Today I want to talk about an element in the milieu in which Ludwig Wittgenstein conceived the Tractatus Logico-Philosophicus that has not been recognized to date: the generalization of the methodology of experimental scale models that occurred just about the time he was writing it. I find it very helpful to keep in mind how this kind of model portrays when reading the Tractatus — in particular, when reading the statements about pictures and models, such as:That a picture is a (...) fact ,That a picture is a model of reality ,That the “pictorial relationship” that makes a picture a picture is part of that picture , andThat a picture must have its pictorial form in common with reality in order to able to depict it. (shrink)

On the assumption that theistic religious commitment takes place in the face of evidential ambiguity, the question arises under what conditions it is permissible to make a doxastic venture beyond one’s evidence in favour of a religious proposition. In this paper I explore the implications for orthodox theistic commitment of adopting, in answer to that question, a modest, moral coherentist, fideism. This extended Jamesian fideism crucially requires positive ethical evaluation of both the motivation and content of religious doxastic ventures. I (...) suggest that, even though the existence of horrendous evil does not resolve evidential ambiguity in favour of atheism, there are reasonable value commitments that would preclude those who hold them from satisfying extended Jamesian fideist conditions for committing themselves to classical theism. I then begin a discussion of a possible revisionary theistic alternative (in the Christian tradition) which – one might hope – may meet those conditions. An earlier, shorter, version of this paper was delivered as a keynote address at the APA Pacific 2007 Mini-Conference on Models of God. (shrink)

Recently, Irad Kimhi has argued that negation and falsehood can be made intelligible by understanding assertions/judgements as acts of two-way logical capacities. These are capacities that are, at the same time, for (1) positive and negative assertions/judgements and (2) positive and negative facts. Kimhi’s account of negation and falsehood, however, faces severe problems. I argue that these problems can be resolved, and that a new understanding of cases of negation and falsehood can be achieved, by regarding two-way logical capacities for (...) assertion/judgement and facts as established and undergirded by what Ludwig Wittgenstein calls “samples”. The standard metre sample, for instance, establishes and undergirds the capacity for asserting that something, x, is one metre long (meaning: x is like the standard metre in length). At the same time, it establishes and undergirds the capacity for the fact that x is one metre long (when x is like the standard metre in length). As I explain, invoking samples means we cannot say, as Kimhi wants to, what assertion/judgement, negation, and facts, in general, are but can only show what they are, one case at a time. This, however, is a boon not a disadvantage. (shrink)

The influence of Heinrich Hertz's The Principles of Mechanics on Ludwig Wittgenstein's Tractatus Logico‐Philosophicus has been studied for decades, but it has never become a mainstream topic in the Wittgensteinian literature. This paper focusses on Tractarian notions of objects, elementary facts and elementary sentences and discusses their similarities with Hertz's concepts of mass, its constituents and their mechanistic images. As the paper demonstrates, the Hertzian context provides some fruitful interpretational leads concerning several controversial ideas endorsed by early Wittgenstein, namely propositional (...) analysis, logical independence of elementary facts, logical independence of elementary sentences, and modalities. (shrink)

Quine maintained that philosophical and scientific theorizing should be conducted in an untyped language, which has just one style of variables and quantifiers. By contrast, typed languages, such as those advocated by Frege and Russell, include multiple styles of variables and matching kinds of quantification. Which form should our theories take? In this article, I argue that expressivity does not favour typed languages over untyped ones.

Individual responsibility is usually articulated either in terms of an individual’s intentions or in terms of the consequences of her actions. However, many of the situations we encounter on a regular basis are structured in such a way as to render the attribution of individual responsibility unintelligible in intentional or consequential terms. Situations of this type require a different understanding of individual responsibility, which I call conditioned responsibility. The conditioned responsibility model advances that, in such situations, responsibility arises directly out (...) of the conditions in which the individual finds herself, irrespective of her intentions or of the consequences of her actions. This model gives rise to a series of challenges, some of which, I propose, can be addressed by drawing on Wittgenstein’s later notion of form of life, together with the notion of honesty implicit in his early approach to ethics. (shrink)

In this paper, I want to claim that, in conformity with overall intuitions, there are some aesthetic properties that are perceivable. For they are high-level properties that are not only grasped immediately, but also attended to holistically—just like the grouping properties they depend on and that are responsible for the Gestalt effects or switches through which they are grasped. Yet, unlike such grouping properties, they are holistically attended to in a disinterested modality, where objects and their properties are regarded for (...) their own sake. (shrink)

