The relation between Wittgenstein's philosophy of mathematics and mathematical Intuitionism has raised a considerable debate. My attempt is to analyse if there is a commitment in Wittgenstein to themes characteristic of the intuitionist movement in Mathematics and if that commitment is one important strain that runs through his Remarks on the foundations of mathematics. The intuitionistic themes to analyse in his philosophy of mathematics are: firstly, his attacks on the unrestricted use of the Law of Excluded Middle; secondly, his distrust (...) of non-constructive proofs; and thirdly, his impatience with the idea that mathematics stands in need of a foundation. These elements are Fogelin's starting point for the systematic reconstruction of Wittgenstein's conception of mathematics. (shrink)

This paper responds to the generous comments by Alexander Klein and Cheryl Misak on my “American Pragmatism and the Vienna Circle: The Early Years”. First, besides offering some clarification of my original thesis, I argue that Jerusalem was not liable to the anti-Spencerian criticisms by James that Klein adduces in the course of defending James against the charge of psychologism. Then I investigate the impact of Wittgenstein’s Ramsey-derived pragmatism, importantly foregrounded by Misak, on the Vienna Circle and argue that it (...) was mainly limited to Schlick but not recognized as pragmatist, also leaving unaffected the impact of James’s pragmatism on Frank, Hahn and Neurath specified in my original paper. That said, Klein’s and Misak’s comments add significantly to our understanding of long-neglected transatlantic philosophical connections in the early twentieth century. (shrink)

Discussions of the relation between pragmatism and logical empiricism tend to focus on the period when the logical empiricists found themselves in exile, mostly in the United States, and then attempt to gauge the actual extent of their convergence. My concern lies with the period before that and the question whether pragmatism had an earlier influence on the development of logical empiricism, especially on the thought of the former members of the “first” Vienna Circle. I argue for a substantially qualified (...) affirmative answer. (shrink)

The main goal of this paper is to reflect on what characterizes the evidence of the propositions that we hold to be necessary. I have tried to show that the evidence of every necessarily true proposition takes the form of a self-contained operational composition. In conclusion, I will point out in what respects the view I defend might help to reconcile some traits of Husserl’s understanding of material a priori truth with some of the later Wittgenstein’s intuitions concerning linguistic meaning.

Uebel has recently claimed that, contrary to popular opinion, none of the philosophers of the Vienna Circle of Logical Positivists were proponents of epistemological foundationalism. According to the considerations of the current discussion, however, Uebel's conclusion is erroneous, especially with respect to the work of Moritz Schlick. The chief reason Uebel offers to support his conclusion is that current attempts to portray Schlick's epistemology as foundationalist fail to overcome its ‘ultimate incoherence’. In contrast, it is argued that current interpretations, based (...) on the unpublished as well as the published record, provide understandings of Schlick's foundationalist epistemology as not only coherent, but plausible. In closing, Uebel's own treatment of Schlick's work, which purports to show that the most feasible candidates for foundational statements are ‘meaning-theoretic’ clarifications of the content of expressions, itself fails to accurately represent Schlick's own characterizations, and pictures Schlick's epistemology as a confused mix of epistemic and semantic insights. (shrink)

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. (shrink)

In Carnap’s autobiography, he tells the story how one night in January 1931, “the whole theory of language structure” in all its ramifications “came to [him] like a vision”. The shorthand manuscript he produced immediately thereafter, he says, “was the first version” of Logical Syntax of Language. This document, which has never been examined since Carnap’s death, turns out not to resemble Logical Syntax at all, at least on the surface. Wherein, then, did the momentous insight of 21 January 1931 (...) consist? We seek to answer this question by placing Carnap’s shorthand manuscript in the context of his previous efforts to accommodate scientific theories and metalinguistic claims within Wittgenstein’s Tractatus theory of meaning. The breakthrough of January 1931 consists, from this viewpoint, in the rejection of the Tractatus theory in favor of the meta-mathematical perspective of Hilbert, Gödel, and Tarski. This was not yet the standpoint of the published Logical Syntax, as we show, but led naturally to the “principle of tolerance” and thus to Carnap’s mature philosophy, in which the inconsistencies between this first view and the principle of tolerance, which survived into the published Syntax, were overcome. (shrink)

