At several points in his later writings Wittgenstein discusses imaginary forms of life and ways of thinking that appear queer or alien from our point of view; concepts so different from ours that those who think from within them seem to be alternatives to us. In this paper I argue that reflection on the notions of difference and possibility in play here shows that imaginary cases of alien conceptual schemes or forms of life such as those considered by Wittgenstein are (...) not all cases of concepts that are entirely unintelligible for us; rather they may represent possible, albeit distant, ways of thinking for us. Such cases serve to aid imaginative reflection on our own case(s). By making us appreciate the possibility of the strange, they help us better to appreciate the arbitrariness of the familiar. I end the paper by considering what the implications of this reading of Wittgenstein’s position might be for Donald Davidson’s rejection of conceptual relativism. (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)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models.Higher-level analyses of these connectionist models reveal subtle relations to symbolic models. Parallel connectionist memory and linguistic processes are hypothesized to give rise to processes that are describable at a higher level as sequential rule application. At the lower level, computation has the character of massively parallel satisfaction of soft numerical constraints; at the higher level, this can lead to competence characterizable by hard rules. Performance will typically deviate from this competence since behavior is achieved not by interpreting hard rules but by satisfying soft constraints. The result is a picture in which traditional and connectionist theoretical constructs collaborate intimately to provide an understanding of cognition. (shrink)

Latest Sermon from the Church of Fundamentalist Naturalism by Pastor Hofstadter. Like his much more famous (or infamous for its relentless philosophical errors) work Godel, Escher, Bach, it has a superficial plausibility but if one understands that this is rampant scientism which mixes real scientific issues with philosophical ones (i.e., the only real issues are what language games we ought to play) then almost all its interest disappears. I provide a framework for analysis based in evolutionary psychology and the work (...) of Wittgenstein (since updated in my more recent writings). -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

In §8 of Remarks on the Foundations of Mathematics (RFM), Appendix 3 Wittgenstein imagines what conclusions would have to be drawn if the Gödel formula P or ¬P would be derivable in PM. In this case, he says, one has to conclude that the interpretation of P as “P is unprovable” must be given up. This “notorious paragraph” has heated up a debate on whether the point Wittgenstein has to make is one of “great philosophical interest” revealing “remarkable insight” in (...) Gödel’s proof, as Floyd and Putnam suggest (Floyd (2000), Floyd (2001)), or whether this remark reveals Wittgenstein’s misunderstanding of Gödel’s proof as Rodych and Steiner argued for recently (Rodych (1999, 2002, 2003), Steiner (2001)). In the following the arguments of both interpretations will be sketched and some deficiencies will be identified. Afterwards a detailed reconstruction of Wittgenstein’s argument will be offered. It will be seen that Wittgenstein’s argumentation is meant to be a rejection of Gödel’s proof but that it cannot satisfy this pretension. (shrink)

Some readers, even though well versed in philosophy, may be bewildered by Wittgenstein's posthumous book on the philosophy of mathematics and unable to find a dominant theme running through even a part of it; to list the main contents–headings would make them none the wiser. Although two main themes may in the end be discerned in it, they do not pervade the book after the usual manner of themes; one has rather the sense of wandering about the corridors of a (...) maze; and, to add to the reader's perplexity, the maze has no definite centre. This mode of presentation, leading one through a maze, whose “centre” is the discovery that there is no centre, in itself conveys some philosophical message. Can we possibly say what Wittgenstein was trying to do? To answer this, seeing that this work is largely in line with the rest of his philosophizing, I propose to bid the present book a long farewell, to take an excursion into the field of Wittgensteinian and related philosophy, and against this background to try to give some picture and assessment of the contents of the work. (shrink)

My aim in this paper is twofold: to establish that Kierkegaard's so‐called theory of the leap strongly anticipates a line of argument that is central to Wittgenstein's so‐called rule‐following considerations; and to begin to show how Kierkegaard's work has fruitful contributions of its own to make to on‐going discussions about rules and rule‐following. The paper focuses throughout on the question of how, if at all, human rule‐following can be distinguished from behaviour that is merely mechanical or instinctual. I identify a (...) central line of argument in Wittgenstein that problematizes this question by establishing the basis our ability to follow rules in our spontaneous responses. I argue that Kierkegaard not only strongly anticipates this line of argument but also offers a distinctive story about what, at bottom, makes the difference between human rule‐following and behaviour that is merely mechanical or instinctual. In a word, on Kierkegaard's story, what makes the difference is: anxiety. (shrink)

Here I defend dispositionalism about meaning and rule-following from Kripkenstein's infamous anti-dispositionalist arguments. The problems of finitude, error, and normativity are all addressed. The general lesson I draw is that Kripkenstein's arguments trade on an overly simplistic version of dispositionalism.

