# 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 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.

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

## Co-authored with Tamara Fakhoury

## (Forthcoming: Visions of Peace & Non-Violence in Popular Culture)

## (penultimate 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.

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 the Analysis of Experience:

A Problem for Early Modern Empiricism? (handout)

## 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.

Later Wittgenstein on 'Truth': A Therapeutic Reading

(slides) (full draft)

Abstract: The most common and influential reading of later Wittgenstein’s remarks on truth is that he was a deflationist. This paper aims to clarify Wittgenstein’s approach to the concept of truth and show why he should not be considered a deflationist as that position is typically defined. Wittgenstein’s therapeutic conception of philosophy rejects traditional theoretical approaches to questions of truth. The formula “‘p’ is true if and only if p” neither explains the various roles of ‘proposition’ nor the various roles of ‘true’ and ‘false’. Further, Wittgenstein claims that ‘truth’ and ‘proposition’ are conceptually on a par, and that neither can be understood independently of the other. His therapeutic method draws attention to the reciprocal relationship between ‘truth’ and ‘proposition’, counteracting misleading pictures of their roles via careful description of word-use rather than strict adherence to a simple formula. I conclude that if one insists on labelling Wittgenstein a ‘deflationist’ according to some broader understanding of the term, then he should be called a ‘therapeutic deflationist’.

## Selfhood and Emptiness: A Comparative Study of Indian Philosophy and Wittgenstein’s Philosophical Evolution

## Abstract: This paper explores how Wittgenstein's development (early-to-late) parallels a divide between Hindu and Buddhist conceptions of self. The Tractatus notion of the philosophical subject as limit of the world resembles the notion of atman as the "unseen seer" which cannot be described; Blue Book and Philosophical Investigations' rejection of the Augustinian picture and their general anti-essentialism resembles the Buddhist insistence that there is no 'substance' or 'essence' underlying our uses of 'I' and 'self'. Further, the aim of many Buddhists is not to theorize, but rather aim at "the relinquishing of all views" (Nagarjuna), which they see as an obstacle to mindfulness and compassion. -- I conclude with a question regarding what these comparisons might suggest regarding the 'ethical' significance of later Wittgenstein.

##

# Dissertation

Three Essays on Later Wittgenstein's Philosophy of Mathematics:

Reality, Determination, & Infinity

(UNC Chapel Hill, 2022)