# Publications

From Pictures to Employments: Later Wittgenstein on 'the Infinite'

(Inquiry 2024) (penultimate) (final)

Abstract: With respect to the metaphysics of infinity, the tendency of standard debates is to either endorse or to deny the reality of ‘the infinite’. But how should we understand the notion of ‘reality’ employed in stating these options? Wittgenstein’s critical strategy shows that the notion is grounded in a confusion: talk of infinity naturally takes hold of one’s imagination due to the sway of verbal pictures and analogies suggested by our words. This is the source of various philosophical pictures that in turn give rise to the standard metaphysical debates: that the mathematics of infinity corresponds to a special realm of infinite objects, that the infinite is profoundly huge or vast, or that the ability to think about infinity reveals mysterious powers in human beings. First, I explain Wittgenstein’s general strategy for undermining philosophical pictures of ‘the infinite’ – as he describes it in Zettel; and then show how that critical strategy is applied to Cantor’s diagonalization proof in Remarks on the Foundations of Mathematics II.

A Cave Allegory

(Forthcoming: Philosophy and Literature) (penultimate)

Abstract: A retelling of Plato's famous cave allegory. Inspired by Dōgen, Nietzsche, and Wittgenstein.

Later Wittgenstein on 'Truth' and Realism in Mathematics (Philosophy 2024) (final: open source)

Abstract: I show that Wittgenstein’s critique of G.H. Hardy’s mathematical realism naturally extends to Paul Benacerraf’s influential paper, ‘Mathematical Truth’. Wittgenstein accuses Hardy of hastily analogizing mathematical and empirical propositions, thus leading to a picture of mathematical reality that is somehow akin to empirical reality despite the many puzzles this creates. Since Benacerraf relies on that very same analogy to raise problems about mathematical ‘truth’ and the alleged ‘reality’ to which it corresponds, his major argument falls prey to the same critique. The problematic pictures of mathematical reality suggested by Hardy and Benacerraf can be avoided, according to Wittgenstein, by disrupting the analogy that gives rise to them. I show why Tarskian updates to our conception of ‘truth’ discussed by Benacerraf do not answer Wittgenstein’s concerns. That is, because they merely presuppose what Wittgenstein puts into question, namely, the essential uniformity of ‘truth’ and ‘proposition’ in ordinary discourse.

Crossing Pictures of 'Determination' in Wittgenstein's Remarks on Rule-Following (Philosophical Investigations 2023) (penultimate) (final)

Abstract: In PI 189, Wittgenstein's interlocutor asks, ‘But are the steps then not determined by the algebraic formula?’. Wittgenstein responds, ‘The question contains a mistake’. What is the mistake contained in the interlocutor's question? Wittgenstein's elaboration is neither explicit nor its intended upshot transparent. In this paper, I offer a reading on which the interlocutor's question arises from illicitly crossing different pictures of ‘determination’. I begin by working through Wittgenstein's machine analogy in PI 193, which illustrates picture‐crossing in our ways of talking about a machine. Using the lessons from this analogy, I show how the interlocutor's ‘mistake’ can be diagnosed in similar terms: their confusion about the power of a rule to determine its applications rests on mistakenly crossing a behavioural and a mathematical sense of ‘determine’—thereby concocting a mystifying picture of rule‐following.

# In Progress

Later Wittgenstein on 'Truth': A Therapeutic Reading

Abstract: What is later Wittgenstein's view of truth? The most common and influential answer has been that he is a deflationist about truth. According to deflationists, all that we need to know about the concept of truth is conveyed by the trivial schema: the proposition that p is true if and only if p. Deflationists claim that the concept of truth is thus thin and superficial. It is true that Wittgenstein clung to this schema frequently in his writings, but I'll argue that attention to the broader context of the Philosophical Investigations shows that later Wittgenstein was not a deflationist about truth (as that position is typically defined). Indeed, his therapeutic method of philosophy is antagonistic to the deflationist program of attempting a simple and trivial story about the role of 'truth' in our lives. In the end, we'll find that although Wittgenstein tells us very little about the concept of truth, he invites many questions about its use (and its interconnections with related concepts) that are closed by the narrow thesis of deflationism.

## Later Wittgenstein on the Analysis of Experience:

A Problem for Early Modern Empiricism?

