Infinite Reasoning. (30th July 2020)

• Record Type: Journal Article
• Authors: Warren, Jared
• Is Part Of: Philosophy and phenomenological research. Volume 103:Number 2(2021)
• Page Start: 385
• Page End: 407
• Publication Date: 2020-07-30
• Subjects: Reasoning -- Inference -- Rule‐following -- Infinity -- Truth -- Omega Rule -- Arithmetic; Philosophy -- Periodicals; Phenomenology -- Periodicals; 100
• DOI: 10.1111/phpr.12694
• Languages: English
• ISSNs: 0031-8205

Abstract

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.