Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for groups of (...) formulas whose top rows differ. For them I provide (i) a tree-style system of ‘row tree proofs’, which is shown to be sound and complete, and (ii) an alternative, re-writing strategy. (shrink)

The paper interprets Wittgenstein’s famous call to silence at the end of his Tractatus – that “whereof one cannot speak, thereof one must be silent” – as a critique of philosophy itself. Wittgenstein was concerned throughout his philosophical life with finding a way to delineate the limits of language. These limits, once we have them clearly in view, rob our attempts to put forth philosophical theories of their legitimacy. In order to give a critical assessment of this Wittgensteinian critique of (...) philosophy, the paper primarily focuses on the roots of that critique in Wittgenstein’s earliest writings – his notebooks, his 1913 “Notes on Logic,” the 1914 set of notes dictated to G. E. Moore, and the Tractatus itself. Wittgenstein’s influence by Fritz Mauthner and, mediated through Mauthner, by Kant receive special attention. The conclusion is that, far from Mauthner’s radical anti-philosophical bias, we can come to see a deep appreciation of the power, the draw, and the significance of philosophical problems in Wittgenstein’s writings. The text closes with a short look at how Wittgenstein’s thinking about the limits of language evolved later in his life. (shrink)

I argue, through appeal to the distinction between analysis and decomposition described by Dummett, that Wittgenstein employs both of those notions in the Tractatus. I then bring this interpretation to bear upon the issue of propositional unity, where I formulate an objection to the views of both Leonard Linksy and José Zalabardo. I show that both Linsky and Zalabardo fail to acknowledge the distinction between analysis and decomposition present in the Tractatus, and that they consequently mischaracterise Wittgenstein’s position with respect (...) to propositional unity. (shrink)

ABSTRACT I argue that some of the central doctrines of Wittgenstein's Tractatus Logico-Philosophicus can be seen as addressing the twin problems of semantic unity and...

In 'On the nature of truth and falsehood' Russell offers both a multiple relation theory of judgment and a correspondence theory of truth. It has been a prevailing understanding of the Tractatus that Wittgenstein rejects Russell’s multiple relation idea but endorses the correspondence theory. Ramsey took the opposite view. In his 'Facts and Propositions', Ramsey endorses Russell’s multiple relation idea, rejects the correspondence theory, and then asserts that these moves are both due to Wittgenstein. This chapter will argue that Ramsey’s (...) ascriptions are both correct. The extent of the agreement between Ramsey and Wittgenstein will be argued, moreover, to count definitively against standard understandings of Ramsey as a redundancy theorist of truth. Wittgenstein is no correspondence theorist and Ramsey is no redundancy theorist; rather, both philosophers offer identity theories of truth. (shrink)

Assertion plays a crucial dual role in Frege's conception of logic, a formal and a transcendental one. A recurrent complaint is that Frege's inclusion of the judgement-stroke in the Begriffsschrift is either in tension with his anti-psychologism or wholly superfluous. Assertion, the objection goes, is at best of merely psychological significance. In this paper, I defend Frege against the objection by giving reasons for recognising the central logical significance of assertion in both its formal and its transcendental role.

Wittgenstein held that Russell’s multiple relation theory of judgment fails to explain an atomic judgment’s representation of entities as combined. He demonstrated this failure as follows. Under the multiple relation theory, an atomic judgment is a complex whose relating relation is judgment, the universal, and whose terms include the entities the judgment represents as combined. Taking such a complex we may arrive through the substitution of constituents at a complex whose relating relation is again judgment but whose terms do not (...) include entities which are logically suited for combination. This second judgment complex will not represent any of its terms as combined, for entities that are logically uncombinable are unrepresentable as combined. Russell’s theory does not, however, explain how the original judgment differs from the complex arrived at by the substitution of constituents such that the former but not the latter represents certain of its terms as combined. (shrink)

The recovery of Aristotle’s logic during the twelfth century was a great stimulus to medieval thinkers. Among their own theories developed to explain Aristotle’s theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. Both schools distinguished formal from material consequence, but in very different ways. In Buridan and his followers in Paris, formal consequence (...) was that preserved under uniform substitution. In Oxford, in contrast, formal consequence included analytic consequences such as ‘If it’s a man, then it’s an animal’. Aristotle’s notion of syllogistic consequence was subsumed under the treatment of formal consequence. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation. (shrink)