Customary interpretations state that Tractarian thoughts are pictures, and, a fortiori, facts. I argue that important difficulties are unavoidable if we assume this standard view, and I propose a reading of the concept taking advantage of an analogy that Wittgenstein introduces, namely, the analogy between thoughts and projective geometry. I claim that thoughts should be understood neither as pictures nor as facts, but as acts of geometric projection in logical space. The interpretation I propose thus removes the root of the (...) identified difficulties. Moreover, it allows important clarification concerning some central aspects of the Tractarian theory of representation, and it yields a unifying elucidation regarding Wittgenstein’s remarks on the solipsistic thesis. (shrink)

A significant discrepancy in Wittgenstein's studies is whether Philosophical Investigations contains any trace of positive philosophy, notwithstanding the author's apparent anti-theoretic position. This study argues that the so-called ‘Chapter on philosophy’ in the Investigations §§89–133 contains negative and positive vocabulary and the use of various voices through which Wittgenstein employs his primary method of language-games, thus providing a surveyable understanding of several philosophical concepts, such as knowledge and time. His positive philosophy aims to reorient our attention from understanding the theories (...) on these concepts to understanding the concepts themselves, regardless of any theorisation. (shrink)

Many researchers are working toward the goal of finding a treatment that halts or even reverses the aging process of the human body, a treatment that would make the recipient potentially immortal. The hope that they will succeed in the relatively near future is gaining ground among academics and laypeople alike. What will happen if this hope becomes reality? Specifically, how will our political and social institutions and practices be affected by that discovery? These are the questions raised in the (...) present paper. Concretely, I will discuss three political and social problems that the invention of an immortality treatment is likely to provoke, namely the struggle for access to that treatment, the threat of overpopulation, and the friction between potentially immortal individuals. (shrink)

It is necessary to reconsider P. M. S. Hacker’s assessment of Kant and Wittgenstein’s philosophical affinities and the question concerning Wittgenstein’s alleged use of “transcendental arguments”. First, Alfred Norman’s reading of the Tractatus Logico-Philosophicus as a thought experiment receives revision to develop a view of the Critique of Pure Reason as a large-scale thought experiment that shares important logical features with the Tractatus. Then the question is addressed whether the middle Wittgenstein and the pre-critical Kant employed any thought experiments that (...) could be equally characterised as “transcendental arguments”. A rational reconstruction of both thinkers’ arguments is carried out in the light of the contemporary literature on thought experimenting. The novelty and relevance of this approach is the emphasis laid upon a largely neglected affinity between Kant and Wittgenstein, namely the systematic use of thought experiments in their epistemological pursuits. The conclusions are: i) Wittgenstein’s and Kant’s magna opera can be seen as philosophical thought experiments that attempt to try out the limits of language and the limits of possible experience respectively; ii) Both philosophers developed arguments that can be designated as transcendental if only from a methodological standpoint; and iii) some key arguments put forward by the middle Wittgenstein in the determination of the structure of visual space could be characterised better as thought experiments than transcendental arguments. (shrink)

The present text discusses whether there is a tension between aphorisms 6.1-6.13 of the Tractatus and the Church-Turing theorem about the decidability of predicate logic. We attempt to establish the following points: (i) Aphorisms 6.1-6.13 are not consistent with the Church-Turing theorem. (ii) The logical symbolism of the Tractatus, built from the N-operator, can (and should) be interpreted as expressively complete with respect to first-order formulas. (iii) Wittgenstein’s reasons for believing that Logic is decidable were purely philosophical and the undecidability (...) result shows that there are aspects of his criticisms of Frege and Russell that become unjustified in light of these results. (shrink)

This paper offers a novel interpretation of Wittgenstein’s early conception of ethics and the good ethical life. Initially, it critically examines the widespread view according to which Wittgenstein’s early conception of ethics and the good ethical life involves having a certain ethical attitude to the world. It points out that this reading incurs in some mistakes and shortcomings, thereby suggesting the need for an alternative reading that avoids and amends these inadequacies. Subsequently, it sets out to offer said reading. Specifically, (...) it is argued that the good ethical life is predicated on a good exercise of the ethical will and solving the riddle of life, both of which demand a certain view of, and not an attitude to, the world. This view is the view of the world sub specie aeterni. (shrink)

