘Aristotelian’ and ‘Socratic’ reasoning. Aristotelian conceptions of reasoning, attributed to Frege and Russell, would see logic as a formal science and rationality as consistency with pre‐existent rules of inference. The Socratic conception, attributed to Wittgenstein, understands rational argument as a form of socially embedded dialogue that involves moral relationships and a dimension of depth. Rational persuasion may also involve use of persuasive images and examples.     

Wittgenstein on Verification and Seeing-As, 1930–1932

This article examines the little-explored remarks on verification in Wittgenstein's notebooks during the period between 1930 and 1932. In these remarks, Wittgenstein connects a verificationist theory of meaning with the notion of logical multiplicity, understood as a space of possibilities: a proposition is verified by a fact if and only if the proposition and the fact have the same logical multiplicity. But while in his early philosophy logical multiplicities were analysed as an outcome of the formal properties of simple objects and simple signs, Wittgenstein in the early 1930s connects the notion of logical multiplicity with the notion of ways of seeing. I will argue that the relevant ways of seeing are closely similar to seeing-as or aspect seeing. According to Wittgenstein's view in the early 1930s, logical multiplicities are part of our perceptual experience of propositions and facts. In this sense, the verification relation depends on how we experience propositions and facts as being surrounded by a logical space of possibilities. Strikingly, Wittgenstein's way of thinking about the verification relation offers solutions to a set of seemingly intractable problems connected with the versions of verificationism developed by members of the Vienna Circle.     

On the Logic of Classes as Many

The notion of a "class as many" was central to Bertrand Russell's early form of logicism in his 1903 Principles of Mathematics. There is no empty class in this sense, and the singleton of an urelement (or atom in our reconstruction) is identical with that urelement. Also, classes with more than one member are merely pluralities — or what are sometimes called "plural objects" — and cannot as such be themselves members of classes. Russell did not formally develop this notion of a class but used it only informally. In what follows, we give a formal, logical reconstruction of the logic of classes as many as pluralities (or plural objects) within a fragment of the framework of conceptual realism. We also take groups to be classes as many with two or more members and show how groups provide a semantics for plural quantifier phrases.     

Dialogues on Causality and the Limits of Empiricism

This paper presents the main lines of reasoning in the Wittgenstein notes entitled 'Cause and Effect: Intuitive Awareness,' in the form of a series of dialogues between Wittgenstein, Russell, and a few other philosophical voices. Two of the dialogues relate to what, in Remarks on the Foundations of Mathematics , Wittgenstein called 'the similarity of my treatment with relativity theory.'     

Philosophy for psychology: Reality ain't what it used to be - perhaps it's evolved!

According to Wittgenstein (<citeref rid="bib37">1980</citeref>): 'Philosophy is the discipline of thinking about thinking'. And 'the object of philosophy is the logical clarification of thoughts. Philosophy is not a theory, but an activity. The theory of knowledge is the philosophy of psychology' (p. 77). This paper is in the nature of a philosophical discourse analysis of the August 2001 issue of The Psychologist (which focused on evolution), illustrating with various examples the need for philosophical rigour in psychological discourse. In particular, Ryle's (<citeref rid="bib31">1966</citeref>) notion of logical category errors is exemplified and explained by samples from the psychological discourse in The Psychologist journal.