Nicholas Danne

According to Jody Azzouni’s “deflationary nominalism,” the singular terms of mathematical language applied or unapplied to science refer to nothing at all. What does exist, Azzouni claims, must satisfy the quaternary condition he calls “thick epistemic access” (TEA). In this paper I argue that TEA surreptitiously reifies some mathematical entities. The mathematical entity that I take TEA to reify is the Fourier harmonic, an infinite-duration monochromatic sinusoid applied throughout engineering and physics. I defend the reality of the harmonic, in Azzouni’s account, not by satisfying all four TEA conditions with respect to it, but by showing that the harmonic renders satisfiable the TEA condition called “grounding,” specifically in Azzouni’s (Talking about nothing: numbers, hallucinations, and fictions. New York: Oxford University Press, 2010) example of a human visually perceiving a vase. The harmonic thereby plays what Azzouni calls an “epistemic role,” and merits inclusion in the deflationary nominalist ontology. Against the “coding” objection of Azzouni and Bueno (Br J Philos Sci 67:781–816, 2016), which would nominalize the harmonic to nonexistent status, I reply that in the context of grounding, the coding objection begs the question.

Hartry Field argues that conservative rather than true mathematical sentences facilitate deductions in nominalist (i.e., abstracta-free) science without prejudging its empirical outcomes. In this paper, I identify one branch of mathematics as nonconservative, for its indispensable role in enabling nominalist language about a fundamental scientific property, in a fictional scientific community. The fundamental property is electromagnetic reflectance, and the mathematics is Fourier analysis, which renders reflectance ascribable, and nominalist reflectance claims utterable, by this community. Using a recent characterization of conservativeness by Kenneth Boyce, I argue that infinitudes can be rendered inherently mathematical and nonnominalizable in the fictional community, and that rendering infinitudes inherently mathematical for all real communities would yield a convincing counterexample to Fieldian conservativeness. © 2023 Elsevier B.V., All rights reserved.

In the debate over whether mathematical facts, properties, or entities explain physical events (in what philosophers call “extra-mathematical” explanations), Aidan Lyon’s (2012) affirmative answer stands out for its employment of the program explanation (PE) methodology of Frank Jackson and Philip Pettit (1990). Juha Saatsi (2012; 2016) objects, however, that Lyon’s examples from the indispensabilist literature are (i) unsuitable for PE, (ii) nominalizable into non-mathematical terms, and (iii) mysterious about the explanatory relation alleged to obtain between the PE’s mathematical explanantia and physical explananda. In this paper, I propose a counterexample to Saatsi’s objections. My counterexample is Frank Jackson’s (1998a) program explanation for color experience, which I argue needs recasting as an extra-mathematical PE due to its implicit reliance on reflectance, a property that suffers conceptual regress unless redefined with Fourier harmonics. Pace Saatsi, I argue that this recast example is an authoritative PE, non-nominalizable, and minimally esoteric. Important for the indispensability debate at large, moreover, is that my counterexample reifies Fourier harmonics without the Enhanced Indispensability Argument (an argument to which Lyon applies PE as a premise). Indispensabilists have long overlooked the conditionalization of a limited mathematical realism on property realism, and my counterexample to Saatsi exploits this conditionalization.

According to Jody Azzouni’s “deflationary nominalism,” the singular terms of mathematical language applied or unapplied to science refer to nothing at all. What does exist, Azzouni claims, must satisfy the quaternary condition he calls “thick epistemic access” (TEA). In this paper I argue that TEA surreptitiously reifies some mathematical entities. The mathematical entity that I take TEA to reify is the Fourier harmonic, an infinite-duration monochromatic sinusoid applied throughout engineering and physics. I defend the reality of the harmonic, in Azzouni’s account, not by satisfying all four TEA conditions with respect to it, but by showing that the harmonic renders satisfiable the TEA condition called “grounding,” specifically in Azzouni’s (Talking about nothing: numbers, hallucinations, and fictions. New York: Oxford University Press, 2010) example of a human visually perceiving a vase. The harmonic thereby plays what Azzouni calls an “epistemic role,” and merits inclusion in the deflationary nominalist ontology. Against the “coding” objection of Azzouni and Bueno (Br J Philos Sci 67:781–816, 2016), which would nominalize the harmonic to nonexistent status, I reply that in the context of grounding, the coding objection begs the question.

To teach the ethics of science to science majors, I follow several teachers in the literature who recommend “persona” writing, or the student construction of dialogues between ethical thinkers of interest. To engage science majors in particular, and especially those new to academic philosophy, I recommend constructing persona dialogues from Henri Poincaré’s essay, “Ethics and Science”, and the non-theological third chapter of Pope Francis’s encyclical on the environment, Laudato si. This pairing of interlocutors offers two advantages. The first is that science students are likely to recognize both names, since Poincaré appears in undergraduate mathematics and physics textbooks, and because Francis is an environmentalist celebrity. Hence students show more interest in these figures than in other philosophers. The second advantage is that the third chapter of Laudato si reads like an implicit rebuttal of Poincaré’s essay in many respects, and so contriving a dialogue between those authors both facilitates classroom discussion, and deserves attention from professional ethicists in its own right. In this paper, I present my own contrived dialogue between Francis and Poincaré, not for assigning to students as a reading, but as a template for an effective assignment product, and as a crib sheet for educators to preview the richly antiparallel themes between the two works.

To justify inductive inference and vanquish classical skepticisms about human memory, external world realism, etc., Richard Fumerton proposes his “inferential internalism,” an epistemology whereby humans ‘see’ by Russellian acquaintance Keynesian probable relations (PRs) between propositions. PRs are a priori necessary relations of logical probability, akin to but not reducible to logical entailments, such that perceiving a PR between one’s evidence E and proposition P of unknown truth value justifies rational belief in P to an objective degree. A recent critic of inferential internalism is Alan Rhoda, who questions its psychological plausibility. Rhoda argues that in order to see necessary relations between propositions E and P, one would need acquaintance with too many propositions at once, since our evidence E is often complex. In this paper, I criticize Rhoda’s implausibility objection as too quick. Referencing the causal status effect (CSE) from psychology, I argue that some of the complex features of evidence E contribute to our type-categorizing it as E-type, and thus we do not need to ‘see’ all of the complex features when we see the PR between E and P. My argument leaves unchanged Fumerton’s justificatory role for the PR, but enhances its psychological plausibility.

Reflectance physicalists define reflectance as the intrinsic disposition of a surface to reflect finite-duration light pulses at a given efficiency per wavelength. I criticize the received view of dispositional reflectance (David R. Hilbert’s) for failing to account for what I call “harmonic dispersion,” the inverse relationship of a light pulse's duration to its bandwidth. I argue that harmonic dispersion renders reflectance defined in terms of light pulses an extrinsic disposition. Reflectance defined as the per-wavelength efficiency to reflect the superimposed, infinite-duration, Fourier harmonics of pulses can be an intrinsic disposition of surfaces. This conclusion raises questions about mathematical realism, about which I nevertheless remain neutral.

Liminal Bodies, Reproductive Health, and Feminist Rhetoric presents composition professor Lydia McDermott's "sonogram" methodology of rhetorical listening, an exercise that discloses feminine voices muted or unjustly disciplined within texts ostensibly written on women's behalf. The texts examined by McDermott range from eighteenth-century pregnancy manuals to speeches by Favorinus, the ancient sophist, who is described from antiquity as a hermaphrodite. Part of McDermott's purpose in sonogramming is to critique modern and contemporary feminists. She objects to the feminist trend of perpetuating and answering a "disability" rhetoric about women, or of demonstrating that women can overcome a...