Knowledge of Arithmetic
Bibliographic Data
| ID | 8399252 |
|---|---|
| Authors | C S Jenkins, Carrie Jenkins (0000-0002-9471-0470, University of St Andrews, corresponding author) |
| Year | 2005 |
| Volume | 56 |
| Issue | 4 |
| Pages | 727-747 |
| Publication date | 2005-12-01 |
| Open Access | No |
| Type | ARTICLE |
| Venue | The British Journal for the Philosophy of Science (JOURNAL) |
| Journal identifiers | ISSN: 0007-0882 • E-ISSN: 1464-3537 |
| Publisher | Oxford University Press (PUBLISHER • GB) |
| DOI | 10.1093/bjps/axi142 |
| OpenAlex | W2031464922 |
| Language | EN |
| Citations received | 4 |
| References cited | 6 |
The goal of the research programme I describe in this article is a realist epistemology for arithmetic which respects arithmetic's special epistemic status (the status usually described as a prioricity) yet accommodates naturalistic concerns by remaining fundamentally empiricist. I argue that the central claims which would allow us to develop such an epistemology are (i) that arithmetical truths are known through an examination of our arithmetical concepts; (ii) that (at least our basic) arithmetical concepts are accurate mental representations of elements of the arithmetical structure of the independent world; (iii) that (ii) obtains in virtue of the normal functioning of our sensory apparatus. The first of these claims protects arithmetic's special epistemic status relative, for example, to the laws of physics, the second preserves the independence of arithmetical truth, and the third ensures that we remain empiricists. 1. Preliminaries 2. Justifying and grounding concepts 3. Cameras and filters 4. An epistemology for arithmetic 5. Concluding remarks
Arithmetic function · Discrete mathematics · Empiricism · Epistemology · Independence (probability theory) · Naturalism · Virtue · Computability, Logic, AI Algorithms · Computer Science · Mathematics · Philosophy · Philosophy and History of Science · Philosophy and Theoretical Science
| Citations per year | 0.22 |
|---|---|
| Citation span | 2008 - 2015 (8) |
| Highly cited | No |