This paper continues a conversation about Wittgenstein’s picture of language and meaning and its potential applications for educational theorising. It takes the form of a response to Wolff-Michael Roth’s earlier paper “Heeding Wittgenstein on “understanding” and “meaning”: A pragmatist and concrete human psychological approach in/for education,” in which Roth problematizes the use of the terms “understanding” and “meaning” in education discourse and proposes their abandonment. Whilst we agree with Roth about a series of central points, at the same time we (...) maintain that he has taken his argument in directions antithetical to our reading of Wittgenstein’s work. We offer four points of departure, exploring themes of: appropriate questioning; eliminativism; language-games and grammar; and productivity, explanation, and a science of learning. We conclude by discussing ways consistent with Wittgenstein’s thought to go on in thinking about education. (shrink)

What if education were not about becoming something, making something of yourself, becoming some thing? What if we were to consider education as becoming-world? These questions are posed against the background of the current populist nationalist backlash against the consequences of globalization, along with growing anti-intellectualism and anti-democratic sentiment. How can education contribute locally and globally to fostering and safeguarding the very possibility of democratic practices against the neoliberal consecration of reified social relations? Becoming Things, Becoming-world contributes to contemporary discussions (...) in philosophy of education by developing a vision of a critical educational cosmopolitanism founded upon a renewed critique of reification. While cosmopolitan education has often been articulated in terms of an ethical and political response to globalization, this thesis proposes a different outlook. I argue that the idea of cosmopolitan education predates the onset of what we now term globalization, and that it provides a meaningful conception of education beyond the present socio-political condition. Moreover, I propose to rethink cosmopolitan education as a critique of reification, i.e. a critique of social relations taking on the character of mere things. The critique of reification helps to foreground aspects that have previously been neglected and marginalized in educational cosmopolitanism, such as its economic-material dimensions. At the same time, a critical cosmopolitan perspective is needed for a timely de-centering of critical social theory. Re-assessing the Cynic tradition and drawing on critical theorists such as Gerard Delanty and Axel Honneth as well as on New Wittgensteinian philosophers as Alice Crary, I advance a post-universalist understanding of cosmopolitanism. This is based on dynamic social relations and a broad understanding of rationality which includes imaginary aspects as well as the education of our sensitivities. Cosmopolitanism is understood as a lived practice which critically challenges reified social and cultural relations, including the strictures of particular socio-economic structures. The notion of reification is distinguished from other forms of alienation, objectification and instrumentalization and is deployed to characterize lasting distortions of our relations to each other, to the world and to ourselves. Against any idealizing take on communicative practice, I show that language, knowledge, and education do not necessarily counter-act reifying tendencies. Indeed, they themselves can become sources for enhancing processes of reification. A fresh look at the critique of reification allows us adequately to describe and understand the interrelation between contemporary capitalism, the forms of subjectivity it produces and the possibilities of democratic education and education towards democracy. Such an understanding is needed in face of the apparent impossibility of imagining a society, and envisioning an education, beyond the conditions formulated by contemporary neoliberal policies. Education as becoming-world maintains a hopeful outlook on the possibilities of our globalizing and pluralizing social reality as well as a keen focus on the tensions and challenges that this poses for contemporary educational endeavors on individual as well as structural levels. (shrink)

In mainstream Anglo-American philosophy, the relation between cognition and community has been defined primarily in terms of the generalization of the mathematical function, especially as a model for the nature of rules, which thus come to be under-stood as algorithms. This leads to the elimination of both the reflexive, synthesizing subject, and the intrinsic communal-historical nature of argumentation and belief-formation. Against this approach, I follow R.G. Collingwood’s hitherto unrecognized strategy in his Essay on Metaphysics and argue that the relation of (...) cognition and community is better understood by way of the ancient and forgotten model of creedal rules of faith or trust. These will be shown to have the logical form of first person performative rules of faith or trust that generate third person declaratives or proposi-tions, and so constitute the possibility conditions for an argumentational logic of question and answer. They restore the synthetic subject, for they are not algorithms but reflexive and interpretive formulae; they are communally constituted and so historically saturated; and they reinstate an ontological theory of truth as disclosure, with coherence and comprehensiveness as its criteria. In these respects, as Collingwood saw, the creedal model provides a fresh interpretation of the historicality of argumentation and redefines the relation of cognition and community in terms of the interdependence of faith and reason. (shrink)

