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, Meta-Normativity and Metaphysics.
Wider AOI: Epistemology, Philosophy of Logic, and Mathematical Philosophy

 

FoNTI-Project

Many Philosophers, and sometimes Mathematicians doing Philosophy, make apparently normative claims about mathematics. They might say things like “one ought adopt some Large Cardinal Axiom in Set theory”, “one ought approximate travelling salesman problems in practical contexts” or “some body of mathematics X is best for representing some physical structure Y”. Sometimes these norms are for relatively uninteresting reasons “one ought adopt Large Cardinal Axioms, because that’s where the grant funding is” makes for a compelling but not philosophically puzzling claim! But sometimes mathematical-normative claims are given for more interesting reasons “one ought adopt Large Cardinal Axioms, because they are more powerful”. My project focuses on the grounds of these sorts of interesting reasons for Normative claims about pure mathematics.

It is my belief that claims about, for instance, which axioms are foundational are significantly theory laden in a way that hasn't been fully appriciated. What one might mean if one were to claim, for instance, that Category Theory is a better foundational theory than Set Theory will depend heavily on what one believes about mathematical truth, metaphysics and epistemology, as well as what one believes about Normativity. The aim of this project is not to pronounce judgement in favour of a particular account of pure Mathematical Normativity, but to outline the conceptual geography of how particular accounts of the metaphysics of mathematics might ground accounts of Mathematical Normativity.

If there is a more general conclusion I might argue for, it is that Axiomatic Monism, the view that there is some set of axioms that are the correct or foundational axioms of mathematics, is rather hard to defend. Axiomatic Pluralism, the view that there are many sets of axioms that are the correct or foundational axioms of mathematics, is a more plausible standpoint.

Supervisors: Georg Schiemer, Esther Ramharter

 

Upcoming & Past Talks

FoNTI Colloquium 2019W: "Do Thin Objects Fall Flat? On the limmits of Dynamic Abstraction"

FoNTI Colloquium 2019W: "Re-thinking Normative Logics: A Unified Approach"

Workshop on Practical and Meta-Ethics with John Broome (also part of the Logic Cafe) Suspended due to Covid-19: "Re-Thinking Normative Logics: A Unified Approach"

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"

Joint Session of the Aristotelian Society and the Mind Association 2020: "Taking a Chance on the Logic of Reasons"

Work in Progress

Outside my FoNTI work, I am working on four independent personal projects:

First, A New Epistemic Argument for Nominalism (a view that opposes the use of abstract objects in philosophy, in particular in the philosophy of Maths). Second, a response to Øystein Linnebo’s recent book “Thin Objects”.  And third, a paper on Gettier Problems. Finally, I intend to defend a version of Mathematical Formalism (the view that mathematical truth amounts to claims about what follows from what, or even what follows from what in which logic). My version of Formalism is called Modal Formalism and is characterised by being a Hellman-style modal structuralist about proof theory, but a Formalist about everything else. This last project is a long way from being ready for publication, though.

The first and last of these projects are drawn from the MA thesis at the University of Bristol “Nominalism & Formalism”.