One calls a lot of things propositions. If one sees this, then one can discard the idea Russell and Frege had that logic is a science of certain objects – propositions, functions, the logical constants – and that logic is like a natural science such as zoology and talks about these objects as zoology talks of animals. Like a natural science, it could supposedly discover certain relations. For example, Keynes claimed to discover a probability relation which was like implication, yet (...) not quite implication. But logic is a calculus, not a natural science, and in it one can make inventions but not discoveries.Giving grounds, however, justifying the evidence, comes to an end; – but the end is not certain propositions' striking us immediately as true, i.e. it is not a kind ofseeingon our part; it is ouracting, which lies at the bottom of the language-game. (shrink)

Two Conceptions of Wittgenstein's Contextualism How should we understand Wittgenstein's proposals that "the meaning of a word is its use in the language" and that a name only has a meaning in a language-game? Are they incompatible with occasion-invariant semantics? In this paper I present two leading interpretations of Wittgenstein's contextualism: James Conant's meaning-eliminativism and Charles Travis's meaning-underdetermination. I argue that, even though these two interpretations are very similar, the latter gives a more nuanced account of Wittgenstein's contextualism which does (...) not involve a commitment to the claim that words have no meaning outside immediate contexts of use. (shrink)

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)

EXPANDED EDITION (eBook): -/- Infinity Is Not What It Seems...Infinity is commonly assumed to be a logical concept, reliable for conducting mathematics, describing the Universe, and understanding the divine. Most of us are educated to take for granted that there exist infinite sets of numbers, that lines contain an infinite number of points, that space is infinite in expanse, that time has an infinite succession of events, that possibilities are infinite in quantity, and over half of the world’s population believes (...) in a divine Creator infinite in knowledge, power, and benevolence. -/- According to this treatise, such assumptions are mistaken. In reality, to be is to be finite. The implications of this assessment are profound: the Universe and even God must necessarily be finite. -/- The author makes a compelling case against infinity, refuting its most prominent advocates. Any defense of the infinite will find it challenging to answer the arguments laid out in this book. But regardless of the reader’s position, FOREVER FINITE offers plenty of thought-provoking material for anyone interested in the subject of infinity from the perspectives of philosophy, mathematics, science, and theology. -/- This electronic edition of FOREVER FINITE is offered free online for all and is expanded with content that does not appear in the published edition due to print production page limitations. From the Introduction to the Conclusion, Chapters 1–27 are identical to the published print edition, including the page numbering for the chapters. This electronic edition adds an appendix and associated content—specifically, updates to the book’s back matter (68 new endnotes, 17 new bibliographic references, 3 new figure credits, 14 new glossary terms) and front matter (an updated table of contents and this preface note). (shrink)

Philosophy strives to give us a firmer hold on our concepts. But what about their hold on us? Why place ourselves under the sway of a concept and grant it the authority to shape our thought and conduct? Another conceptualization would carry different implications. What makes one way of thinking better than another? This book develops a framework for concept appraisal. Its guiding idea is that to question the authority of concepts is to ask for reasons of a special kind: (...) reasons for concept use, which tell us which concepts to adopt, adhere to, or abandon, thereby shoring up—or undercutting—the reasons for action and belief that guide our deliberations. Traditionally, reasons for concept use have been sought either in timeless rational foundations or in concepts’ inherent virtues, such as precision and consistency. Against this, the book advances two main claims: that we find reasons for concept use in the conceptual needs we discover when we critically distance ourselves from a concept by viewing it from the autoethnographic stance; and that sometimes, concepts that conflict, or exhibit other vices such as vagueness or superficiality, are just what we need. By considering not what concepts are absolutely best, but what concepts we now need, we can reconcile ourselves to the contingency of our concepts, determine the proper place of efforts to tidy up thought, and adjudicate between competing conceptions of things,—even things as contested as liberty or free will. A needs-based approach separates helpful clarification from hobbling tidy-mindedness, and authoritative definition from conceptual gerrymandering. (shrink)

In Pascal Boyer’s book Religion Explained inference systems are made to do a lot of work in his attempts to explain cognition in religion. These inference systems are systems in the brain that produces inferences when they are activated by things we perceive in our environment. According to Boyer they perceive things, produce explanations, and perform calculations. However, if Wittgenstein’s observation, that “only of a living human being and what resembles (behaves like) a living human being can one say: it (...) has sensations; it sees; is blind; hears; is deaf; is conscious or unconscious” is correct then it seems that Boyer’s talk of inference systems perceiving and inferring is confused. (shrink)