## Abstract: Philosophical Investigations 47 offers a compelling critique of the metaphysical notion of 'absolute simples' -- either of language, reality, or of (visual) experience. In short: since any distinction between 'simple' and 'composite' is relative to how we (inter-)define those terms, and many such definitions are available to us in any given case, there is no 'absolute' notion of 'simple' or 'composite'. To what extent does this critique of philosophical atomism bear on the common distinction between 'simple' and 'complex' elements of experience in early modern empiricism? I investigate this question with a particular focus on Hume's proposed "science of human nature". The bearing of PI 47 on Hume largely depends on our understanding of his project -- an interpretive question that has received relatively little attention. Namely: is Hume's distinction between 'simple' and 'complex' ideas/impressions intended to follow from the phenomenology of our experience or is it instead a theoretical stipulation with specific explanatory or pragmatic aims? If the former, then the critique found in PI 47 is devastating for Hume's theory, as 'experience itself' is compatible with many such ways of distinguishing 'simple' and 'complex' elements; but if the latter, then Hume may have anticipated the problem raised by Wittgenstein, and would (perhaps) justify his theoretical stipulations on pragmatic grounds.

## Crossing Pictures as a Source of Metaphysics

## Abstract: Metaphysical inquiry tends to begin by noting a shortcoming in our ordinary notion of some thing X (whether it’s consciousness, numbers, free will, etc.). For instance, perhaps our ordinary notion of X is caught in certain ambiguities that philosophers can resolve through precisification and analysis. Or, perhaps our ordinary notion of X suggests metaphysical commitments (e.g., to abstract objects, to mysterious properties of mind or human agency, etc.) that need to be reckoned with. Having noted these shortcomings in our ordinary notion of X, philosophers typically seek to clarify (through precisification and analysis) our ordinary notion of X in order to resolve its ambiguities and to better prepare us for a critique of its metaphysical commitments – assuming analysis reveals any such commitments at all (e.g., certain analyses might show that there are no such metaphysical commitments that need to be reckoned with). Wittgenstein is unique among philosophers in questioning the initial move in this standard approach to metaphysical inquiry. That is, to question whether our ordinary notion of X possesses shortcomings that can only be resolved via the methods of precisification and analysis that are characteristic of analytic philosophy. A more detailed description of the ordinary notion of X in combination with a scrutiny of its alleged ‘shortcomings’ will reveal (1) that imprecision in our ordinary notion of X is not generally a mark against it and (2) that the impression of any metaphysical commitment or implication is a result of misinterpretation of the ordinary notion. In this paper, I will only briefly sketch the first part of Wittgenstein’s critique of standard metaphysical debate, since this part is most familiar and has been articulated by many readers of Wittgenstein. More importantly, I will explain what I see as Wittgenstein’s most powerful argument for (2): that the impression of metaphysical commitment in our ordinary notion of X is a result of ‘crossing pictures’, i.e., of forming misleading analogies between our concept of X and other concepts that only superficially resemble it. Wittgenstein’s critique of metaphysics is thus akin to an attempt to show that there are no metaphysical commitments via technical analysis – but it differs in suggesting that no such technical analysis is required. Rather, the ordinary notion of X is in good working order and presents no special problems or mysteries.

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## Feminist Philosophy and Film: The Conditions of Sexual Violence in Marilyn Frye's 'Sexism' and Joyce Chopra's Smooth Talk

## Co-authored with Tamara Fakhoury (draft)

## Abstract: Eliminating sexual violence requires understanding where it comes from and why it happens. We must learn to detect when the grounds for violence are being built up so that we can promptly take them down. How can we improve our ability to notice the subtle practices of sexism and make them a matter of critical reflection? The aim of this paper is to show how film can enhance critical perception of the social conditions that give rise to sexual violence in particular. We will do this by way of a specific example, showing how Joyce Chopra’s 1985 film Smooth Talk serves to display the complex circumstances that make sexual violence possible – thereby illustrating (and allowing us to see) Frye’s philosophical insight about the interconnected mechanisms of oppression.

# Dissertation

Three Essays on Later Wittgenstein's Philosophy of Mathematics:

Reality, Determination, & Infinity

(UNC Chapel Hill, 2022)