On Certainty,Change, and “Mathematical Hinges”

Annalisa Coliva (Int J Study Skept 10(3–4):346–366, 2020) asks, “Are there mathematical hinges?” I argue here, against Coliva’s own conclusion, that there are. I further claim that this affirmative answer allows a case to be made for taking the concept of a hinge to be a useful and general-purpose tool for studying mathematical practice in its real complexity. Seeing how Wittgenstein can, and why he would, countenance mathematical hinges additionally gives us a deeper understanding of some of his latest thoughts on mathematics. For example, a view of how mathematical hinges relate to Wittgenstein’s well-known river-bed analogy enables us to see how his way of thinking about mathematics can account nicely for a “dynamics of change” within mathematical research—something his philosophy of mathematics has been accused of missing (e.g., by Robert Ackermann (Wittgenstein’s city, The University of Massachusetts Press, Amherst, 1988) and Mark Wilson (Wandering significance: an essay on conceptual behavior, Oxford University Press, Oxford, 2006). Finally, the perspective on mathematical hinges ultimately arrived at will be seen to provide us with illuminating examples of how our conceptual choices and theories can be ungrounded but nevertheless the right ones (in a sense to be explained).

     

Rule-Following and Objective Spirit

This paper deals with Wittgenstein’s rule-following paradox, focussing on the infinite rule-regress as featured in Kripke’s Wittgenstein on Rules and Private Language. I argue that one of the most salient and popular proposed solutions (championed by John McDowell), which argues that rule-following is grounded in “custom,” “practice” or “form of life, remains unsatisfactory because part of this proposal is the rejection of further “theory” (commonly attributed to Wittgenstein) which seemingly makes it impossible to substantiate the claim of how customs, practices or forms of life ground rule-following. I argue that this conundrum can be solved by introducing Wilhelm Dilthey’s overlooked notion of objective spirit as the objectivated sediment of historical human communality. This proposal allows us to substantiate Wittgenstein’s hints at the connection between rule-following and customs, practices, and forms of life without introducing “problematic theories.” Combining Wittgenstein’s views with Dilthey’s notion of objective spirit results in a solution that is neither skeptical nor straight, but therapeutic.     

The Structure’s Legacy: Not from Philosophy to Description

In the paper I consider how empirical material, from either history or sociology, features in Kuhn’s account of science in The Structure of Scientific Revolutions and argue that the study of scientific practice did not offer him data to be used as evidence for defending hypotheses but rather cultivated a sensitivity for detail and difference which helped him undermine an idealized conception of science. Recent attempts in the science studies literature, appealing to Wittgenstein’s philosophy, have aimed at reducing philosophy to multifaceted empirical research in relation to science. I discuss how this turn which is at odds with Wittgenstein’s philosophy, cannot be a continuation of Kuhn’s project which bears similarities to Wittgenstein’s.     

“It is not a something,but not a nothing either!”—McDowell on Wittgenstein

This paper corrects a mistake in John McDowell’s influential reading of Wittgenstein’s attack on the idea of private sensations. McDowell rightly identifies a primary target of Wittgenstein’s attack to be the Myth of the Given. But he also suggests that Wittgenstein, in the ferocity of his battles with this myth, sometimes goes into overkill, which manifests itself in seemingly behavioristic denials about sensations. But this criticism of Wittgenstein is a mistake. The mistake is made over two important but notoriously difficult sections in the so-called Private Language Argument, namely §304 and §293 of the Philosophical Investigations. Wittgenstein, maximally charitably read, commits no overkill in these two sections. This correction strengthens McDowell’s overall reading, but it is only a first step toward fully bringing out the deep but obscurely expressed insights in §304 and §293, the full treatment of which must await another occasion.     

Wittgenstein’s influence on Austin’s philosophy of language

Many philosophers have assumed, without argument, that Wittgenstein influenced Austin. More often, however, this is vehemently denied, especially by those who knew Austin personally. We compile and assess the currently available evidence for Wittgenstein’s influence on Austin’s philosophy of language. Surprisingly, this has not been done before in any detail. On the basis of both textual and circumstantial evidence we show that Austin’s work demonstrates substantial engagement with Wittgenstein’s later philosophy. In particular, Austin’s 1940 paper, ‘The Meaning of a Word’, should be construed as a direct response to and development of ideas he encountered in Wittgenstein’s Blue Book. Moreover, we argue that Austin’s mature speech-act theory in How to Do Things with Words was also significantly influenced by Wittgenstein.     

