Infinite value and finitely additive value theory

Journal of Philosophy 94 (1):5-26 (1997)
  Copy   BIBTEX

Abstract

000000001. Introduction Call a theory of the good—be it moral or prudential—aggregative just in case (1) it recognizes local (or location-relative) goodness, and (2) the goodness of states of affairs is based on some aggregation of local goodness. The locations for local goodness might be points or regions in time, space, or space-time; or they might be people, or states of nature.1 Any method of aggregation is allowed: totaling, averaging, measuring the equality of the distribution, measuring the minimum, etc.. Call a theory of the good finitely additive just in case it is aggregative, and for any finite set of locations it aggregates by adding together the goodness at those locations. Standard versions of total utilitarianism typically invoke finitely additive value theories (with people as locations). A puzzle can arise when finitely additive value theories are applied to cases involving an infinite number of locations (people, times, etc.). Suppose, for example, that temporal locations are the locus of value, and that time is discrete, and has no beginning or end.2 How would a finitely additive theory (e.g., a temporal version of total utilitarianism) judge the following two worlds? Goodness at Locations (e.g. times) w1:..., 2, 2, 2, 2, 2, 2, 2, 2, 2, ..... w2:..., 1, 1, 1, 1, 1, 1, 1, 1, 1, ..... Example 1 At each time w1 contains 2 units of goodness and w2 contains only 1. Intuitively, we claim, if the locations are the same in each world, finitely additive theorists will want to claim that w1 is better than w2. But it's not clear how they could coherently hold this view. For using standard mathematics the sum of each is the same infinity, and so there seems to be no basis for claiming that one is better than the other.3 (Appealing to Cantorian infinities is of no help here, since for any Cantorian infinite N, 2xN=1xN.)

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 98,169

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Analytics

Added to PP
2009-01-28

Downloads
497 (#48,065)

6 months
28 (#116,336)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Peter Vallentyne
University of Missouri, Columbia
Shelly Kagan
Yale University

Citations of this work

Infinite Aggregation and Risk.Hayden Wilkinson - 2023 - Australasian Journal of Philosophy 101 (2):340-359.
Intrinsic vs. extrinsic value.Michael J. Zimmerman - 2019 - Stanford Encyclopedia of Philosophy.
Consequentialism.Douglas W. Portmore - 2023 - In Christian B. Miller (ed.), The Bloomsbury Handbook of Ethics. Bloomsbury Academic.
Infinite Value and the Best of All Possible Worlds.Nevin Climenhaga - 2018 - Philosophy and Phenomenological Research 97 (2):367-392.
Infinite Ethics.Nick Bostrom - 2011 - Analysis and Metaphysics 10:9–59.

View all 54 citations / Add more citations

References found in this work

No references found.

Add more references