Once upon a time, logical conventionalism was the most popular philosophical theory of logic. It was heavily favored by empiricists, logical positivists, and naturalists. According to logical conventionalism, linguistic conventions explain logical truth, validity, and modality. And conventions themselves are merely syntactic rules of language use, including inference rules. Logical conventionalism promised to eliminate mystery from the philosophy of logic by showing that both the metaphysics and epistemology of logic fit into a scientific picture of reality. For naturalists of all (...) stripes, this was paradise. Alas, paradise was lost. By the end of the twentieth century, logical conventionalism had been almost universally abandoned. But more recently, it has been revitalized. This chapter provides an overview of logical conventionalism and its history, clears away misunderstandings, and briefly responds to both the canonical objections to conventionalism (from Quine, Dummett, Boghossian, and many others) as well as new objections (from Field and Golan). From paradise lost, to paradise regained: logical conventionalism is back. (shrink)

The third issue of the Journal for the Philosophy of Language, Mind and the Arts is centered on a series of questions related to the nature of images. What properties characterize them? Do they exist also in our minds? What relationship do they have with phenomena such as perception, memory, language and interpretation? The authors participating in this issue have been asked to answer these and other questions starting from and in dialogue with the two philosophical perspectives that have most (...) enriched the study of our object of research since the second half of the twentieth century: analytical philosophy and visual culture studies. The first four essays address problems related to ontology (Didi-Huberman, Prinz, Bantinaki, Manzotti). In their pages the question will be asked not only about the nature of images but also about what it means for an image to represent an object or an action realistically. The second part contains discussions related to the topics of perception, appreciation and creation of pictures (Ferretti; Gavaler, Goldberg; Pigoni, Coraci, Carlenzi). The third section goes through the problems related to the very concept of representing by images (Biggs; Weichert; Derby). The last section of the issue is devoted to two cases in which images are used not so much and not only to represent something, but also to convey ethical-political values (Fasnacht; Olesiejuk). (shrink)

Between the later views of Wittgenstein and those of connectionism on the subject of the mastery of language there is an impressively large number of similarities. The task of establishing this claim is carried out in the second section of this paper.

This paper investigates the issue whether metaphors have a metaphorical or secondary meaning and how this question is related to the borderline between philosophy and linguistics. On examples by V. Woolf and H. W. Auden, it will be shown that metaphor accomplishes something more than its literal meaning expresses and this “more” cannot be captured by any secondary meaning. What is essential in the metaphor is not a secondary meaning but an internal relation between a metaphorical proposition and a description (...) of its effects. In order to understand metaphors, we have to share an ability to construe metaphorical meanings at once. The aim of this ability is to uncover an internal relation, which lies behind a particular metaphor. (shrink)

This book is about the idea that some true statements would have been true no matter how the world had turned out, while others could have been false. It develops and defends a version of the idea that we tell the difference between these two types of truths in part by reflecting on the meanings of words. It has often been thought that modal issues—issues about possibility and necessity—are related to issues about meaning. In this book, the author defends the (...) view that the analysis of meaning is not just a preliminary to answering modal questions in philosophy; it is not merely that before we can find out whether something is possible, we need to get clear on what we are talking about. Rather, clarity about meaning often brings with it answers to modal questions. In service of this view, the author analyzes the notion of necessity and develops ideas about linguistic meaning, applying them to several puzzles and problems in philosophy of language. Meaning and Metaphysical Necessity will be of interest to scholars and advanced students working in metaphysics, philosophy of language, and philosophical logic. [See my homepage for a sample chapter.]. (shrink)

In this essay I argue the extent to which meaning and judgment in aesthetics figures in Wittgenstein’s later conception of language, particularly in his conception of how philosophy might go about explaining the ordinary functioning of language. Following a review of some biographical and textual matters concerning Wittgenstein’s life with music, I outline the connection among (1) Wittgenstein’s discussions of philosophical clarity or perspicuity, (2) our attempts to give clarity to our aesthetic experiences by wording them, and (3) the clarifying (...) experience of the dawning of an aspect, which Wittgenstein pictures as the perception of an internal relation. By examining Wittgenstein’s use of “internal relation” from the Tractatus to his later writings, I come to challenge the still prevalent understanding of Wittgenstein’s appeals to grammar as an appeal to something given (e.g., to a set of grammatical rules). Instead, as I argue, Wittgensteinian appeals to grammatical criteria should be understood as modeled by the form of justification found in our conversations about art. (shrink)