A "concept" in the sense favoured by Wittgenstein is a paradigm for a transition between parts of a notational system. A concept-determining sentence such as "There is no reddish green" registers the absence of such a transition. This suggests a plausible account of what is perceived in an experiment that was first designed by Crane and Piantanida, who claim to have induced perceptions of reddish green. I shall propose a redescription of the relevant phenomena, invoking only ordinary colour concepts. This (...) redescription is not ruled out by anything the experimenters say. It accounts for certain peculiarities in both their descriptions and their subjects', and suggests that instead of discovering forbidden colours the experimenters introduced a new use of "-ish". Still, there is a point in speaking of "reddish green" in their context, which can be motivated by invoking what Wittgenstein calls a "physiognomy". (shrink)

Tutkin tässä artikkelissa Kurt Gödelin epätäydellisyysteoreemojen tulkintoja filosofiassa. Aihepiiri kattaa valtavan määrän eri tulkintoja tekoälystä fysiikkaan ja runouteen asti. Osoitan, että kriittisesti tarkasteltuna kaikki radikaalit epätäydellisyysteoreemojen sovellukset ovat virheellisiä.

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)

In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of the concept (...) of ‘denumerability’ as it is presented in set theory as well as his philosophic refutation of Cantor’s Diagonal Argument and the implications of such a refutation onto the problems of the Continuum Hypothesis and Cantor’s Theorem. Throughout, the discussion will be placed within the historical and philosophical framework of the Grundlagenkrise der Mathematik and Hilbert’s problems. (shrink)

This paper argues that Cora Diamond's interpretation of Wittgenstein's early and later work, and her specific attempts to apply it in religious and ethical contexts, show a willingness to sacrifice elements of Wittgenstein's signature concepts to the demands of what she calls his 'realistic spirit'. The paper also argues that this willingness relates her project to a certain understanding of modernism in the arts.

What is an inference? Logicians and philosophers have proposed various conceptions of inference. I shall first highlight seven features that contribute to distinguish these conceptions. I shall then compare three conceptions to see which of them best explains the special force that compels us to accept the conclusion of an inference, if we accept its premises.

In 1982 Saul A. Kripke proposed a reconstruction of the central insights of Ludwig Wittgenstein's remarks on rule-following. The reconstruction prominently featured a sceptical challenge which soon was recognised as a new and very radical form of scepticism. According to the challenge there is no fact of the matter which constitutes meaning. As there is no such fact, the first-person authority people intuitively seem to have concerning what they mean is also baseless. In response to the sceptic, many solutions have (...) been proposed. This thesis is about one family of solutions, according to which facts about meaning are sui generis and can neither be reduced to other facts about the world nor to non-semantic facts about the human mind. The non-reductionist proposals by Colin McGinn and Crispin Wright will be assessed in detail and arguments against both will be introduced. The arguments stem only partially from Kripke himself, some are based on recent literature, others are completely new. The emerging situation will be used as a basis to propose an alternative non-reductionism about meaning-facts. (shrink)

This dissertation is on infinite regress arguments in philosophy. Its main goals are to explain what such arguments from many distinct philosophical debates have in common, and to provide guidelines for using and evaluating them. Two theories are reviewed: the Paradox Theory and the Failure Theory. According to the Paradox Theory, infinite regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is settled, or the statement that (...) discussions are settled only if there is an agreed-upon criterion to settle them). According to the Failure Theory, infinite regress arguments can be used to demonstrate that a certain solution fails to solve an existentially or universally quantified problem (e.g. to demonstrate that a certain solution fails to settle all discussions, or that it fails to settle even one discussion). In the literature, the Paradox Theory is fairly well-developed, and this dissertation provides the Failure Theory with the same tools. (shrink)

Reply to eight critical reviews of my paper "Franz Brentano and Higher-Order Theories of Consciousness" in the same issue of the journal Argumentos.

Che cos'è la verità? A questa domanda le teorie deflazioniste rispondono in modo sorprendente: niente, o quasi. Secondo il deflazionismo la verità, come proprietà, semplicemente non esiste o è priva di qualsiasi sostanza. In questo contributo presenterò tale posizione offrendo un breve resoconto critico dell'evoluzione della proposta e una disamina delle sue tesi centrali.

We approach the topic of solution equivalence of propositional problems from the perspective of non-constructive procedural theory of problems based on Transparent Intensional Logic (TIL). The answer we put forward is that two solutions are equivalent if and only if they have equivalent solution concepts. Solution concepts can be understood as a generalization of the notion of proof objects from the Curry-Howard isomorphism.

outrageous remarks about contradictions. Perhaps the most striking remark he makes is that they are not false. This claim first appears in his early notebooks (Wittgenstein 1960, p.108). In the Tractatus, Wittgenstein argued that contradictions (like tautologies) are not statements (Sätze) and hence are not false (or true). This is a consequence of his theory that genuine statements are pictures.

http://www.cs.bham.ac.uk/research/projects/cogaff/62-80.html#1967-01.