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From Good to Better: Using Contextual Shifts to Define Preference in Terms of Monadic Value

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Johan van Benthem on Logic and Information Dynamics

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 5))

Abstract

It has usually been assumed that monadic value notions can be defined in terms of dyadic value notions, whereas definitions in the opposite direction are not possible. In this paper, inspired by van Benthem’s work, it is shown that the latter direction is feasible with a method in which shifts in context have a crucial role. But although dyadic preference orderings can be defined from context-indexed monadic notions, the monadic notions cannot be regained from the preference relation that they gave rise to. Two formal languages are proposed in which reasoning about context can be represented in a fairly general way. One of these is a modal language much inspired by van Benthem’s work. Throughout the paper the focus is on relationships among the value notions “good”, “bad”, and “better”. Other interpretations like “tall” and “taller” are equally natural. It is hoped that the results of this paper can be relevant for the analysis of natural language comparatives and of vague predicates in general.

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Notes

  1. 1.

    Here we follow Graham’s numbering of the Canons. He made a hybrid text from Xiaoqu and part of Daqu under the title “Names and Objects” (abbreviated “NO”) We also use his translations.

  2. 2.

    Halldén [11, p. 28], von Wright [22, pp. 24–25, 40, 60]. For further references see Hansson [13, pp. 89–90].

  3. 3.

    In the logic of exclusionary preferences we use the letters \(x, y, z \dots \) to denote the objects of evaluation. When the objects of evaluation have sentential structure we use the letters \(p, q, r\dots \).

  4. 4.

    To simplify the notation, we contract series of two-place predicate expressions, thus writing \(x \! \ge \! y \! \ge \! z\) for \( x \! \ge \! y \ \& \ y \! \ge \! z\), and similarly \(x \! > \! y \! \approx \! z\) for \( x \! > \! y \ \& \ y \! \approx \! z\), etc.

  5. 5.

    See Mitchell [18, pp. 103–105], Halldén [11, p. 109], von Wright [22, p. 34] and [23, p. 162], and Åqvist [3].

  6. 6.

    Other variants of the same basic approach replace Chisholm and Sosa’s indifferent sentences by tautologies [8, p. 37], or contradictions [23, p. 164]. This approach gives rise to the following formal definitions:

    \(G_{\scriptstyle \top }p \leftrightarrow p \! > {\scriptstyle \top }\) (tautology-related good)

    \(B_{\scriptstyle \top }p \leftrightarrow {\scriptstyle \top }> \!p\) (tautology-related bad)

    \(G_{\scriptstyle \perp }p \leftrightarrow p \! > {\scriptstyle \perp }\) (contradiction-related good)

    \(B_{\scriptstyle \perp }p \leftrightarrow {\scriptstyle \perp }> \!p\) (contradiction-related bad)

    However, the interpretation of what it means for something to be better or worse than a tautology or (in particular) a contradiction is quite problematic.

  7. 7.

    An even weaker property than reflexivity, namely ancestral reflexivity (\(p \! \ge \! \! \! ^\star p\)), is sufficient for this result.

  8. 8.

    For an attempt to deal with some such differences, see Hansson [14]. See also Stalnaker [20].

  9. 9.

    This also applies to many other adjectives, hence we would say that \(x\) is longer than \(y\) if and only if \(y\) is shorter than \(x\).

  10. 10.

    The term “polarization” indicates that if \(x\) and \(y\) differ in terms of goodness and badness in the context \(\{x,y\}\), then they are at opposite sides of the value scale, i.e. one of them is good and the other is bad.

  11. 11.

    The subformula \({\large <} up {\large >}\,{\large <} dn {\large >}\) is used as a means to reach (any) other reachable context while remaining in the same actual state. Its plausibility for this purpose depends on conditions that we will not discuss further here, namely (i) \( {\large <} up {\large >}\,{\large <} up {\large >} \phi \leftrightarrow {\large <} up {\large >} \phi \), (ii) \( {\large <} dn {\large >}\,{\large <} dn {\large >} \phi \leftrightarrow {\large <} dn {\large >} \phi \), and (the somewhat more questionable) \( {\large <} up {\large >}\,{\large <} dn {\large >} \phi \leftrightarrow {\large <} dn {\large >}\,{\large <} up {\large >} \phi \).