The distinction between the a priori and the a posteriori is an old and influential one. But both the distinction itself and the crucial notion of a priori knowledge face powerful philosophical challenges. Many philosophers worry that accepting the a priori is tantamount to accepting epistemic magic. In contrast, this Element argues that the a priori can be formulated clearly, made respectable, and used to do important epistemological work. The author's conception of the a priori and its role falls short (...) of what some historical proponents of the notion may have hoped for, but it allows us to accept and use the notion without abandoning either naturalism or empiricism, broadly understood. This Element argues that we can accept and use the a priori without magic. (shrink)

In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics, meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian (...) conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

This article will consider the claim that the possession of concepts is innate rather than learned. Innatism about concept learning is explained through consideration of the work of Fodor and Chomsky. First, an account of concept formation is developed. Second the argument against the claim that concepts are learned through the construction of a learning paradox developed by Fodor is considered. It is argued that, despite initial plausibility, the learning paradox is not, in fact, a paradox at all as it (...) rests on eliding the distinction between recognising something and recognising it as a something. The plausibility of eliding this distinction rests, in turn, on begging the question as to whether concept possession is a necessary condition for recognition of objects, events, properties etc. Fodor's positive arguments for innatism, as set out in LOT2 are considered and parallels with his account of stereotype formation and associationist accounts of concept formation are considered. The explanatory persuasiveness of this revised account of concept activation through the generation of stereotypes is weak. The article then examines the distinction between concept possession and concept mastery in greater detail, arguing that innatists have difficulty in accounting for the phenomenon of concept mastery, including within the contexts of formal and professional education. (shrink)

A number of prominent philosophers advance the following ideas: (1) Meaning is use. (2) Meaning is an intrinsically normative notion. Call (1) the use thesis, hereafter UT, and (2) the normativity thesis, hereafter NT. They come together in the view that for a linguistic expression to have meaning is for there to be certain proprieties governing its employment.1 These ideas are often associated with a third.

Wittgenstein wrote: “No supposition seems to me more natural than that there is no process in the brain correlated with associating or with thinking; so that it would be impossible to read off thought-processes from brain processes.” In general, he rejects what he calls “psycho-physical parallelism.” In Sect. 1, I explain Wittgenstein’s position on this topic and how his followers defend it. In Sect. 2, I argue against Wittgenstein, contending that there is “thought” in a wider sense and that it (...) can be “manifested” without expression. Thought does not need to be ordinarily expressed or even expressible, and it can be read off from the brain, provided one has sufficient technology, data, and understanding of the subject’s interaction with the environment. In Sect. 3, I offer results from brain-science in support of my claims. (shrink)

This paper reexamines Kierkegaard's work with respect to the question whether truth is one or many. I argue that his famous distinction between objective and subjective truth is grounded in a unitary conception of truth as such: truth as self-coincidence. By explaining his use in this context of the term ‘redoubling’ [Fordoblelse], I show how Kierkegaard can intelligibly maintain that truth is neither one nor many, neither a simple unity nor a complex multiplicity. I further show how these points shed (...) much-needed light on the relationship between objective and subjective truth, conceived not as different kinds or species of truth but as different ways in which truth manifests itself as a standard of success across different contexts of inquiry. (shrink)

This paper re-examines Kierkegaard's work with respect to the question whether truth is one or many. I argue that his famous distinction between objective and subjective truth is grounded in a unitary conception of truth as such: truth as self-coincidence. By explaining his use in this context of the term ‘redoubling’ [ Fordoblelse ], I show how Kierkegaard can intelligibly maintain that truth is neither one nor many, neither a simple unity nor a complex multiplicity. I further show how these (...) points shed much-needed light on the relationship between objective and subjective truth, conceived not as different kinds or species of truth but as different ways in which truth manifests itself as a standard of success across different contexts of inquiry. (shrink)

