# Gareth R. Pearce, MA BA

# Gareth R. Pearce, MA BA

##### Præ Doc

Gareth R. Pearce

Department of Philosophy

University of Vienna

Universitätsstraße 7 (NIG)

1010 Vienna

Room: C 0211 (NIG)

Phone: +43-1-4277-46073 **Mail: **gareth.pearce@univie.ac.at

#### Areas of Specialization

Philosophy of Mathematics, Philosophy of Logic and Metaphysics.

Wider AOI: Epistemology & Epistemic Normativity, Philosophy of Language, Philosophy of Science, History of Analytic Philosophy, and Mathematical or Formal approaches to Philosophy.

#### Thesis Project: Essays on the Foundations of Axiom and Logic Selection

My thesis is a collection of seven (six and a half, one of them is short) papers on the philosophy of logic and philosophy of mathematics. The overarching theme connecting them is the question "How should we pick our axioms and logics?"

Three of these papers are on the philosophy of logic where I defend a particular (Neo)Carnapian view of logical pluralism. On this view logics are correct to the extent that they endorse the valid (truth perserving) inferences. But truth is a language-relative notion, given a particular Carnapian/Tarskian view of truth. So logical correctness is language relative, and there are lots of logics true for some language. The three papers in this section are:

- Language, Truth and Logics: A Neo-Carnapian Account of Logical Pluralism. A survey paper outlining the position and defending it from well known objections.
- Epistemic Normativitiy for Non-Classical Truth. This paper outlines how and when truth is epistemically valuable, given the range of possible non-classical languages. My proposed solution is to take information, not truth, to be of fundamental epistemic value. Non-classical truth is valuable only if its true (or designated) propositions provide information about the world.
- Metaphysical Realism with Logical Pluralism. Dummet believed that the principle of bivalence is constitutive of realism. Tahko has recently argued that metaphysical realism entails logical "realism" (monism). This paper argues that this is a mistake. A (Neo)carnapian logical pluralist can be a metaphysical realist as logical correctness depends on facts about one's language, not about the world.

Three of these papers are on topics in the Philosophy of Mathematics. This section of my thesis is a little more speculative. Whilst there has been a great deal of interest in the philosophy of mathematics about which axiom system is correct (or best, preferable, etc; depending on what honourific one wishes to use), there has been comparably little work outlining what conditions an axiom system needs to satisfy in order to be correct. Most often, philosophers have left their theory of axiom selection implicit, and those who make it explicit infrequently defend the criteria they apply. These three papers aim to address this gap.

- On Axiom Selection. This paper argues for the claim that philosophers of maths should do more work explicitly outlining their theory of axiom selection and defending its criteria. It does this by setting out a taxonomy of possible views of axiom selection and arguing that there's a non-trivial debate to be had between them.
- Mathematics doesn't need a (philosophical) Foundation. This paper argues that mathematics doesn't need a foundation, in the philosophical sense of the term. That's to say that mathematics, as a whole, does not need to select a single axiom system that acts as its epistemic, ontic and conceptual foundation.
- A Nominalist Theory of Axiom Selection. This paper outlines a possible nominalist view of axiom selection. The paper builds on an idea outlined in "On Axiom Selection" to present a possible nominalist theory of axiom selection. The idea is that mathematics, as a scientific institution, has a unique role that it ought play in the wider scientific community. This generates a socio-epistemic normative framework in which to evaluate mathematical practice. One possible object of evaluation is axiom selection. Certain axiom systems might do more or less work in contributing towards the socio-epistemic role of mathematics. In virtue of that, they would be better or worse axiom systems.

Lastly, I have one paper on epistemic normativity. It's a short paper (less than 2000 words) entitled The Epistemic Value of Precision. The paper provides an independent argument for the view of epistemic normativity outlined in Epistemic Normativity for Non-Classical Truth. This paper was really just a bit of fun, but is relevant so makes it into the thesis!

I have also recently published my first paper A Nominalist Alternative to Reference by Abstraction in the Theora special issue on Linnebo's 2018 book "Thin Objects. It can be found here and is open access.

Supervisors: Georg Schiemer, Esther Ramharter

#### Teaching:

- Current: Wissenschaftlisches Arbeiten (Eng: Research Methods in Philosophy - though the translation is inexact)
- W21 & W20: Exercise course in Logic
- TA, with Iulian Toader: two courses on the Philosophy of Quantum Mechanics

#### Selection of Upcoming & Past Talks

- European Early Career Philosophers Workshop Suspended due to Covid-19: "Grounding Mathematical Normativity"

- Society for the Study of the History of Analytic Philosophy conference 2020: "Why Formalism died too early and why Lewis should have brought it back"

- Tilburg History of Analytic Philosophy Workshop 2020: "Why Formalism died too early and why Lewis should have brought it back"

- OZSW Graduate Conference 2020: "What does it take for some Axioms to be a Foundation for Mathematics?"

- Joint Session of the Aristotelian Society and the Mind Association 2020: "Some comments on the Logic of Reasons".