Wittgenstein responds in his Notes on Logic to a discussion of Russell's Principles of Mathematics concerning assertion. Russell writes: "It is plain that, if I may be allowed to use the word assertion in a non-psychological sense, the proposition "p implies q" asserts an implication, though it does not assert p or q. The p and the q which enter into this proposition are not strictly the same as the p or the q which are separate propositions." (PoM p35) Wittgenstein (...) replies: "Assertion is merely psychological. In not-p, p is exactly the same as if it stands alone; this point is absolutely fundamental." (NB p95) Wittgenstein's response is intriguing, not least because of the centrality to his Tractatus of the idea that a proposition says something. This paper will examine that idea, distinguishing it from 'merely psychological' assertion, and explore in this context how we should understand the occurrence of a Tractarian proposition within another. (shrink)

Wittgenstein’s atomist picture, as embodied in his Tractatus, is initially very appealing. However, it faces the famous colour-exclusion problem. In this paper, I shall explain when the atomist picture can be defended in the face of that problem; and, in the light of this, why the atomist picture should be rejected. I outline the atomist picture in Section 1. In Section 2, I present a very simple necessary and sufficient condition for the tenability of the atomist picture. The condition is: (...) logical space is a power of two. In Sections 3 and 4, I outline the colour-exclusion problem, and then show how the cardinality-condition supplies a response to exclusion problems. In Section 5, I explain how this amounts to a distillation of a proposal due to Moss, which goes back to Carruthers. And in Section 6, I show how all this vindicates Wittgenstein’s ultimate rejection of the atomist picture. The brief reason is that we have no guarantee that there are any solutions to a given exclusion problem but, if there are any, then there are far too many. (shrink)

This paper systematically outlines Wittgenstein's ab-notation. The purpose of this notation is to provide a proof procedure in which ordinary logical formulas are converted into ideal symbols that identify the logical properties of the initial formulas. The general ideas underlying this procedure are in opposition to a traditional conception of axiomatic proof and are related to Peirce's iconic logic. Based on Wittgenstein's scanty remarks concerning his ab-notation, which almost all apply to propositional logic, this paper explains how to extend his (...) method to a subset of first-order formulas, namely, formulas that do not contain dyadic sentential connectives within the scope of any quantifier. (shrink)

Beliefs have what I will call ‘propositional content’. A belief is always a belief that so-and-so: a belief that grass is green, or a belief that snow is white, or whatever. Other things have propositional content too, such as sentences, judgments and assertions. The Standard View amongst philosophers is that what it is to have a propositional content is to stand in an appropriate relation to a proposition. Moreover, on this view, propositions are objects, i.e. the kind of thing you (...) can refer to with singular terms. For example, on the Standard View, we should parse the sentence ‘Simon believes that Sharon is funny’ as: [Simon] believes [that Sharon is funny]; ‘Simon’ is a term referring to a thinking subject, ‘that Sharon is funny’ is a term referring to a proposition, and ‘x believes y’ is a dyadic predicate expressing the believing relation. In this paper, I argue against the Standard View. This is how I think we should parse ‘Simon believes that Sharon is funny’: [Simon] believes that [Sharon is funny]; here we have a singular term, ‘Simon’, a sentence ‘Sharon is funny’, and a ‘prenective’ joining them together, ‘x believes that p’. On this Prenective View, we do not get at the propositional content of someone’s belief by referring to a reified proposition with a singular term; we simply use the sentence ‘Sharon is funny’ to express that content for ourselves. I argue for the Prenective View in large part by showing that an initially attractive version of the Standard View is actually vulnerable to the same objection that Wittgenstein used against Russell’s multiple-relation theory of judgment. (shrink)

This paper investigates Wittgenstein's "notorious" criticism of Russell's theory of judgment. Instead of advancing a further new interpretation of it, though, I analyze and discuss some of the most promising readings of the Russell/Wittgenstein dispute put forward in the secondary literature; I aim to show that, despite their alleged reciprocal opposition, they cohere with each other because they are, at bottom, different ways of highlighting the same question. I then connect Wittgenstein's criticism of Russell to the account of the nature (...) of the proposition presented in the Tractatus, arguing that the latter can be seen as a natural development of the former. Finally, I make a quick connection between Wittgenstein's criticism of Russell and the conception of the world as the totality of facts, as presented in the Tractatus. (shrink)

I offer an interpretation of Wittgenstein's claim that Russell's theory of judgment fails to show that it's not possible to judge nonsense.

This paper investigates Wittgenstein’s account of the relation between elementary and molecular propositions (and thus, also, the propositions of logic) in the Tractatus Logico-Philosophicus. I start by sketching a natural reading of that relation – which I call the “bipartite reading” – holding that the Tractatus gives an account of elementary propositions, based on the so-called picture theory, and a different account of molecular ones, based on the principle of truth- functionality. I then show that such a reading cannot be (...) attributed to Wittgenstein, because he holds the view that an explanation of logical complexity is already given by a correct account of the (pictorial) nature of elementary propositions; this is implied in his claim that “an elementary proposition contains all logical constants/operations in itself”. After clarifying Wittgenstein’s notion of an operation from the Notes on Logic to the Tractatus, I finally explain why Wittgenstein claims that an elementary proposition contains all logical operations in itself, and hence why he can be said to provide a unified (and thus not bipartite) account of language and logic. (shrink)

This book attempts to explicate and expand upon Frank Ramsey's notion of the realistic spirit. In so doing, it provides a systematic reading of his work, and demonstrates the extent of Ramsey's genius as evinced by both his responses to the Tractatus Logico-Philosophicus , and the impact he had on Wittgenstein's later philosophical insights.