In “Truth by Convention” W.V. Quine gave an influential argument against logical conventionalism. Even today his argument is often taken to decisively refute logical conventionalism. Here I break Quine’s arguments into two— the super-task argument and the regress argument—and argue that while these arguments together refute implausible explicit versions of conventionalism, they cannot be successfully mounted against a more plausible implicit version of conventionalism. Unlike some of his modern followers, Quine himself recognized this, but argued that implicit conventionalism was explanatorily (...) idle. Against this I show that pace Quine’s claim that implicit conventionalism has no content beyond the claim that logic is firmly accepted, implicit rules of inference can be used to distinguish the firmly accepted from the conventional. As part of my case, I argue that positing syntactic rules of inference as part of our linguistic competence follows from the same methodology that leads contemporary linguists and cognitive scientists to posit rules of phonology, morphology, and grammar. The upshot of my discussion is a diagnosis of the fallacy in Quine’s master critique of logical conventionalism and a re-opening of possibilities for an attractive conventionalist theory of logic. (shrink)

This essay clarifies quantifier variance and uses it to provide a theory of indefinite extensibility that I call the variance theory of indefinite extensibility. The indefinite extensibility response to the set-theoretic paradoxes sees each argument for paradox as a demonstration that we have come to a different and more expansive understanding of ‘all sets’. But indefinite extensibility is philosophically puzzling: extant accounts are either metasemantically suspect in requiring mysterious mechanisms of domain expansion, or metaphysically suspect in requiring nonstandard assumptions about (...) mathematical objects. Happily, the view of quantifier meanings that underwrites quantifier variance can be used to provide an account of indefinite extensibility that is both metasemantically and metaphysically satisfying. Section 1 introduces the puzzle of indefinite extensibility; section 2 develops and clarifies the metasemantics of quantifier variance; section 3 solves section 1's puzzle of indefinite extensibility by applying section 2's account of quantifier meanings; and section 4 compares the theory developed in section 3 to several other theories in the literature. (shrink)

Conventionalism about mathematics claims that mathematical truths are true by linguistic convention. This is often spelled out by appealing to facts concerning rules of inference and formal systems, but this leads to a problem: since the incompleteness theorems we’ve known that syntactic notions can be expressed using arithmetical sentences. There is serious prima facie tension here: how can mathematics be a matter of convention and syntax a matter of fact given the arithmetization of syntax? This challenge has been pressed in (...) the literature by Hilary Putnam and Peter Koellner. In this paper I sketch a conventionalist theory of mathematics, show that this conventionalist theory can meet the challenge just raised , and clarify the type of mathematical pluralism endorsed by the conventionalist by introducing the notion of a semantic counterpart. The paper’s aim is an improved understanding of conventionalism, pluralism, and the relationship between them. (shrink)

I propose to sketch my views on several aspects of the philosophy of mathematics that I take to be especially relevant to philosophy as a whole. The relevance of my discussion would, I think, become more evident, if the reader keeps in mind the function of (the philosophy of) mathematics in philosophy in providing us with more transparent aspects of general issues. I shall consider: (1) three familiar examples; (2) logic and our conceptual frame; (3) communal agreement and objective certainty; (...) (4) the transcommunal universality of mathematics; (5) the big jump to the potential infinite; (6) the reconciliation of local creation with the hypothesis of discovery; (7) Platonism as realism plus conceptualism; (8) foundational studies and mathematical practice; and (9) the decomposition of philosophical disagreements. The views of Gödel and Wittgenstein are emphasized in order to add specificity to the discussions. (shrink)

There is definitely a family resemblance between what contemporary contextualism maintains in philosophy of language and some of the claims about meaning put forward by the later Wittgenstein. Yet the main contextualist thesis, namely that linguistic meaning undermines truth-conditions, was not defended by Wittgenstein. If a claim in this regard can be retrieved in Wittgenstein despite his manifest antitheoretical attitude, it is instead that truth-conditions trivially supervene on linguistic meaning. There is, however, another Wittgensteinian claim that truly has a contextualist (...) flavour, namely that linguistic meaning is itself wide-contextual. To be sure, this claim does not lead to the eliminativist/intentionalist conception of linguistic meaning that radical contextualists have recently developed. Rather, it goes together with a robust conception of linguistic meaning as intrinsically normative. Yet it may explain why Wittgenstein is taken to be a forerunner of contemporary contextualism. (shrink)

