Abstract
Epistemology is concerned with the fundamental laws of thought, belief, or judgment. It may inquire the fundamental relations among the objects or contents of thought and belief, i.e., among propositions or sentences. Then we enter the vast realm of formal logic. Or it may inquire the activity of judging or the attitude of believing itself. Often, we talk as if this would be a yes or no affair. From time immemorial, though, we know that judgment is firm or less than firm, that belief is a matter of degree. This insight opens another vast realm of formal epistemology.
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Notes
- 1.
- 2.
Only Pearl (1988) showed how to systematically deal with probabilities without exponential computational explosion.
- 3.
There I called its objects ordinal conditional functions. Goldszmidt and Pearl (1996) started calling them ranking functions, a usage I happily adapted.
- 4.
In the meantime, my comprehensive book on ranking theory (Spohn 2012) has appeared. This paper may also serve as an introduction to this book. Reversely, various topics, which are only touched here and then referred back to older papers of mine, are developed in this book in a better and more comprehensive way.
- 5.
For systematic reasons I am slightly rearranging my terminology from earlier papers. I would be happy if the present terminology became the official one.
- 6.
I am choosing the ranks in an arbitrary, though intuitively plausible way (just as I would have to arbitrarily choose plausible subjective probabilities, if the example were a probabilistic one). The question how ranks may be measured will be taken up in section “The dynamics of belief and the measurement of belief”, pp. 316ff.
- 7.
In earlier papers I called this a belief function, obviously an unhappy term which has too many different uses. This is one reason fort the mild terminological reform proposed in this paper.
- 8.
I am grateful to Matthias Hild for making this point clear to me.
- 9.
Thanks again to Matthias Hild for pointing this out to me.
- 10.
A case in point is the so-called problem of old evidence, which has a simple solution in terms of Popper measures and the second inequality; cf. Joyce (1999, pp. 203ff.).
- 11.
In earlier publications I spoke of weak instead of insufficient reasons. Thanks to Arthur Merin who suggested the more appropriate term to me.
- 12.
I attempted to give a partial overview and argument in Spohn (2001a).
- 13.
Although there is a (by far not trivial) decision rule telling that costless memory is never bad, just as costless information; cf. Spohn (1976/78, sect. 4.4).
- 14.
Generalized probabilistic conditionalization as originally proposed by Jeffrey was result-oriented as well. However, Garber (1980) observed that there is also an evidence-oriented version of generalized probabilistic conditionalization. The relation, though, is not quite as elegant.
- 15.
- 16.
If we accept the idea in section “Basics” (p. 311) of taking the interval [−z, z] of two-sided ranks as the range of neutrality, contraction seems to become ambiguous as well. However, the contraction just defined would still be distinguishable as a central contraction since it gives the contracted proposition central neutrality.
- 17.
- 18.
It has been done in the meantime. See Hohenadel (2013).
- 19.
I have analyzed the relation between Spirtes’ et al. axiomatic approach to causation and my definitional approach a bit more thoroughly in Spohn (2001b).
- 20.
For a recent presentation of the account of deterministic causation in terms of ranking functions and its comparison in particular with David Lewis’ counterfactual approach see Spohn (2006).
- 21.
For quite a different way of relating probabilities and ranks appealing neither to infinitesimals nor to Popperian conditional probabilities see Giang and Shenoy (1999).
- 22.
Cf., however, Maher’s (2002) criticism of Joyce’s argument.
- 23.
- 24.
If a speaks a foreign language, the principle takes a more complicated, but obvious form. There is also a disquotation principle for the hearer, which, however, requires a careful exchange of the hearer’s and the speaker’s role.
- 25.
- 26.
However, I had already mentioned that Hild (t.a.) finds a much closer connection of probabilities and ranks within statistical methodology.
- 27.
I attempted to substantiate this suggestion with my account of strict and ceteris paribus laws in Spohn (2002) and with my translation of de Finetti’s representation theorem into ranking theory in Spohn (2005a). (New addendum: For the most recent ranking-theoretic account of ceteris paribus laws see Spohn (2014).)
- 28.
I must confess, though, that I had not yet noticed his work when I basically fixed my ideas on ranking functions in 1983.
- 29.
This is particularly obvious from Cohen (1970, p. 219, def. 5).
- 30.
- 31.
For my ideas how to treat conditionals in ranking-theoretic terms see Spohn (2015).
- 32.
Does this contradict the fact that ranking functions are equivalent to possibility measures (with their second kind of conditionalization), that possibility measures may be conceived as a special case of DS belief (or rather: plausibility) functions, and that Jeffrey conditionalization works for possibility measures as defined by Halpern (2003, p. 107)? No. The reason is that Jeffrey conditionalization for possibility measures is not a special case of Jeffrey conditionalization for DS belief functions in general. Cf. Halpern (2003, p. 107).
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Spohn, W. (2016). A Survey of Ranking Theory. In: Arló-Costa, H., Hendricks, V., van Benthem, J. (eds) Readings in Formal Epistemology. Springer Graduate Texts in Philosophy, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-20451-2_17
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