In this article I offer a novel explanation of Wittgenstein’s claim, in his Tractatus, that to represent the logical form of a proposition would require our being positioned outside of logic. The account here presented aims to exploit a connection, widely noticed, between the logical forms of objects and those of the propositions in which the names of those objects figure. I show that the logical forms of propositions may, on Wittgenstein’s view, be identified with places in logical space, and (...) that places in logical space are reducible to the forms of both objects and their names. I argue, though, that according to Wittgenstein the representation of a proposition’s logical form would require the existence of a place in logical space not so reducible. I conclude that on Wittgenstein’s position, the attempt to represent logical forms cannot, therefore, succeed. (shrink)

Dialetheism is the view that some contradictions are true. Resorting to either metaphysical dialetheism or semantic dialetheism may seem like an appropriate resolve to certain theological contradictions. At least for those who concede to theological contradictions, and take dialetheism seriously. However, I demonstrate that neither of these types of dialetheism would serve to be amenable in resolving an Islamic theological contradiction. This is a theological contradiction that I refer to as ‘the paradox of an unknowable and ineffable God’. As a (...) result of this, I propose an alternative type of dialetheism which aims to resolve the paradox of an unknowable and ineffable God. I call this type of dialetheism, ‘mystical dialetheism’. (shrink)

Those of us who are captivated by new television, often find ourselves rewatching episodes or whole series. Why? What is the philosophical significance of the phenomenon of rewatching? In what follows, I engage with the ontology of television series in order to think about these questions around rewatching. I conclude by reflecting on what the entire discussion might suggest about the medium of new television, about ourselves, and also about our world and the possibilities of art in it.

En los textos de Kant sobre los deberes hacia uno mismo cabe distinguir dos líneas argumentativas diferentes: una en las Lecciones de ética de 1784/1785, y la otra en la Metafísica de las costumbres. Este artículo defiende la línea argumentativa de las Lecciones de ética y reivindica un deber hacia uno mismo: el deber de no dejarse utilizar por otros. Posteriormente se analizan algunas objeciones que se han formulado o que es posible formular contra este concepto.

ABSTRACT Despite all fundamental divergences, the similarities formed between some interpretations of the later-Wittgenstein’s philosophy of religion and the tradition of Islamic Mysticism, can yet be philosophically recognized. These basic analogies are as follows: 1) The inextricability of belief and practice and the priority of practice over knowledge 2) The characterization of the core religious beliefs as the primal ground of man’s perception and understanding, in contrast to the view that considers fundamental religious beliefs as theoretical conclusions derived from purely (...) rational courses of reflection 3) A new practice-laden narrative of religious realism. Given that, one can even shed a new Wittgensteinian light on even the most abstract and metaphysical elements of the mystical worldview. If fundamental religious beliefs are interpreted not as metaphysical doctrines but as a set of descriptions arising from a specific form of practical life, then the ability to see a sort of transcendent and sacred unity in the whole universe will be based on a way of purposive engagement and wayfaring in the natural and social world. (shrink)

The article argues for a contextualised reading of Wittgenstein’s Tractatus. It analyses in detail the role that use and application play in the text and how that supports a conception of transcendentality of logic that allows for contextualisation. The article identifies a tension in the text, between the requirement that sense be determinate and the contextual nature of application, and suggests that it is this tension that is a major driver of Wittgenstein’s later ideas.

Wittgenstein’s experiments on rhythm, conducted in Charles Myers’s laboratory in Cambridge during the years 1912–13, are his earliest recorded engagement in thinking about music, not just appreciating it, and philosophizing by means of musical thinking. In this essay, I set these experiments within their appropriate intellectual, scientific, and philosophical context in order to show that, its minor scientific importance notwithstanding, this onetime excursion into empirical research provided an early onset for Wittgenstein’s career-long exploration of the philosophically pervasive implications of aspects. (...) Dramatically moving beyond the conceptual limitations, which were inscribed by Charles Myers’s scientific program, Wittgenstein got a glimpse of a philosophical angle, which was bound to become very important to him not only in aesthetics, but also for his overarching philosophical development. He became interested in what we actually do when we re-phrase, compare, come up with good similes in order to illuminate something definite within the space of possibility, so a new aspect may come to life. (shrink)

