### Justification by Infinite Loops

David Atkinson and Jeanne Peijnenburg
Source: Notre Dame J. Formal Logic Volume 51, Number 4 (2010), 407-416.

#### 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.

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Primary Subjects: 60A99
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1285765795
Digital Object Identifier: doi:10.1215/00294527-2010-025
Zentralblatt MATH identifier: 05822353
Mathematical Reviews number (MathSciNet): MR2741833

### References

[1] Atkinson, D., and J. Peijnenburg, "Justification by an infinity of conditional probabilities", Notre Dame Journal of Formal Logic, vol. 50 (2009), pp. 183--93.
Mathematical Reviews (MathSciNet): MR2535583
Zentralblatt MATH: 1181.60008
Digital Object Identifier: doi:10.1215/00294527-2009-005
Project Euclid: euclid.ndjfl/1242067709
[2] Atkinson, D., and J. Peijnenburg, "The solvability of probabilistic regresses. A reply to Frederik Herzberg [mr2608027]", Studia Logica, vol. 94 (2010), pp. 347--53.
Mathematical Reviews (MathSciNet): MR2608028
Zentralblatt MATH: pre05705230
Digital Object Identifier: doi:10.1007/s11225-010-9240-z
[3] Sellars, W., "Empiricism and the philosophy of mind", pp. 253--329 in The Foundations of Science and the Concepts of Psychology and Psychoanalysis, edited by H. Feigl and M. Scriven, vol. 1 of Minnesota Studies in the Philosophy of Science, University of Minnesota Press, Minneapolis, 1956.