According to Barry Stroud, Wittgenstein thought that language is social only in this minimal way: we cannot make sense of the idea of someone having a language unless we can describe her as using signs in conformity with the linguistic practices of some community. Since a solitary person could meet this condition, Stroud concludes that, for Wittgenstein, solitary languages are possible. I argue that Wittgenstein in fact thought that language is social in a much more robust way. Solitary languages are (...) not possible because we cannot make sense of the idea of someone having a language unless we can think of her as actively participating in the linguistic practices that fix the standards governing the applications of her words. (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models. Higher-level analyses of these connectionist models reveal subtle relations to symbolic models. Parallel connectionist memory and linguistic processes are hypothesized to give rise to processes that are describable at a higher level as sequential rule application. At the lower level, computation has the character of massively parallel satisfaction of soft numerical constraints; at the higher level, this can lead to competence characterizable by hard rules. Performance will typically deviate from this competence since behavior is achieved not by interpreting hard rules but by satisfying soft constraints. The result is a picture in which traditional and connectionist theoretical constructs collaborate intimately to provide an understanding of cognition. (shrink)

Drawing on experience teaching secondary philosophy students, I investigate meaningful engagement with Wittgenstein in a Grade 12 epistemology unit. The premise is that without some introduction to landmark philosophers of the early twentieth century, students are left out of many contemporary philosophical conversations: linguistic idealism or relativism, and nominalism versus realism. Wanting to share with students Foucault, Rorty, and Hacking, I need expedient avenues of approach. Using Wittgenstein's methods I offer practical, ‘shallow grounds’ for an eclectic syllabus conveying post-foundational epistemology, (...) justifying Wittgenstein's inclusion in a textbook written for diverse teenagers. Acknowledging teens’ marginality, I draw on Hekman and Scheman's appropriation of Wittgenstein to advance feminist critiques of enthralling traps in [masculinist] language: exploring nature/nurture boundaries (ferals, cyborgs, and ‘gender performativity’) toward combating discrimination in schools. Heeding Cavell, I.. (shrink)

Responding to Michael Luntley's article, ‘Learning, Empowerment and Judgement’, the author shows he cannot successfully make the following three moves: (1) dissolve the analytic distinction between learning by training and learning by reasoning, while advocating the latter; (2) diminish the role of training in Wittgenstein's philosophy, nor attribute to him a rationalist model of learning; and (3) turn to empirical research as a way of solving the philosophical problems he addresses through Wittgenstein. Drawing on José Medina's analysis of the fundamental (...) role of training in Wittgenstein's later philosophy, the paper offers a tour of key passages in the Investigations and other works to develop an understanding of what Wittgenstein meant by ‘mastery of techniques’. In opposition to Luntley's liberal‐individual, or his subject as rational agent, the author explores Wittgenstein's non‐foundationalist, forms of life approach to how we act with agreement. More effort must be given to differentiating Wittgenstein's view from that of the analytic school, which Luntley appears to echo despite his criticism of the analytic divide. (shrink)

Over a decade after publication of Thinking Again: Education After Postmodernism (1998) contention still emerges among Foucaultians over whether discursively made‐up things really exist, and whether removal of the constituent subject leaves room for agency within techniques of caring for the self. That these questions are kept alive shows that some readers have not rethought Foucault, finding what possibly comes after postmodernism. Using Wittgenstein to ‘reciprocally illuminate’ Foucault (after Tully and Marshall), I open teacher inspection and reforms to problematization, as (...) relations to bedrock rules governing games of truth. ‘How, upon entering classrooms, do inspectors know “teaching” is taking place and not crazy and fuzzy things in its name?’ Taking up Hirst's vexing question, I move beyond liberal‐analytic concept‐mapping and neo‐liberal individualism to more fully assay the political ground for judging teaching practices through genealogy. Epistemological, political and ethical concerns intersect as we approach the problem through Foucault's three axes of an historical‐ontology of the present: knowledge(s), power relations, and arts of the self. Drawing on recent Governmentality Studies in Education (Peters., 2009), we aver the impasses of postmodern relativism while finding limited ranges of agency along each axis, as teachers practice freedoms by critiquing and renegotiating rules. (shrink)