Work on the nature and scope of formal logic has focused unduly on the distinction between logical and extra-logical vocabulary; which argument forms a logical theory countenances depends not only on its stock of logical terms, but also on its range of grammatical categories and modes of composition. Furthermore, there is a sense in which logical terms are unnecessary. Alexandra Zinke has recently pointed out that propositional logic can be done without logical terms. By defining a logical-term-free language with the (...) full expressive power of first-order logic with identity, I show that this is true of logic more generally. Furthermore, having, in a logical theory, non-trivial valid forms that do not involve logical terms is not merely a technical possibility. As the case of adverbs shows, issues about the range of argument forms logic should countenance can quite naturally arise in such a way that they do not turn on whether we countenance certain terms as logical. (shrink)

Categories play a major role in contemporary metaphysics. They have not only been invoked in a number of philosophical theories but are themselves objects of epistemological and metaphysical scrutiny. In this article, we will discuss the following questions: How do we know when something belongs to a certain category? Is there a fundamental category of the world? Can we give a satisfactory account of the number of categories and the completeness of systems of categories? Are categories the genuine subjects of (...) ontology? (shrink)

In recent years, philosophers have used expressions of Wittgenstein’s (e.g. “language-games,” “form of life,” and “family resemblance”) in attempts to conceive of the discipline of philosophy in a broad, open, and perhaps global way. These Wittgenstein-inspired approaches indicate an awareness of the importance of cultural and historical diversity for approaching philosophical questions. While some philosophers have taken inspiration from Wittgenstein in embracing contextualism in philosophical hermeneutics, Wittgenstein himself was more instrumental than contextual in his treatment of other philosophers; his focus (...) in his writings was on his own philosophical problems. Does this mean that Wittgensteinian philosophy is a poor resource after all for comparative, cross-cultural, or globally-engaged philosophy (i.e. if it is properly Wittgensteinian)? In this article, I examine the relevance of Wittgenstein to contextually-sensitive philosophy through studies of his conceptions of history and culture, his interest in Spengler’s philosophy of history, and recent scholarship by Hans-Johann Glock and Hans Sluga on the place of contextualism in Wittgenstein’s analysis of philosophical problems. Ultimately, this article advances the view that there are strong resources in Wittgenstein’s philosophy for those seeking a more globally-engaged approach to the field. (shrink)

Why did such highly abstract ideas as truth, knowledge, or justice become so important to us? What was the point of coming to think in these terms? This book presents a philosophical method designed to answer such questions: the method of pragmatic genealogy. Pragmatic genealogies are partly fictional, partly historical narratives exploring what might have driven us to develop certain ideas in order to discover what these do for us. The book uncovers an under-appreciated tradition of pragmatic genealogy which cuts (...) across the analytic-continental divide, running from the state-of-nature stories of David Hume and the early genealogies of Friedrich Nietzsche to recent work in analytic philosophy by Edward Craig, Bernard Williams, and Miranda Fricker. However, these genealogies combine fictionalizing and historicizing in ways that even philosophers sympathetic to the use of state-of-nature fictions or real history have found puzzling. To make sense of why both fictionalizing and historicizing are called for, the book offers a systematic account of pragmatic genealogies as dynamic models serving to reverse-engineer the points of ideas in relation not only to near-universal human needs, but also to socio-historically situated needs. This allows the method to offer us explanation without reduction and to help us understand what led our ideas to shed the traces of their practical origins. Far from being normatively inert, moreover, pragmatic genealogy can affect the space of reasons, guiding attempts to improve our conceptual repertoire by helping us determine whether and when our ideas are worth having. (shrink)

Undoubtedly, A Priori needs to be clarified if we are to understand the heart of Critique of Pure Reason; and Kant, precisely for this very reason, devoted a considerable part of Critique to explaining the epistemic status of A Priori, searching its origin, specifying its validity scope, and illustrating its instances. Although he, more or less, in both editions of Critique, put forward some characteristics intrinsic to A Priori since they have been also used in post-Kantian traditions, especially in a (...) meaning different from what Kant meant, so they may simply bring about some confusions cause failing to appropriately grasp the heart of Critique. With reference to such confusions the authors make an attempt to shed light on this point in part. Then, in part, based on the text of Critique and its commentators’ views, authors proceed to show that to evade such confusions one should re-define necessary to “what is emerged from the nature of the human mind”, strictly universal to “applicable just in the realm of phenomenon”, pure to “merely focused on the contribution of mind itself in collaboration with the objects themselves to form empirical knowledge”, clear to “what the scope of searching for is limited to within ourselves not outside of it” and certain to “what its scope is immutable –either regarding to its instances themselves or to their numbers”. In part, by scrutinizing the other characteristic, we shall show that this characteristic, besides of referring to mere structure, can refer to some kind of knowledge on which every possible experience is based; moreover, we shall determine the relation of above characteristic to pre-Kantian traditions. (shrink)

