Collapse and the Varieties of Quantifier Variance

The aim of this chapter is to bring clarity regarding the doctrine of quantifier variance (due to Eli Hirsch), and two prominent arguments against this doctrine, the collapse argument and the Eklund-Hawthorne argument. Different versions of the doctrine of quantifier variance are distinguished, and it is shown that the effectiveness of the arguments against it depends on what version of the doctrine is at issue. The metaontological significance of the different versions of the doctrine is also assessed. Roughly, quantifier variance concerns there being different possible existential quantifier meanings, and often the doctrine involves a claim to the effect there is no unique “best” quantifier meaning. Much of the discussion in the chapter concerns what it is to be an existential quantifier meaning in the sense at issue.

Metaontology, Existence, and Reference

This chapter presents and defends a conventionalist-friendly metaontology, thereby showing how conventionalism manages to vindicate trivial ontological realism in mathematics. After clarifying and demonstrating this entailment of conventionalism, it clarifies the metaontology involved. The chapter then defends metadeflationism about quantifiers, which entails a version of quantifier pluralism. This is a form of what has recently been called “modest quantifier variance” in joint work with Eli Hirsch. After laying out this view, it is defended from several objections. With this groundwork set out, the chapter then explains how this answers Kant’s challenge for trivial realism that was explained in the previous chapter. Finally, the chapter closes by discussing the metaphysics of mathematical objects, in conventionalist terms, addressing the Julius Caesar problem and structuralism, among other things.

Hirsch, E. (2018). Radical Skepticism and the Shadow of Doubt: A Philosophical Dialogue. London, England: Bloomsbury

Un libro refrescante y profundo. El contenido de Radical Skepticism and the Shadow of Doubt no es nuevo: originalmente titulado Epistemology noir, fue, desde diciembre del 2014 hasta su republicación en diciembre del 2017, un texto de público acceso en la página personal del autor (https://sites. google.com/a/brandeis.edu/eli-hirsch/). ¿Hay razón para dudar de si tenemos contacto con la realidad externa? Si tuviéramos razones para dudarlo, ¿dudaríamos? ¿O es imposible tener semejantes dudas? Éstas son algunas de las preguntas que Eli Hirsch nos plantea y aborda junto a nosotros y tres pintorescos personajes en su libro. Y lo hace en tantos niveles que tendrá que emerger (pues se reduplican en cada acto) una última duda: aun si descubriésemos que para los protagonistas es lícito dudar del Yo, de la realidad externa y de la filosofía como el o cio de la duda por excelencia, ¿es lícito para nosotros (y para Hirsch) dudarlo?

Deflationary metaphysics and ordinary language

Amie Thomasson and Eli Hirsch have both attempted to deflate metaphysics, by combining Carnapian ideas with an appeal to ordinary language. My main aim in this paper is to critique such deflationary appeals to ordinary language. Focussing on Thomasson, I draw two very general conclusions. First: ordinary language is a wildly complicated phenomenon. Its implicit ontological commitments can only be tackled by invoking a Context Principle; but this will mean that ordinary language ontology is not a trivial enterprise. Second: a wide variety of existence questions cannot be deflated using ordinary language, trivially or otherwise, for ordinary language often points in different directions simultaneously.Published in Synthese.

Eli Hirsch: Quantifier Variance and Realism: Essays in Metaontology. Trees and Tables Crackpot Ontology: Jury Still Out

A review of Eli Hirsch "Quantifier Variance and Realism: Essays in Metaontology".