The Analytic Tradition in Philosophy is an excellent successor to an excellent book : It is a fine an example of the necromantic style in the history of philosophy where the object of the exercise is to resurrect the mighty dead in order to get into an argument with them, either because we think them importantly right or instructively wrong. However what was a pardonable a simplification and a reasonable omission in the earlier book has now metamorphosed into a sin (...) of omission and an oversimplification in its successor—the book lacks is an adequate discussion of the Ramified Theory of Types and Russell’s reasons for adopting it. I conclude with a brief meditation on Open Question Arguments and the threats that they pose to some of the analyses proposed by Russell and Moore themselves. (shrink)

G. F. Stout is famous as an early twentieth century proselyte for abstract particulars, or tropes as they are now often called. He advanced his version of trope theory to avoid the excesses of nominalism on the one hand and realism on the other. But his arguments for tropes have been widely misconceived as metaphysical, e.g. by Armstrong. In this paper, I argue that Stout’s fundamental arguments for tropes were ideological and epistemological rather than metaphysical. He moulded his scheme to (...) fit what is actually given to us in perception, arguing that our epistemic practices would break down in an environment where only universals were given to us. (shrink)

This paper aims to shed light on the broader significance of Frege’s logicism against the background of discussing and comparing Wittgenstein’s ‘showing/saying’-distinction with Brandom’s idiom of logic as the enterprise of making the implicit rules of our linguistic practices explicit. The main thesis of this paper is that the problem of Frege’s logicism lies deeper than in its inconsistency : it lies in the basic idea that in arithmetic one can, and should, express everything that is implicitly presupposed so that (...) nothing is left unsaid. This, in fact, is the target of Wittgenstein’s critique. Rather than the Tractatus, with its claim that logicism attempts to say something that can only be shown, it is the Philosophical Investigations, with its argument by regress against the thesis that every rule which one can follow must be of an explicit nature, that is of real significance here. (shrink)

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. (shrink)

In writings prior to the publication of The Principles of Mathematics (PoM), Russell denies that relations “in the abstract” ever relate and holds instead that only particularized relations, or relational tropes, do so; however, in PoM section 55, he argues against his former view and adopts the view that relations “in the abstract” are capable of a “twofold use” – either as “relations in themselves” or as “actually relating”. I argue that while Russell rightly came to recognize that rejecting his (...) earlier view is necessary for avoiding the Bradleyan view that complex wholes are unanalyzable, his later view can appear as an ad hoc means of avoiding Bradley's argument against “relational thought”. (shrink)

Expressively equivalent logical languages can enunciate logical notions in notationally diversified ways. Frege’s Begriffsschrift, Peirce’s Existential Graphs, and the notations presented by Wittgenstein in the Tractatus all express the sentential fragment of classical logic, each in its own way. In what sense do expressively equivalent notations differ? According to recent interpretations, Begriffsschrift and Existential Graphs differ from other logical notations because they are capable of “multiple readings.” We refute this interpretation by showing that there are at least three different kinds (...) of such multiple readings. While readings of the first kind do not capture any essential difference among notations but only among vocabularies, corresponding to readings of the second and the third kind two general parameters according to which notations may differ are defined: linearity vs. non-linearity, and tabularity vs. non-tabularity. This answers the question of how there can be substantially different but expressively equivalent logical notations. (shrink)

En este trabajo trato de dar respuesta a la cuestión acerca de si los conceptos formales del Tractatus Logico-Philosophicus de Wittgenstein son o no categorías ontológicas. Mi respuesta es que no. Así, después de ofrecer una definición de ‘ontología’ y diferentes lecturas sobre las proposiciones iniciales del Tractatus, presento la noción de concepto formal o lógico, así como diferentes interpretaciones en relación con el papel de esos conceptos en el Tractatus. Después, y teniendo en consideración lo dicho en las secciones (...) precedentes, presento mi propia lectura de las proposiciones iniciales en términos de expresiones conceptuales o gramaticales, la distinción tanto en extensión como en intensión de las nociones de concepto formal o lógico y categoría ontológica y la disolución de la ontología, que no de la lógica. Finalmente ofrezco unas conclusiones finales que recogen aspectos centrales de la discusión precedente. (shrink)