The notion of more truth, or of more truth and less falsehood, is central to epistemology. Yet, I argue, we have no idea what this consists in, as the most natural or obvious thing to say—that more truth is a matter of a greater number of truths, and less falsehood is a matter of a lesser number of falsehoods—is ultimately implausible. The issue is important not merely because the notion of more truth and less falsehood is central to epistemology, but (...) because an implicit, false picture of what this consists in underpins and gives shape to much contemporary epistemology. (shrink)

A world is trivial if it makes every proposition true all at once. Such a world is impossible, an absurdity. Our world, we hope, is not an absurdity. It is important, nevertheless, for semantic and metaphysical theories that we be able to reason cogently about absurdities—if only to see that they are absurd. In this note we describe methods for ‘observing’ absurd objects like the trivial world without falling in to incoherence, using some basic techniques from modal logic. The goal (...) is to begin to locate the trivial world’s relative position in modal space; the outcome is that the less we assume about relative possibility, the more detail we can discern at the edge of reason. (shrink)

We argue that the view that we misperceive time as passing is self-undermining.

Proposition 5.122 of Wittgenstein’s Tractatus has been the source of much puzzlement among interpreters, so much so that no fully satisfactory account is yet available. This is unfortunate, if only because the containment account of logical consequence has a venerable tradition behind it. Pasquale Frascolla’s interpretation of proposition 5.122 is based on a valid argument and one true premise. However, the argument explains sense containment only in an indirect way, leaving some crucial questions unanswered. Besides, Frascolla does not address the (...) issue of how to make sense containment notationally perspicuous, an essential theme in Wittgenstein’s reflections. In this paper, we elaborate on Frascolla’s account by looking at the issue through the Tractarian notion of logical space. Our analysis shows that, for containment to be fully appreciated, one should adopt a negative perspective on the notion of sense, in line with the exclusionary theory of conceptual content, as labelled by Ian Rumfitt. Besides this, we introduce and discuss two methods—one envisaged by Wittgenstein himself—for making sense containment notationally perspicuous. (shrink)

In much educational theory there is concern about claims that the concept of truth has no place anymore in educational thinking. These claims are generally identified as ‘postmodernist’ or ‘poststructuralist’. The fear is that when abandoning the quest for truth we enter the domain of mere belief, and in this way leave education without firm grounds. In this article I examine some examples of what is often crudely lumped together as ‘postmodernist’ educational research. What is at stake here, I argue, (...) is not so much a rejection of the quest for truth as rather a shift of focus to a different set of questions and interests: for example, existential questions. Against the contemporary, dominant focus on evidence-based practice, which conceals the person behind the method (textbook, rules, techniques), here the embodied person with her individual investment in education is brought into the light again. (shrink)

In this article, I show and discuss the relevance of Wittgenstein's arguments as to the spatial structure of sight to recent issues in the philosophy of mind. The first, bearing upon the dimensionality of the manifolds at play in depiction, plays a critical role in Clark's attempt to provide an independent account ofqualiaand of their differentiative properties. The second, pertaining to the properly spatial structure formed by the data of sight, is explicitly appealed to in the debate on the realistic (...) character of any genuinely spatial scheme. I argue that if Wittgenstein rightly assumes that the simultaneous presence of sensible places in vision is a key condition for objectivity, he fails nevertheless to warrant the allegedly realistic character of the scheme employed in his own search for a phenomenological description of the visual field. (shrink)

RésuméPaul Boghossian soutient contre Wittgenstein que le normativisme au sujet de la logique et des mathématiques est incompatible avec le fait de tenir les énoncés logiques et mathématiques pour vrais et que le normativisme entraîne une régression indue. Je soutiens, pour ma part, que le normativisme n'entraîne pas une telle régression, parce que les normes peuvent être implicites et que le normativisme peut bien être «factualiste» si l'on rejette ce que Rockney Jacobsen appelle le «cognitivisme sémantique». Je tiens en outre (...) que la position de Boghossian repose sur la façon trompeuse dont il découpe le terrain conceptuel. (shrink)