Offering a cautionary tale about the abuses of paradigm‐shift rhetoric in secondary school reforms, the paper shows potential misuses and ethical effects of the relativistic language‐game in post‐compulsory education. Those initiating the shift often shelter their reform from the criticism of non‐adepts, marginalizing expert teachers that adhere to ‘antiquated’ or ‘folk’ pedagogies. The rhetoric herds educators uncritically into the citadel of new discourses and policies that often lack practical foundations; consequently, teachers often dissimulate compliance to the reform in order to (...) evade surveillance within such disciplinary apparatuses as teacher training and regimes of inspection. Turning to Foucault, the author views education reforms in terms of power relations within a form of governance: ‘games of truth’, or political and veridical discourses in which dividing practices for sorting out ‘sound’ and ‘unsound’ teaching practices become institutionalised. Wittgenstein's attention to initiate training in practices points to an alternative to naïve forms of relativism; educators must incorporate the new techniques they gradually master and adapt within a viable, shared form of life. Instead of teachers’ normalization and subjugation in what Foucault refers to as education ‘blocks’, new pedagogic practices are better adopted ‘freely’ as arts of self‐transformation. With Hacking, Foucault and Wittgenstein's accounts of the true‐and‐false are blended into an ‘historical ontology’ of present and emergent paradigms: a critique of the limits set down within education reforms that sanction or legitimize certain conduct. Sympathetic to the journal call, this kind of philosophical investigation and genealogical critique of teaching practices gives us a perspicuous view of the local, contingent and at times arbitrary nature of change initiatives. Critical awareness of how our pictures (models) of education can captivate us heightens respect for professional eclecticism. Without ignoring the mandates and official scripts of public education reforms, experienced educators need to be able to conserve their tried and warranted ‘best practices’, while negotiating ranges of tolerance for alternative means. (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models. (shrink)

Elvira Schnabel; Wittgenstein on Rules: what follows and what does not, Journal of Philosophy of Education, Volume 25, Issue 1, 30 May 2006, Pages 83–94, https.

Elvira Schnabel; Wittgenstein on Rules: what follows and what does not, Journal of Philosophy of Education, Volume 25, Issue 1, 30 May 2006, Pages 83–94, https.

According to Wittgenstein, mathematics is embedded in, and partly constituting, a form of life. Hence, to imagine different, alternative forms of elementary mathematics, we should have to imagine different practices, different forms of life in which they could play a role. If we tried to imagine a radically different arithmetic we should think either of a strange world or of people acting and responding in very peculiar ways. If such was their practice, a calculus expressing the norms of representation they (...) applied could not be called false. Rather, our criticism could only be to dismiss such a practice as foolish and to dismiss their norms as too different from ours to be called ‘mathematics’. (shrink)

This article aims first at showing that Russell's general doctrine according to which all mathematics is deducible ‘by logical principles from logical principles’ does not require a preliminary reduction of all mathematics to arithmetic. In the Principles, mechanics (part VII), geometry (part VI), analysis (part IV–V) and magnitude theory (part III) are to be all directly derived from the theory of relations, without being first reduced to arithmetic (part II). The epistemological importance of this point cannot be overestimated: Russell's logicism (...) does not only contain the claim that mathematics is no more than logic, it also contains the claim that the differences between the various mathematical sciences can be logically justified—and thus, that, contrary to the arithmetization stance, analysis, geometry and mechanics are not merely outgrowths of arithmetic. The second aim of this article is to set out the neglected Russellian theory of quantity. The topic is obviously linked with the first, since the mere existence of a doctrine of magnitude, in a work dated from 1903, is a sign of a distrust vis-à-vis the arithmetization programme. After having shown that, despite the works of Cantor, Dedekind and Weierstrass, many mathematicians at the end of the 19th Century elaborated various axiomatic theories of the magnitude, I will try to define the peculiarity of the Russellian approach. I will lay stress on the continuity of the logicist's thought on this point: Whitehead, in the Principia, deepens and generalizes the first Russellian 1903 theory. (shrink)