Computation and Simulation have always played a role in economics – whether it be pure economic theory or any variant of applied, especially policy-oriented, macro- and microeconomics or what has increasingly come to be called empirical or experimental economics. Computations and simulations are also intrinsically dynamic. This triptych – computation, simulation and dynamic – is given natural foundations, mainly as a result of developments in the mathematics underpinnings in the potentials of computing, using digital technology. A running theme in this (...) essay is the recognition that, increasingly, the development of economic theory seems to go hand in hand with advances in the theory and practice of computing, which is, in turn, a catalyst for the move away from too much reliance on any kind of mathematics for the formalisation of economic entities that is inconsistent with the mathematical, methodological and epistemological foundations of the theory of computation. (shrink)

In this paper Section 1 distinguishes between two modes of interpreting legal rules: rehearsal and discourse, arguing that the former takes priority over the latter in law, as in many other contexts. Section 2 offers two arguments that following a legal rule in the rehearsing mode presents a riddle. The first argument develops from law, and submits that legal rules do not tell us anything, because they are tautological. The second one develops from philosophy (Wittgenstein's later works), confronting us with (...) the paradox that incompatible courses of action may be derived from any rule. My solution presents a theory of rules as icons (Section 3). I use “icon” rather than “picture,” partly to avoid confusion with what is known among philosophers as “the picture theory of meaning.” Interpretation in the rehearsing mode hinges on imagination: imagining oneself in the space of reasons for action rather than reasoning oneself. In this act of imagination, we project ourselves into the rule in ways that are similar to the way we grasp the sense of paintings, music, stories, or poems. Finally (Section 4) I will defend the position that my view solves the puzzles in the second section, by arguing (a) that it is a better account of what Wittgenstein wrote than two competing theories (intuitionism and conventionalism), and (b) that it provides a more satisfactory account of how lawyers deal with legal rules in actual practice. (shrink)

According to the dominant view, the later Wittgenstein identified the meaning of an expression with its use in the language and vehemently rejected any kind of mentalism or intentionalism about linguistic meaning. I argue that the dominant view is wrong. The textual evidence, which has either been misunderstood or overlooked, indicates that at least since the Blue Book Wittgenstein thought speakers' intentions determine the contents of linguistic utterances. His remarks on use are only intended to emphasize the heterogeneity of natural (...) language. Taking into account remarks written after he finished the Investigations, I show how Wittgenstein anticipated the basic tenets of Gricean intention-based semantics. These are, in particular, the distinction between ‘natural’ and ‘non-natural’ meaning and the distinction between what a speaker means by an utterance and what the expression uttered means in the speaker’s natural language. Importantly, Wittgenstein also believed that only the meaning of the speaker determined the content of ambiguous expressions, such as ‘bank’, on a particular occasion of utterance. (shrink)

In his “The Foundations of Mathematics”, Ramsey attempted to marry the Tractarian idea that all logical truths are tautologies and vice versa, and the logicism of the Principia. In order to complete his project, Ramsey was forced to introduce propositional functions in extension (PFEs): given Ramsey's definitions of 1 and 2, without PFEs even the quantifier-free arithmetical truth that 1 ≠ 2 is not a tautology. However, a number of commentators have argued that the notion of PFEs is incoherent. This (...) response was first given by Wittgenstein but has been best developed by Sullivan. While I agree with Wittgenstein and Sullivan's common conclusion, I believe that even the most compelling of Sullivan's arguments is importantly mistaken and that Wittgenstein's remarks are too opaque to be left as the end of the matter. In this article I uncover the fault in Sullivan's argument and present an alternative criticism of PFEs which is Wittgensteinian in spirit without being too mystifying. (shrink)

Neo-Fregeans need their stipulation of Hume's Principle — $NxFx=NxGx \leftrightarrow \exists R (Fx \,1\hbox {-}1_R\, Gx)$ — to do two things. First, it must implicitly define the term-forming operator ‘Nx…x…’, and second it must guarantee that Hume's Principle as a whole is true. I distinguish two senses in which the neo-Fregeans might ‘stipulate’ Hume's Principle, and argue that while one sort of stipulation fixes a meaning for ‘Nx…x…’ and the other guarantees the truth of Hume's Principle, neither does both.