Wittgenstein as a Philosopher of Technology: Tool Use,Forms of Life,Technique, and a Transcendental Argument

The work of Ludwig Wittgenstein is seldom used by philosophers of technology, let alone in a systematic way, and in general there has been little discussion about the role of language in relation to technology. Conversely, Wittgenstein scholars have paid little attention to technology in the work of Wittgenstein. In this paper we read the Philosophical Investigations and On Certainty in order to explore the relation between language use and technology use, and take some significant steps towards constructing a framework for a Wittgensteinian philosophy of technology. This framework takes on board, and is in line with, insights from postphenomenological and hermeneutic approaches, but moves beyond those approaches by benefiting from Wittgenstein’s insights into the use of tools, technique, and performance, and by offering a transcendental interpretation of games, forms of life, and grammar. Focusing on Wittgenstein’s philosophy of language in the Investigations, we first discuss the relation between language use and technology use, understood as tool use, by drawing on his analogy between language and tools. This suggests a more general theory of technology use, understood as performance. Then we turn to his epistemology and argue that Wittgenstein’s understanding of language use can be embedded within a more general theory about technology use understood as tool use and technique, since language-in-use is always already a skilled and embodied technological practice. Finally, we propose a transcendental interpretation of games, forms of life, and grammar, which also gives us a transcendental way of looking at technique, technological practice, and performance. With this analysis and interpretation, further supported by comments on robotics and music, we contribute to using and integrating Wittgenstein in a more systematic way within philosophy of technology and engage with perennial questions from the philosophical tradition.     

‘Meaning-dawning’ in Wittgenstein’s Notebooks: a Kierkegaardian reading and critique

In this paper, I am going to propose a new reading of Wittgenstein’s cryptic talk of ‘accession or loss of meaning’ (or the world ‘waxing and waning’ as a whole) in the Notebooks that draws both on Wittgenstein’s later work on aspect-perception, as well as on the thoughts of a thinker whom Wittgenstein greatly admired: Søren Kierkegaard. I will then go on to argue that, its merits apart, there is something existentially problematic about the conception that Wittgenstein is advocating. For the renunciation of the comforts of the world that Wittgenstein proposes as a way of coping with the brute contingencies of life seems only to come as far as what Kierkegaard calls ‘infinite resignation’, and this falls far short of the joyful acceptance of existence that appears necessary for inhabiting what Wittgenstein calls a happy world. That is to say, I will show that what Wittgenstein’s proposal lacks is a way of reconnecting with the finite after one has renounced it – the kind of transformation of existence achieved by the person Kierkegaard calls the ‘knight of faith’.     

Making Sense of Sense Containment

Proposition 5.122 of Wittgenstein’s Tractatus (‘If p follows from q, the sense of [p] is contained in the sense of [q]’) 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 (which is taken into consideration also by Wittgenstein), 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.     

Wittgenstein and the Phenomenological Movement: Reply to Monk

Abstract

Monk’s ‘The Temptations of Phenomenology’ examines what the term ‘Phänomenologie’ meant for Wittgenstein. Contesting various other scholars, Monk claims that Wittgenstein’s relation to ‘Phänomenologie’ began and ended during 1929. Monk only partially touches on the question of Wittgenstein’s relation to the phenomenological movement during this time. Though Monk does not mention this, 1929 was also the year in which Ryle and Carnap turned their critical attention toward Heidegger. Wittgenstein also expressed his sympathy for Heidegger in 1929. Furthermore, though in 1929 Wittgenstein agrees with the early Husserl on relating logic and science to phenomenology, it is not clear that they mean the same thing by either logic or phenomenology, or that they agree on what the relation between the two should be.     

