## Notre Dame Journal of Formal Logic

- Notre Dame J. Formal Logic
- Volume 51, Number 4 (2010), 407-416.

### Justification by Infinite Loops

David Atkinson and Jeanne Peijnenburg

#### Abstract

In an earlier paper we have shown that a proposition can have a well-defined probability value, even if its justification consists of an infinite linear chain. In the present paper we demonstrate that the same holds if the justification takes the form of a closed loop. Moreover, in the limit that the size of the loop tends to infinity, the probability value of the justified proposition is always well-defined, whereas this is not always so for the infinite linear chain. This suggests that infinitism sits more comfortably with a coherentist view of justification than with an approach in which justification is portrayed as a linear process.

#### Article information

**Source**

Notre Dame J. Formal Logic Volume 51, Number 4 (2010), 407-416.

**Dates**

First available in Project Euclid: 29 September 2010

**Permanent link to this document**

http://projecteuclid.org/euclid.ndjfl/1285765795

**Digital Object Identifier**

doi:10.1215/00294527-2010-025

**Mathematical Reviews number (MathSciNet)**

MR2741833

**Zentralblatt MATH identifier**

1205.60011

**Subjects**

Primary: 60A99: None of the above, but in this section

**Keywords**

probabilistic justification coherentism infinitism

#### Citation

Atkinson, David; Peijnenburg, Jeanne. Justification by Infinite Loops. Notre Dame J. Formal Logic 51 (2010), no. 4, 407--416. doi:10.1215/00294527-2010-025. http://projecteuclid.org/euclid.ndjfl/1285765795.