Throughout his whole work, Wittgenstein seizes on a distinction between logical and physical possibility, and impossibility. Despite this continuity and although, Wittgenstein brings in this distinction in various contexts and from different vantage points, he often solely brushes over it without elaborating in detail. In the so-called Big Typescript, however, he dedicates himself not only to the distinction between logical and physical possibility but also to the distinction between logical possibility and impossibility in particular investigations. In the course of these (...) investigations, another aspect arises and is tossed and turned repeatedly by Wittgenstein – namely, the place of “imaginability” in these considerations. On the basis of three focussed chapters in the Big Typescript, I argue that “imaginability” as an utterance of the form “being able to imagine ‘what it would be like’” can be allocated the place of a criterion for logical possibility. To this end, I will first outline the chapters 96., 27. and 26. in one section each. Although in these chapters, Wittgenstein only indicates rather than claiming explicitly “imaginability” to be a criterion for logical possibility, I will discuss in the last section how this conclusion can be drawn by combining the results of the previous sections. (shrink)

Since the rise of modern natural science there has been deep tension between the conceptual and the natural. Wittgenstein's discussion of how we learn a sensation-language contains important resources that can help us relieve this tension. The key here, I propose, is to focus our attention on animal nature, conceived as partially re-enchanted. To see how nature, so conceived, helps us relieve the tension in question, it is crucial to gain a firm and detailed appreciation of how the primitive-instinctive, a (...) central part of animal nature, actually serves the conceptual. I offer such an appreciation by closely examining §244 of the Philosophical Investigations and Peter Winch's discussion of it. The general aim is to bring out a certain kind of Wittgensteinian “naturalism”, a “naturalism” that is fully alive to the rootedness of conceptuality in nature. A concomitant aim is to illustrate the truth of Wittgenstein's saying that in philosophy one often has to pay close attention to details. (shrink)

I start from Phillips' discussion of Rhees's dissatisfaction with the idea of a language‐game. Then, from a rereading of Moore, I go on to exemplify interconnected uses of the expressions “language‐game,”“recurrent procedure,”“world‐picture,”“formal procedure,”“agreement in judgment,”“genre picture” and “form of life.” The discussion is related to sense perception, our knowledge of time and space, and the picture‐theory. These topics connect with Wittgenstein's earlier treatment of the will – which changed markedly later. The subtext (in footnotes) confronts (i) the sceptical methods of (...) Descartes and Hume with the grammatical methods of Leibniz, Kant and Wittgenstein, and (ii) the realism of Leibniz and the Tractatus with the transcendental idealism of Kant. My conclusion is that, although the method of Wittgenstein's later work remains in a sense grammatical, (i) in its new form it can free us from the conviction that the intellect can and must resolve one way or the other the conflicts that arise in the course of the latter confrontation, and that (ii), although release from such a conviction is to be seen as the aim of philosophical discourse in general, it allows philosophy to retain its overriding significance. A positive element in that lies in the respect the method demands for that in a human life which is transcendental to the activity of scientific theorising: respect, therefore, for the unique perspective of the individual historical agent. (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 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)

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)

Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem (...) and its proof. An attempt is made to meet directly some of Wittgenstein’s critical comments on the mathematical treatment of infinity and irrational numbers. (shrink)

In this article, I want to do two things. The first is to conduct a sympathetic yet critical review of some of the salient features of the ideas in the notes that have come to us from Wittgenstein's Lectures on Religious Belief. This requires close reading, analysis and critique. The second, which comes out of the first, is to give some indication of Wittgenstein's failure to apply to his thinking about religious and moral matters some of the insights that he (...) had already achieved as his philosophical thinking progressed. (shrink)

In this paper, I present and criticize a number of influential anti-skeptical strategies inspired by Wittgenstein’s remarks on ‘hinges’. Furthermore, I argue that, following Wittgen- stein’s analogy between ‘hinges’ and ‘rules of grammar’, we should be able to get rid of Cartesian skeptical scenarios as nonsensical, even if apparently intelligible, combinations of signs.

In this article I construe Russell's definite description notation as a fragment of an "ideal language"– a language in which, as Russell puts it in the "Logical Atomism" lectures, "the words in a proposition correspond one by one with the components of the corresponding fact." Russell's notation – containing as it does variables, quantifiers and the identity sign – commits him to an ontology that is lavish indeed. It thus conflicts with the spirit of the theory of descriptions, which is (...) developed in the service of ontological frugality. I make use of arguments derived from the Tractatus to show that an ideal language need not contain logical signs. I thus defend the spirit of the theory of descriptions while departing from its letter. (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)