One of the central logical ideas in Wittgenstein’sTractatus logico-philosophicusis the elimination of the identity sign in favor of the so-called “exclusive interpretation” of names and quantifiers requiring different names to refer to different objects and (roughly) different variables to take different values. In this paper, we examine a recent development of these ideas in papers by Kai Wehmeier. We diagnose two main problems of Wehmeier’s account, the first concerning the treatment of individual constants, the second concerning so-called “pseudo-propositions” (Scheinsätze) of (...) classical logic such as$a=a$or$a=b \wedge b=c \rightarrow a=c$. We argue that overcoming these problems requires two fairly drastic departures from Wehmeier’s account: (1) Not every formula of classical first-order logic will be translatable into asingleformula of Wittgenstein’s exclusive notation. Instead, there will often be a multiplicity of possible translations, revealing the original “inclusive” formulas to beambiguous. (2) Certain formulas of first-order logic such as$a=a$will not be translatable into Wittgenstein’s notation at all, being thereby revealed as nonsensical pseudo-propositions which should be excluded from a “correct” conceptual notation. We provide translation procedures from inclusive quantifier-free logic into the exclusive notation that take these modifications into account and define a notion of logical equivalence suitable for assessing these translations. (shrink)

This article provides an English translation of a historic discussion on the foundations of mathematics, during which Kurt GÖdel first announced his incompleteness theorem to the mathematical world. The text of the discussion is preceded by brief background remarks and commentary.

According to the received view, the Tractatus would present a realistic conception of the meaning of a declarative sentence: that meaning would be explained in terms of evidence-transcending, not epistemically-constrained, truth-conditions. In this paper, I make a case against such a contention. If states of affairs are identified with possible combinations of phenomenal objects, the truth-conditions of an elementary proposition inevitably collapse onto its assertability-conditions: the existence of the state of affairs depicted by the proposition would be both the condition (...) for its being true and, at the same time, the condition for our recognition of its being true. Moreover, the finiteness of logical space (the set of all phenomenal states of affairs) would ensure the decidability, in principle, of all meaningful propositions, and hence would preserve the general validity of the laws of classical logic. Lastly, the problem of the relationship between the overt verificationism of Wittgenstein's 1929-1933 writings and the Tractatus's ontological and semantic views, is dealt with. (shrink)

Dem "Manifestationsargument" zufolge steht eine realistische Semantik der Wahrheitsbedingungen im Widerspruch zu dem Gedanken, dass das Verstehen von Sätzen eine Fähigkeit ist, die sich im Handeln manifestieren können muss. – Der Aufsatz zeigt, dass sowohl Realisten als auch Anti-Realisten die These aufzugeben haben, dass das Verstehen eines Satzes im Erfassen der jeweiligen Wahrheitsbedingungenbesteht. Die realistische Annahme der Existenz verifikationstranszendenter Wahrheiten steht – unabhängig vom Manifestationsprinzip – im Widerspruch zu einer wahrheitskonditionalen Semantik. Die von heutigen Anti-Realisten vertretenen Theorien des Verstehens sind (...) allerdings einem ähnlichen Einwand ausgesetzt, insofern sie gleichfalls nicht unsere Fähigkeit, unentscheidbare Sätze zu verstehen, erklären können. (shrink)

One of the reasons colours, or better the conceptual organisation of the colour system, could be relevant to the philosophy of logic is that they necessitate some mutilation of truth tables by restricting truth functionality. This paper argues that the so-called ‘Colour Exclusion Problem’, the first great challenge for Wittgenstein’s Tractatus, is a legitimate philosophical motivation for a systematic mutilation of truth tables. It shows how one can express, through these mutilations, some intensional logical relations usually expressed by the Aristotelian (...) Square of Oppositions, as contrariety and subcontrariety. (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)

Inferentialism is the conviction that to be meaningful in the distinctively human way, or to have a 'conceptual content', is to be governed by a certain kind of inferential rules. The term was coined by Robert Brandom as a label for his theory of language; however, it is also naturally applicable (and is growing increasingly common) within the philosophy of logic.

Ideas on meaning, rules and mathematical proofs abound in Wittgenstein’s writings. The undeniable fact that they are present together, sometimes intertwined in the same passage of Philosophical Investigations or Remarks on the Foundations of Mathematics, does not show, however, that the connection between these ideas is necessary or inextricable. The possibility remains, and ought to be checked, that they can be plausibly and consistently separated. I am going to examine two views detectable in Wittgenstein’s works: one about proofs, the other (...) about meaning and rules. The first is the denial of the objectivity of proof. The second is a conception of meaning stemming from the rule-following considerations. I shall argue that, though Wittgenstein seems to conjoin the two views, they can be, and should be, separated1. (shrink)