Michael Dummett presents a modus tollens argument against a Wittgensteinian conception of meaning. In a series of papers, Dummett claims that Wittgensteinian considerations entail strict finitism. However, by a “sorites argument”, Dummett argues that strict finitism is incoherent and therefore questions these Wittgensteinian considerations.In this paper, I will argue that Dummett’s sorites argument fails to undermine strict finitism. I will claim that the argument is based on two questionable assumptions regarding some strict finitist sets of natural numbers. It will be (...) shown that strict finitism entails none of these assumptions. Hence, the argument does not prove that the view is internally incoherent, and consequently, Dummett fails to undermine the Wittgensteinian conception of meaning. (shrink)

The long‐standing issue of Wittgenstein's controversial remarks on Gödel's Theorem has recently heated up in a number of different and interesting directions [,, ]. In their, Juliet Floyd and Hilary Putnam purport to argue that Wittgenstein's‘notorious’ “Contains a philosophical claim of great interest,” namely, “if one assumed. that →P is provable in Russell's system one should… give up the “translation” of P by the English sentence ‘P is not provable’,” because if ωP is provable in PM, PM is ω ‐inconsistent, (...) and if PM is ω‐inconsistent, we cannot translate ‘P’as ’P is not provable in PM’because the predicate‘NaturalNo.’in ‘P’“cannot be…interpreted” as “x is a natural number.” Though Floyd and Putnam do not clearly distinguish the two tasks, they also argue for “The Floyd‐Putnam Thesis,” namely, that in the 1930's Wittgenstein had a particular understanding of Gödel's First Incompleteness Theorem. In this paper, I endeavour to show, first, that the most natural and most defensible interpretation of Wittgenstein's and the rest of is incompatible with the Floyd‐Putnam attribution and, second, that evidence from Wittgenstein's Nachla strongly indicates that the Floyd‐ Putnam attribution and the Floyd‐Putnam Thesis are false. By way of this examination, we shall see that despite a failure to properly understand Gödel's proof—perhaps because, as Kreisel says, Wittgenstein did not read Gödel's 1931 paper prior to 1942‐Wittgenstein's 1937–38, 1941 and 1944 remarks indicate that Gödel's result makes no sense from Wittgenstein's own perspective. (shrink)

This paper offers a new interpretation for Wittgenstein`s treatment of mathematical identities. As it is widely known, Wittgenstein`s mature philosophy of mathematics includes a general rejection of abstract objects. On the other hand, the traditional interpretation of mathematical identities involves precisely the idea of a single abstract object – usually a number –named by both sides of an equation.

Ludwig Wittgenstein was a reclusive and enigmatic philosopher, writing his most significant work off campus in remote locations. He also held a chair in the Philosophy Department at Cambridge, and is one of the university’s most recognized even if, as Ray Monk says, ‘reluctant professors’ of philosophy. Paradoxically, although Wittgenstein often showed contempt for the atmosphere at Cambridge and for academic philosophy in particular, it is hard to conceive of him making his significant contributions without considerable support from his academic (...) colleagues, his research fellowship and later teaching career at Cambridge. It is this conflicted relationship we explore, between the revolutionary thinker and his base within an educational institution. Starting from a brief biographical sketch of Wittgenstein’s academic life at Cambridge, including his involvement as a student and faculty member in the Moral Sciences Club, we look at how he reconceived the role of philosophy throughout this... (shrink)

Volume 52, Issue 7, July 2020, Page 699-703.

The emperor's new mind (hereafter Emperor) is an attempt to put forward a scientific alternative to the viewpoint of according to which mental activity is merely the acting out of some algorithmic procedure. John Searle and other thinkers have likewise argued that mere calculation does not, of itself, evoke conscious mental attributes, such as understanding or intentionality, but they are still prepared to accept the action the brain, like that of any other physical object, could in principle be simulated by (...) a computer. In Emperor I go further than this and suggest that the outward manifestations ofconscious mental activity cannot even be properly simulated by calculation. To support this view, I use various arguments to show that the results of mathematical insight, in particular, do not seem to be obtained algorithmically. The main thrust ofthis work, however, is to present an overview ofthe present state of physical understanding and to show that an important gap exists at the point where, quantum and classical physics meet, as well as to speculate on how the conscious brain might be taking advantage ofwhatever new physics is needed to fill this gap to achieve its nonalgorithmic effects. (shrink)