References

  1. Aristotle (1952) Topics, translated by WA Pickard-Cambridge. In: WD Ross, JA Smith (eds) Works, vol 1. Encyclopædia Britannica, Chicago, pp 139–223

    Google Scholar 

  2. Alchourrón C, Gärdenfors P, Makinson D (1985) On the logic of theory change: partial meet functions for contraction and revision. J Symb Logic 50:510–530

    Article  Google Scholar 

  3. Åqvist L (1967) Good samaritans, contrary-to-duty imperatives, and epistemic obligations. Noûs 1:361–379

    Article  Google Scholar 

  4. van Benthem J (1982) Later than late: on the logical origin of the temporal order. Pac Philos Q 63:193–203

    Google Scholar 

  5. Brogan AP (1919) The fundamental value universal. J Philos Psychol Sci Methods 16:96–104

    Google Scholar 

  6. Buvac S, Buvac V, Mason IA (1995) Metamathematics of contexts. Fundam Informaticae 23(2–3):263–301

    Google Scholar 

  7. Chisholm RM, Sosa E (1966) On the logic of ‘intrinsically better’. Am Philos Q 3:244–249

    Google Scholar 

  8. Danielsson S (1968) Preference and obligation. Filosofiska Föreningen, Uppsala

    Google Scholar 

  9. Graham AC (1978) Later Mohist logic, ethics and science. Chinese University Press, Hong Kong

    Google Scholar 

  10. Grüne-Yanoff T, Hansson SO (2009) Preference change: approaches from philosophy, economics and psychology. Theory and Decision Library. Springer, Berlin

    Google Scholar 

  11. Halldén S (1957) On the logic of ‘Better’. Gleerup, Lund

    Google Scholar 

  12. Hansson SO (1990) Defining ‘Good’ and ‘Bad’ in terms of ‘Better’. Notre Dame J Formal Logic 31:136–149

    Article  Google Scholar 

  13. Hansson SO (2001) The structure of values and norms. Cambridge University Press, Cambridge

    Google Scholar 

  14. Hansson SO (2006) Category-specified value statements. Synthese 148:425–432

    Article  Google Scholar 

  15. Hill J (2008) Leibniz, relations, and rewriting projects. Hist Philos Q 25:115–135

    Google Scholar 

  16. Liu F (2011) A two-level perspective on preference. J Philos Logic 40(3):421–439

    Google Scholar 

  17. Liu F (2011) Reasoning about preference dynamics, Series synthese library. Springer, Heidelberg, p 354

    Google Scholar 

  18. Mitchell ET (1950) A system of ethics. Charles Scribner’s Sons, New York

    Google Scholar 

  19. Sen A (1970) Collective choice and social welfare. Holden-Day, San Francisco

    Google Scholar 

  20. Stalnaker R (1996) On the representation of context. In: Galloway T, Spence J (eds) SALT VI. Cornell University, Ithaca, New York, pp 279–294

    Google Scholar 

  21. Ultan R (1972) Some features of basic comparative constructions. In: Stanford working papers on language universals, vol 9. Stanford University Press, Stanford, pp 117–162

    Google Scholar 

  22. von Wright GH (1963) The logic of preference. Edinburgh University Press, Edinburgh

    Google Scholar 

  23. von Wright GH (1972) The logic of preference reconsidered. Theor Decis 3:140–169

    Google Scholar 

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Acknowledgments

We would like to thank Alexandru Baltag and Sonja Smets for their efforts in putting together this volume. We would like to thank Johan van Benthem for his useful comments. Fenrong Liu is supported by Project 13AZX01B of the National Social Science Foundation of China and the Tsinghua University Initiative, Scientific Research Program 20131089292.

Author information

Authors and Affiliations

  1. Division of Philosophy, Royal Institute of Technology, Stockholm, Sweden

    Sven Ove Hansson

  2. Department of Philosophy, Tsinghua University, Beijing, China

    Fenrong Liu

Authors
  1. Sven Ove Hansson
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  2. Fenrong Liu
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Correspondence to Sven Ove Hansson .

Editor information

Editors and Affiliations

  1. University of Amsterdam Inst Logic,Language & Computation, Amsterdam, The Netherlands

    Alexandru Baltag

  2. Amsterdam, The Netherlands

    Sonja Smets

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Hansson, S.O., Liu, F. (2014). From Good to Better: Using Contextual Shifts to Define Preference in Terms of Monadic Value. In: Baltag, A., Smets, S. (eds) Johan van Benthem on Logic and Information Dynamics. Outstanding Contributions to Logic, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06025-5_27

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