Abstract
Starting from the 1960s of the past century theory change has become a main concern of philosophy of science. Two of the best known formal accounts of theory change are the post-Popperian theories of verisimilitude (PPV for short) and the AGM theory of belief change (AGM for short). In this paper, we will investigate the conceptual relations between PPV and AGM and, in particular, we will ask whether the AGM rules for theory change are effective means for approaching the truth, i.e., for achieving the cognitive aim of science pointed out by PPV. First, the key ideas of PPV and AGM and their application to a particular kind of propositional theories – the so called “conjunctive propositions” – will be illustrated. Afterwards, we will prove that, as far as conjunctive propositions are concerned, AGM belief change is an effective tool for approaching the truth.
Although we are separately responsible for particular sections (Gustavo Cevolani: Sections 5.1.2, 5.2 and 5.3; Francesco Calandra: Section 5.1.1), we have each benefited from regular discussions and the rereading of each other’s contributions, which produced a unified exposition of all the subjects dealt with in the paper.
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Notes
- 1.
For a discussion of the problem of rational theory change and its relations with the aims of science, see Cevolani and Festa (2009).
- 2.
In the present paper, the terms “verisimilitude” and “truth approximation” are used as synonymous. The first full-fledged account of verisimilitude was provided by Karl Popper (1963, 1972). Later, David Miller (1974) and Pavel Tichý (1974) showed that Popper’s account was untenable, thus opening the way to the post-Popperian theories of verisimilitude, emerged since 1975. An excellent survey of the modern history of verisimilitude is provided by Niiniluoto (1998).
- 3.
In the literature, the terms “belief dynamics”, “belief change”, and “belief revision” are used as synonymous. AGM, which is named after Alchourrón, Gärdenfors, and Makinson (1985), was developed, starting from the 1970s, by researchers in philosophy of science, logic and Artificial Intelligence. The first monograph devoted to AGM was written by Gärdenfors (1988), and the first textbook presentation by Hansson (1999).
- 4.
Quite recently, however, some AGM theorists have criticized the lack of any concern for truth in AGM. For instance, Hans Rott argues that AGM “should worry more about truth” considered as one of the basic aims of scientific inquiry (see Rott 2000, pp 513, 518 and ff., and in particular note 38).
- 5.
Distance \({\Delta }_{\mathit{ms}}^{\gamma {\gamma }^{{\prime}} }\) is a weighted sum of two simpler (extended) distances, the minimum distance Δmin(T, C i ) and the normalized sum distance Δ sum (T, C i ). The minimum distance of T from C i is the distance from C i of the closest constituent entailing T, defined as: Δmin(T, C i ) = min j ∈ { T} Δ ij . The normalized sum distance of T from C i is the sum of the distances from C i of all the constituents entailing Tnormalized with respect to the sum of the distances of all the elements of C from \({C}_{i} :\ {\Delta }_{\mathit{sum}}(T,{C}_{i}) = \sum_{j\in {\bf T}}{\Delta }_{\mathit{ij}}/\sum_{{C}_{ j}\in {\bf C}}{\Delta }_{\mathit{ij}}\).
- 6.
There are good reasons to think that any plausible measure of verisimilitude should respect (Vs.1–Vs.3) (see Niiniluoto 1987, pp 232–233).
- 7.
- 8.
- 9.
A similar definition can be given with respect to any verisimilitude measure Vs, by selecting a suitable threshold value σ and calling “verisimilar” and “t-distant” those sentences whose verisimilitude is greater or lower than σ, respectively.
- 10.
See Cevolani et al. (forthcoming) for a discussion of contraction.
- 11.
See Niiniluoto (1999), pp 7–9.
- 12.
If T is the theory of an agent X, then T + , T − , and T ? can be seen as the set of the b-propositions which Xaccepts, rejects, and on which suspends the judgment, respectively.
- 13.
These theorems are proved in Cevolani et al. (forthcoming) together with a number of results about contraction.
- 14.
The problem of the effectiveness of contraction for approaching the truth is considered in Cevolani et al. (forthcoming).
- 15.
See Niiniluoto (1999), Eq. 5.10.
- 16.
One of the few verisimilitude measures violating (Vs.1) has been proposed by Graham Oddie (1986).
- 17.
See Niiniluoto (1999), pp. 10–13, in particular equations 10, 17 and 20.
- 18.
The proviso is needed in order to exclude the trivial case where A is already contained in T, i.e., the case where A xT = T and \({T}_{A}^{+} = T\).
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Acknowledgments
The authors wish to express their gratitude to Roberto Festa and Theo A. F. Kuipers for commenting on an early draft of the paper.
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Cevolani, G., Calandra, F. (2009). Approaching the Truth via Belief Change in Propositional Languages. In: Suárez, M., Dorato, M., Rédei, M. (eds) EPSA Epistemology and Methodology of Science. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3263-8_5
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