## Project Details

### Description

It is common to say that we know today that Fermat’s Last Theorem

is true, although we still do not know whether Goldbach’s conjecture

is. Obviously, such knowledge ascriptions are implicitly attributed to

the mathematical community or a subgroup thereof. But what is the

nature of such collective knowledge? Is it simply reducible to the sum

of the knowledge of individual mathematical agents, or shall the

mathematical community be conceived as a full- fledged social

epistemic subject? What are the mechanisms ensuring the reliability

of collective knowledge in mathematics, and thus the stability of the

mathematical edifice? Although the social dimensions of

mathematics have received increasing attention within the so-called

philosophy of mathematical practice, we are still lacking clear

philosophical proposals to answer the above set of questions. The

general aim of this research project is to contribute to fill this gap by

developing an account of collective knowledge in mathematics. Our

focus will be specifically on the notion of collective justification and

how it is acquired by a group of mathematicians through proofs. We'll

also be concerned with characterizing groups of mathematical agents

as epistemic subjects in their own right. The notions thus developed

will be used to address the fundamental epistemological issue of the

reliability of mathematical knowledge. Finally, implications for

epistemology and general philosophy of science will be spelled out

and discussed

is true, although we still do not know whether Goldbach’s conjecture

is. Obviously, such knowledge ascriptions are implicitly attributed to

the mathematical community or a subgroup thereof. But what is the

nature of such collective knowledge? Is it simply reducible to the sum

of the knowledge of individual mathematical agents, or shall the

mathematical community be conceived as a full- fledged social

epistemic subject? What are the mechanisms ensuring the reliability

of collective knowledge in mathematics, and thus the stability of the

mathematical edifice? Although the social dimensions of

mathematics have received increasing attention within the so-called

philosophy of mathematical practice, we are still lacking clear

philosophical proposals to answer the above set of questions. The

general aim of this research project is to contribute to fill this gap by

developing an account of collective knowledge in mathematics. Our

focus will be specifically on the notion of collective justification and

how it is acquired by a group of mathematicians through proofs. We'll

also be concerned with characterizing groups of mathematical agents

as epistemic subjects in their own right. The notions thus developed

will be used to address the fundamental epistemological issue of the

reliability of mathematical knowledge. Finally, implications for

epistemology and general philosophy of science will be spelled out

and discussed

Acronym | FWOAL1068 |
---|---|

Status | Active |

Effective start/end date | 1/01/23 → 31/12/26 |

### Flemish discipline codes

- Philosophy of mathematics

### Keywords

- mathematical practice
- collective justification
- epistemic trust/reliability
- mathematical proof
- distributed cognition