Wittgenstein,Quasi-fideism,and Scepticism

In the discussion of certainties, or ‘hinges’, in Wittgenstein’s On Certainty some of the examples that Wittgenstein uses are religious ones. He remarks on how a child might be raised so that they ‘swallow down’ belief in God (§107) and in discussing the role of persuasion in disagreements he asks us to think of the case of missionaries converting natives (§612). In the past decade Duncan Pritchard has made a case for an account of the rationality of religious belief inspired by On Certainty which he calls ‘quasi-fideism’. Pritchard argues that religious beliefs are just like ordinary non-religious beliefs in presupposing fundamental arational commitments. However, Modesto Gómez-Alonso has recently argued that there are significant differences between the kinds of ‘hinges’ discussed in Wittgenstein’s On Certainty and religious beliefs such that we should expect an account of rationality in religion to be quite different to the account of rational practices and their foundations that we find in Wittgenstein’s work. Fundamental religious commitments are, as Wittgenstein said, in the foreground of the religious believer’s life whereas hinge commitments are said to be in the background. People are passionately committed to their religious beliefs but it is not at all clear that people are passionately committed to hinges such as that ‘I have two hands’. I argue here that although there are differences between religious beliefs and many of the hinge-commitments discussed in On Certainty religious beliefs are nonetheless hinge-like. Gómez-Alonso’s criticisms of Pritchard mischaracterise his views and something like Pritchard’s quasi-fideism is the correct account of the rationality of religious belief.

     

Language Learning in Wittgenstein and Davidson

In this paper, I discuss language learning in Wittgenstein and Davidson. Starting from a remark by Bakhurst, I hold that both Wittgenstein and Davidson’s philosophies of language contain responses to the problem of language learning, albeit of a different form. Following Williams, I hold that the concept of language learning can explain Wittgenstein’s approach to the normativity of meaning in the Philosophical Investigations. Turning to Davidson, I hold that language learning can, equally, explain Davidson’s theory of triangulation. I sketch an account of triangulation as Davidson’s response to the problem of the normativity of meaning and explain the role that language learning plays in this account.     

The philosophy of science at the turn of the millenium

Abstract

Central to a new, or ‘resolute’, reading of Wittgenstein’s Tractatus LogicoPhilosophicus is the idea that Wittgenstein held there an ‘austere’ view of nonsense: the view, that is, that nonsense is only ever a matter of our failure to give words a meaning, and so that there are no logically distinct kinds of nonsense. Resolute readers tend not only to ascribe such a view to Wittgenstein, but also to subscribe to it themselves; and it is also a feature of some readings which in other respects are clearly not Resolute. This paper forms part of a reply to Hans-Johann Glock’s work in which he argues (in part) that Wittgenstein in the Tractatus held a view of nonsense other than the austere view. Instead, Glock argues, Wittgenstein there held that there are many logically distinct kinds of nonsense. Here, I outline and defend the austere view, together with its attribution to the early Wittgenstein, against a number of Glock’s criticisms, and focussing especially on Wittgenstein’s reformulation in the Tractatus of Frege’s context-principle.     

A Comfortable Sureness: Knowledge,Animality and Conceptual Investigations in Wittgenstein’s On Certainty

This essay analyses some remarks of Wittgenstein’s On Certainty in which Wittgenstein compares human behaviour to that of animals and says he wants to consider man as an animal. The essay’s main purpose is to show that these remarks are essentially understood as part and parcel of what Wittgenstein calls “conceptual investigations” and that, consequently, they give little support to On Certainty’s naturalistic interpretations. A second purpose of the essay is to show that Wittgenstein does not intend to combat the use of “I know” in contexts such as those evoked by Moore; rather he wants to draw attention to the different ways in which we say or can say “I know.”

     

Truth in the Investigations

According to a widespread interpretation, in the Investigations Wittgenstein adopted a deflationary or redundancy theory of truth. On this view, Wittgenstein’s pronouncements about truth should be understood in the light of his invocation of the equivalences ‘p’ is true = p and ‘p’ is false = not p. This paper shows that this interpretation does not do justice to Wittgenstein’s thoughts. I will be claiming that, in fact, in his second book Wittgenstein is returning to the pre-Tractarian notion of bipolarity, and that his new development of this notion in the Investigations excludes the redundancy-deflationary reading. Wittgenstein’s thoughts about truth are instead compatible with another interpretative option: Wittgenstein remains faithful to his methodological pronouncements, and he merely presents us with (grammatical) platitudes about the notions of “true” and “false”.

