A Sketchy Logical Conventionalism
Logical Conventionalism & the Adoption Problem
It’s a curious fact that anti-realist views in the foundations of logic are as rare as they are. My goal in this essay is to start making some space for such views. As will become clear, I can hardly give a knock down argument for them. What I can do is limn a few features of logic that point towards an anti-realist treatment and offer a toy model of logical conventionalism that captures these features without undue pain. This will show that anti-realism about logic, at least the conventionalism brand thereof, can be purchased at an attractive price. And it thus ought to be on the foundational shelf.
In this paper, I take issue with a core commitment of logical conventionalism: that we impose a logic on ourselves by adopting linguistic conventions governing our use of logical terms, thereby determining which of our inferences are valid. Drawing on Kripke’s‘adoption problem’, I argue that there are some logical principles that cannot be adopted, either explicitly or implicitly. I go on to argue that since inferences conforming to these principles may nonetheless be valid, validity cannot depend on our adoption of logico-linguistic conventions.
Jack Woods is University Academic Fellow in Mathematical Philosophy at the University of Leeds. He writes across several fields, including mathematical logic, philosophical logic, philosophy of language, and ethics. His work has been published in Ethics, The Philosophical Review, Nous, and other such locations. He has a special interest in that nebulous area in-between the normative and the not-obviously-natural, and a somewhat burning desire to resuscitate some version of logical positivism. He also likes Greggs, Primark, and the work of Lionel Richie.
Anandi Hattiangadi is Professor of Philosophy at Stockholm University. She received a BA in Philosophy from York University, Toronto, and a Ph.D from the Department of History and Philosophy of Science and Trinity College, University of Cambridge. In 2000, she took up a Research Fellowship at Trinity College, Cambridge, and from 2005 to 2013, she was Lecturer and Tutorial Fellow in Philosophy at St Hilda’s College, Oxford.
Hattiangadi specializes in the philosophy of mind and language, and has research interests in the philosophy of logic, the philosophy of cognitive science, epistemology, metaphysics, metaethics, and cultural evolution. Her monograph, Oughts and Thoughts: Rule Following and the Normativity of Content responds to Kripke’s (1982) argument for scepticism about meaning and content. She has published extensively on the normativity of meaning and content; the nature and normativity of belief; reductive accounts of meaning and intentionality; the metaphysics of time, and moral supervenience. She is currently working on a monograph in which she argues that intentionality does not metaphysically supervene on the non-intentional, but is only contingently grounded in it.