This article first surveys the established views on Wittgenstein's relation to analytic philosophy. Next it distinguishes among different ways of defining analytic philosophy—topical, doctrinal, methodological, stylistic, historical, and the idea that it is a family‐resemblance concept. It argues that while certain stylistic features are important, the historical and the family‐resemblance conceptions are the most auspicious, especially in combination. The answer to the title question is given in section 3. Contrary to currently popular “irrationalist” interpretations, Wittgenstein was an analytic philosopher in (...) all phases of his career, albeit an exceedingly exotic one whose style transcends the limits of academic philosophy in general. On the historical understanding he qualifies because he was influenced by and in turn influenced mainly analytic philosophers. On the family‐resemblance conception he qualifies both because he developed and employed logico‐linguistic analysis and because he initiated the linguistic turn and the distinction between philosophy and science that characterizes one important strand in analytic philosophy. (shrink)

I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. -/- There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably (...) infinite, then the property of being a tautology is \Pi^1_1-complete. But third, it is only granted the assumption of countability that the class of tautologies is \Sigma_1-definable in set theory. -/- Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects. (shrink)

We argue that all general concepts are family resemblance concepts. These include concepts introduced by ostension, such as colour. Concepts of colour and of each of the specific colours are family resemblance concepts because similarities concerning an open-ended range of colour or of appearance features crop up and disappear. After discussing the notion of “same colour” and Wittgenstein's use of the phrase “our colours”, we suggest family resemblance concepts in one tradition can often be extended to family resemblance concepts in (...) another tradition, illustrated by Wittgenstein's use of the words Spiel and “game”. (shrink)

Here, the logical behaviour of negation in Wittgenstein's Tractatus is compared with Demos' account of denial. Even if we hold negation as a pure syntactical device, at least in some context, it brings a handful of complex semantic information – potentially an infinite amount. We advocate then the existence of at least two negations due to the existence of two different and non-reducible types of exclusion. The first negation is a Tractarian and classical one, based on the notion of contradiction, (...) whereas the second is a non-classical negation, based on the notion of contrariety. (shrink)

This paper examines the view of ethical language that Wittgenstein took in later years. It argues that according to this view, ethics falls into place as a part of our natural history, while every sense of the mystical or supernatural that once surrounded it is irrevocably lost. Moreover, Wittgenstein argues that ethical language does not correspond to reality “in the way” in which a physical theory does. I propose an interpretation of this claim that shows how it sets his view (...) apart from a “realist” theory of ethics. The reality of which he speaks is the reality of human life. (shrink)

I argue for the Wittgensteinian thesis that mathematical statements are expressions of norms, rather than descriptions of the world. An expression of a norm is a statement like a promise or a New Year's resolution, which says that someone is committed or entitled to a certain line of action. A expression of a norm is not a mere description of a regularity of human behavior, nor is it merely a descriptive statement which happens to entail a norms. The view can (...) be thought of as a sort of logicism for the logical expressivist---a person who believes that the purpose of logical language is to make explicit commitments and entitlements that are implicit in ordinary practice. The thesis that mathematical statements are expression of norms is a kind of logicism, not because it says that mathematics can be reduced to logic, but because it says that mathematical statements play the same role as logical statements. ;I contrast my position with two sets of views, an empiricist view, which says that mathematical knowledge is acquired and justified through experience, and a cluster of nativist and apriorist views, which say that mathematical knowledge is either hardwired into the human brain, or justified a priori, or both. To develop the empiricist view, I look at the work of Kitcher and Mill, arguing that although their ideas can withstand the criticisms brought against empiricism by Frege and others, they cannot reply to a version of the critique brought by Wittgenstein in the Remarks on the Foundations of Mathematics. To develop the nativist and apriorist views, I look at the work of contemporary developmental psychologists, like Gelman and Gallistel and Karen Wynn, as well as the work of philosophers who advocate the existence of a mathematical intuition, such as Kant, Husserl, and Parsons. After clarifying the definitions of "innate" and "a priori," I argue that the mechanisms proposed by the nativists cannot bring knowledge, and the existence of the mechanisms proposed by the apriorists is not supported by the arguments they give. (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.