     

Wittgenstein and the groundlessness of our believing

In his final notebooks, published as On Certainty, Wittgenstein offers a distinctive conception of the nature of reasons. Central to this conception is the idea that at the heart of our rational practices are essentially arational commitments. This proposal marks a powerful challenge to the standard picture of the structure of reasons. In particular, it has been thought that this account might offer us a resolution of the traditional scepticism/anti-scepticism debate. It is argued, however, that some standard ways of filling out the details of this proposal ultimately lead to an epistemology which is highly problematic. The goal here is to present a more compelling version of Wittgenstein??s account of the structure of reasons which can evade these difficulties.     

Calling Solomon’s Bluff: Ethics,Aspect-Perception and the Unity of the Tractatus

In this paper, I consider how we ought to read the aspect-perception passages in the Tractatus Logico-Philosophicus (TLP) in the light of its ethics. I engage with a recent proposal, of Genia Schönbaumsfeld's, that we should replace the TLP account of aspect-perception with that which Wittgenstein puts forward in the Philosophical Investigations (PI). I show that, far from helping us to grasp the ethical vision contained in the TLP, this proposal obscures it. I go on to draw some conclusions from this as to how to read the TLP in its relation to Wittgenstein's other work.     

Harry Silverstein’s Four‐Dimensionalism and the Purported Evil of Death

Abstract

Amongst those views sometimes attributed to the later Wittgenstein are included both a deflationary theory of truth, as well as a non-factualism about certain regions of discourse. Evidence in favor of the former attribution, it is thought, can be found in Wittgenstein’s apparent affirmation of the basic definitional equivalence of ‘p’ is true and p in §136 of his Philosophical Investigations. Evidence in favor of the latter attribution, it might then be presumed, can be found in the context of the so-called ‘private language argument’, wherein Wittgenstein provides an expressivist treatment of first-person present tense sensation utterances. In this paper, by contrast, I will argue that Wittgenstein’s later philosophy is best understood as endorsing neither a non-factualism about sensation utterances, nor a deflationism about truth. Wittgenstein should instead be understood as offering a ‘mixed’ view of sensation utterances according to which some while not others are apt for expressivist treatment. Moreover, he should be thought of as identifying truth-conditions with semantic ‘correctness-conditions’, and thus truth with semantic ‘assertibility’.     

Religious Hinges: Some Historical Precursors

Recently, hinge epistemologists have applied Wittgenstein’s metaphor of hinges to religious belief. The most prominent proposal in this context is Pritchard’s “quasi-fideism”. This paper examines some historical precursors of the notion of religious hinges, with the aim of shedding more light on it. After outlining the framework of hinge epistemology and its application to religious belief, I briefly examine the views of Thomas Reid and John Henry Newman as acknowledged forerunners of this framework (or cognate views). Next, I turn to two hitherto unacknowledged forerunners, the pragmatists William James and Charles S. Peirce. I then focus on some insights that the pragmatists offer. On this basis, I conclude that religious beliefs are a special class of hinges. As such, while they can be defended through hinge epistemology, they cannot constitute a model through which we can interpret the nature of hinges in general.

     

Wittgenstein on the duration and timing of mental phenomena: episodes,understanding and rule-following

ABSTRACT

Wittgenstein’s later works are full of questions about the timing and duration of mental phenomena. These questions are often awkward ones, and Wittgenstein seems to take their awkwardness to be philosophically revealing, but if we ask what it is that these questions reveal then different interpretations are possible. This paper suggests that there are at least six different ways in which the timing of mental phenomena can be awkward. By identifying these we can give sense to some of Wittgenstein’s more cryptic remarks, and doing this enables us to clarify some obscure elements in his picture of the mind, including the distinction between sensations and feelings, and his account of the rational status of those processes out of which rule-following is built.