Authors
Jared Warren
Stanford University
Abstract
Our relationship to the infinite is controversial. But it is widely agreed that our powers of reasoning are finite. I disagree with this consensus; I think that we can, and perhaps do, engage in infinite reasoning. Many think it is just obvious that we can't reason infinitely. This is mistaken. Infinite reasoning does not require constructing infinitely long proofs, nor would it gift us with non-recursive mental powers. To reason infinitely we only need an ability to perform infinite inferences. I argue that we have this ability. My argument looks to our best current theories of inference and considers examples of apparent infinite reasoning. My position is controversial, but if I'm right, our theories of truth, mathematics, and beyond could be transformed. And even if I'm wrong, a more careful consideration of infinite reasoning can only deepen our understanding of thinking and reasoning. (Note for readers: the paper's brief discussion of uniform reflection and omega inconsistency is misleading. The imagined interlocutor's argument makes an assumption about the PA-provability of provability generalizations that, while true for the Godel sentence's instances, is unjustified, in general. This means my position is stronger against this objection than the paper suggests, since omega inconsistent theories are not automatically inconsistent with their uniform reflection principles, you also need to assume the arithmetically true Pi-2 sentences.)
Keywords Arithmetic  Infinity  Inference  Omega Rule  Reasoning  Rule‐following  Truth
Categories (categorize this paper)
DOI 10.1111/phpr.12694
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 58,786
Through your library

References found in this work BETA

An Argument for the Identity Theory.David Lewis - 1966 - Journal of Philosophy 63 (1):17-25.
What is Inference?Paul Boghossian - 2014 - Philosophical Studies 169 (1):1-18.
What is Reasoning?Conor McHugh & Jonathan Way - 2018 - Mind 127 (505):167-196.
Comment on Paul Boghossian, "What is Inference".Crispin Wright - 2014 - Philosophical Studies 169 (1):27-37.

View all 44 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

What Reasoning Might Be.Markos Valaris - 2017 - Synthese 194 (6).
Small Steps and Great Leaps in Thought: The Epistemology of Basic Deductive Rules.Joshua Schechter - 2019 - In Magdalena Balcerak Jackson & Brendan Balcerak Jackson (eds.), Reasoning: New Essays on Theoretical and Practical Thinking. Oxford: Oxford University Press.
Knowledge of Validity.Sinan Dogramaci - 2010 - Noûs 44 (3):403-432.
Broome on Reasoning and Rule-Following.Philip Pettit - 2016 - Philosophical Studies 173 (12):3373-3384.
Deflationism and Logic.Christopher Gauker - 1999 - Facta Philosophica (1):167-199.
Belief Revision, Non-Monotonic Reasoning, and the Ramsey Test.Charles B. Cross - 1990 - In Kyburg Henry E., Loui Ronald P. & Carlson Greg N. (eds.), Knowledge Representation and Defeasible Reasoning. Kluwer Academic Publishers. pp. 223--244.
Practical Reasoning.Antti Kauppinen - 2018 - In Daniel Star (ed.), The Oxford Handbook of Reasons and Normativity. Oxford University Press.
How Reasoning Aims at Truth.David Horst - 2021 - Noûs 55 (1):221-241.
Deontic Modality in Rationality and Reasoning.Alessandra Marra - 2019 - Dissertation, Tilburg University

Analytics

Added to PP index
2020-07-31

Total views
149 ( #66,765 of 2,425,543 )

Recent downloads (6 months)
60 ( #12,838 of 2,425,543 )

How can I increase my downloads?

Downloads

My notes