The paper considers one of the most enigmatic problems of Wittgenstein`s Tractatus - the problem of solipsism. The authorś task is to reveal how the discussion of solipsism illuminates Wittgenstein`s metaphysical view in this treatise. Wittgenstein`s method is considered as one through which the status of what cannot be said is demonstrated. Wittgenstein has not embrased solipsism or idealism in the Tractatus, and neither has he rejected metaphysics as a whole. His attack has been directed against dogmatic philosophy and ethics, (...) against the effort to say what cannot be said in true/false propositions. The discussion of solipsism brings into philosophy the importance of metaphysical "I" as a transcendental limit of the world and language. Wittgenstein`s aim in the Tractatus has been twofold: a) to show the nonsensicality of philosophical, ethical, aesthetical propositions , b) to emphasize, that the inexpresibility of the higher is the most important thing in our lives. (shrink)

The first section of this paper introduces talk about absolutely everything -- the world as a totality -- as an integral element in the project of natural theology, as it has been presented by Fergus Kerr and Denys Turner respectively. The following section presents talk about the world as a totality of facts as a theme in philosophical logic and outlines a problem it has given rise to there. After confronting the solution originally suggested by Bertrand Russell and defended by (...) David Armstrong, the paper points to key elements of the solution presented by Wittgenstein in Tractatus Logico-Philosophicus. I show how Wittgenstein’s answer to the question of unrestricted quantification draws on his notion of showing and the inexpressible. Against this background, the concluding section draws attention to an important difference in ambition between Kerr’s and Turner’s description of the prospects for natural theology. (shrink)

Between April and November 1912, Bertrand Russell and Ludwig Wittgenstein were engaged in a joint philosophical program. Wittgenstein‘s meeting with Gottlob Frege in December 1912 led, however, to its dissolution – the joint program was abandoned. Section 2 of this paper outlines the key points of that program, identifying what Russell and Wittgenstein each contributed to it. The third section determines precisely those features of their collaborative work that Frege criticized. Finally, building upon the evidence developed in the preceding two (...) sections, section 4 recasts along previously undeveloped lines Wittgenstein‘s logical–philosophical discoveries in the two years following his encounter with Frege in 1912. The paper concludes, in section 5, with an overview of the dramatic consequences the Frege-Wittgenstein critique had for Russell‘s philosophical development. (shrink)

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)

Wittgenstein’s remarks on religious and magical practices are often thought to harbour troubling fideistic and relativistic views. Unsurprisingly, commentators are generally resistant to the idea that religious belief constitutes a ‘language‐game’ governed by its own peculiar ‘rules’, and is thereby insulated from the critical assessment of non‐participants. Indeed, on this fideist‐relativist reading, it is unclear how mutual understanding between believers and non‐believers (even between different sorts of believers) would be possible. In this paper I do three things: (i) show why (...) the fideist‐relativist reading of Wittgenstein is not wildly implausible (Sections 1–2); (ii) argue that, despite its initial plausibility, this reading fails to take into account Wittgenstein’s naturalism (Sections 3–4); and (iii) explain what sort of naturalism this is, and how it sheds light on Wittgenstein’s remarks on religious belief (Sections 5–6). (shrink)

When it comes to Wittgenstein's philosophy of mathematics, even sympathetic admirers are cowed into submission by the many criticisms of influential authors in that field. They say something to the effect that Wittgenstein does not know enough about or have enough respect for mathematics, to take him as a serious philosopher of mathematics. They claim to catch Wittgenstein pooh-poohing the modern set-theoretic extensional conception of a real number. This article, however, will show that Wittgenstein's criticism is well grounded. A real (...) number, as an 'extension', is a homeless fiction; 'homeless' in that it neither is supported by anything nor supports anything. The picture of a real number as an 'extension' is not supported by actual practice in calculus; calculus has nothing to do with 'extensions'. The extensional, set-theoretic conception of a real number does not give a foundation for real analysis, either. The so-called complete theory of real numbers, which is essentially an extensional approach, does not define (in any sense of the word) the set of real numbers so as to justify their completeness, despite the common belief to the contrary. The only correct foundation of real analysis consists in its being 'existential axiomatics'. And in real analysis, as existential axiomatics, a point on the real line need not be an 'extension'. (shrink)

Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) is (...) not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary. (shrink)