Grounding concepts : an empirical basis for arithmetical knowledge
This dissertation is a philosophical discussion of arithmetical knowledge. I investigate the possibility of a new kind of epistemology for arithmetic, one which will respect three intuitions. (a) that arithmetic is a priori, (b) that arithmetical realism is correct, i.e. that arithmetical truth is independent of us, and (c) that scientific or naturalistic concerns enforce empiricism, the view that all knowledge of the independent world is obtained through the senses. I propose that we could develop an epistemology respecting these three intuitions if we were prepared to accept three claims: (1) that arithmetical truths are known through an examination of our arithmetical concepts, (2) that (at least our basic) arithmetical concepts map the arithmetical structure of the independent world. (3) that this mapping relationship obtains a virtue of the normal functioning of our sensory apparatus. Roughly speaking, the first of these claims protects a priorism, the second realism and the third empiricism. In the first chapter I try to determine in exactly what sense the realist should say that arithmetic is independent of us. Other preliminaries necessary at this stage include a defence of epistemic externalism and
Jenkins, C.
Grounding concepts : an empirical basis for arithmetical knowledge. This dissertation is a philosophical discussion of arithmetical knowledge. I investigate the possibility of a new kind of epistemology for arithmetic, one which will respect three intuitions. (a) that arithmetic is a priori, (b) that arithmetical realism is correct, i.e. that arithmetical truth is independent of us, and (c) that scientific or naturalistic concerns enforce empiricism, the view that all knowledge of the independent world is obtained through the senses. I propose that we could develop an epistemology respecting these three intuitions if we were prepared to accept three claims: (1) that arithmetical truths are known through an examination of our arithmetical concepts, (2) that (at least our basic) arithmetical concepts map the arithmetical structure of the independent world. (3) that this mapping relationship obtains a virtue of the normal functioning of our sensory apparatus. Roughly speaking, the first of these claims protects a priorism, the second realism and the third empiricism. In the first chapter I try to determine in exactly what sense the realist should say that arithmetic is independent of us. Other preliminaries necessary at this stage include a defence of epistemic externalism and
grounding concept empirical_basis knowledge philosophical_discussion knowledge investigate_possibility new_kind epistemology arithmetic respect intuition arithmetic priori realism correct truth independent scientific naturalistic concern enforce empiricism view knowledge independent world obtain sens propose could_develop epistemology respect intuition prepare accept claim truth know examination concept least basic concept map structure independent world mapping relationship obtain virtue normal function sensory apparatus roughly speaking first claim protect second realism third empiricism first try determine exactly sense realist say arithmetic independent preliminary necessary stage include defence epistemic externalism