Abstract
This chapter is about the notion of reduction in the philosophy of science. Going through the most influential (families of) characterizations of reduction, it is argued that a particular version of identity-based reduction plays a crucial role in the reduction debate in the philosophy of science. Again, it is a notion that reconciles diversity and directionality with strong unity, without relying on elimination. However, it captures a relation the primary relata of which are theories. It is argued that models of reduction, in a straightforward sense of ‘reduction’, as well as models of mere replacement heavily build upon this notion. At the same time, the present section paves the way for an evaluation of the relation between versions of theory-reduction, or what will be called ‘holistic’ approaches to reduction, and the explication proposed in Chaps. 4 and 5. In passing, it will be shown that models of reduction in the philosophy of science do not draw a sharp distinction between issues regarding replacement and issues regarding genuine reduction. This may be partly due to the fact that different kinds of methods have been employed when it came to characterizing reduction within the philosophy of science. Possible problems that may result from this methodological pluralism are hinted at.
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Notes
- 1.
Let me briefly comment on Nagel’s four main publications that are directly concerned with reduction. Nagel (1935) gives an intuitive sketch of reduction that is almost fully lost in his later writings, It is, however, interesting for a number of interpretative purposes discussed in (van Riel 2011); it sheds light onto the relation between reductive and mechanistic explanation. Nagel (1949) is almost fully included in chapter 11 of his 1961 book. The point of departure for his interpreters is chapter 11 of Nagel (1961), so I will mainly focus on this chapter. Nagel (1970) is interesting in three respects: first, it includes an interpretation of bridge laws that is much more precise than the interpretation offered in Nagel (1961); second, it includes a discussion of the role of correction in reduction; and, finally, it sheds light onto issues regarding the question of the relata of the reduction relation (for an interpretation, see my van Riel 2011).
- 2.
Alternatively, one might suggest that non-contextualized theories reduce in virtue of some relation between their reduction base on the one hand, and its contextualized versions on the other.
- 3.
- 4.
This last point is astonishing, since the idea that Nagel’s model does not allow for reduction has been the basis for the most prominent criticisms, initially raised by Feyerabend (1962, 1966). However, already Putnam (1965, 206 ff., esp. n. 3) was well aware of the fact that correction could easily be incorporated in Nagel’s model of reduction (for similar reasons, Nickles (1973) suggests that these criticisms do not succeed).
- 5.
- 6.
If this characterization is correct, Nagel anticipates Schaffner’s partial reductions (Schaffner 2006).
- 7.
The characterization given here is based on Balzer and Moulines (1996, 12–13). The authors are concerned with larger structures of theory-nets and theory-holons. Some aspects they include in the notion of a theory seem to transcend the minimal requirement. I merely focus on the minimal aspects, because they suffice to give the picture needed for present purposes.
- 8.
Moulines himself tried to face the problem introducing further purely formal conditions on reduction which are supposed to exclude problematic cases (Moulines 1984). This idea was picked up by Bickle (1998, 79ff.). Both, however, admit that these conditions, which are, again, specified in purely formal terms, will not rule out all possible counterexamples (Bickle 1998, 79; Moulines 1984, 55). It should be clear that, independent of how we shape the formal additional criteria, we will not end up with better candidates than those given by straightforward ontological descriptions that relevantly employ the concept of identity.
- 9.
It is, however, important to see that structuralist notions of a theory do not depend upon the idea that an actual theory has to conform to structuralist standards; rather, the idea is that it can be reconstructed in a structuralist way.
- 10.
This is reflected by Schaffner when he describes the method he employs. It is to be conceived of as ‘logical pragmatism’ the basic idea of which can be cashed out as follows: Try to incorporate not only the relevant conceptual aspects, but also what actually happens in science; pragmatic or procedural aspects of theorizing, deciding and so forth are relevant, too. These different aspects are to be combined in a model that mirrors the multidimensional endeavor of the pragmatics, epistemics and logic of science (Schaffner 1993, 515 f.).
- 11.
According to the GRR-model, it is possible to formulate the corrected replaced theory in the language of the replaced theory or in the language of the replacing theory, or, differently: To derive a theory-variant from the replacing theory plus boundary conditions in order to get the mapping we need for reduction/replacement. This is not our target here, so I ignore this aspect.
- 12.
In an earlier model, the general reduction paradigm, Schaffner uses a similar framework and contends that such an ambiguity is possible (Schaffner 1967, 145).
- 13.
There are exactly 8 ways to make the right-hand side of the bi-conditional of (3) in the model given above true, if we interpret ‘it may be that p’ as used in (3) as implying ‘p or not p’. Otherwise, there are 6. Therefore, the term ‘continuum’ is highly misleading.
- 14.
In addition, Schaffner mentions that part-whole relation might hold between the objects of the reduced and the reducing sciences’ domains. We shall come back to this later on (Chap. 8). Note that the way Schaffner’s model is presented here, all cases of 1a/b and 2a/b combinations in Schaffner’s definition are met. Depending on how we interpret “derivability of domain” in Schaffner’s model, this condition will be the one that does maybe not require cross-theoretic identities (if, say, an extensional relation is sufficient).
- 15.
- 16.
A similar point was made by Kim. Kim seems to oppose the Nagelian picture, stating that it uses bridge-laws as premises without explaining them, and, thus, fails to give a model of explanatory reduction (Kim 1998, 90). In addition, he describes bridge-laws as stating contingent facts, and, therefore, not identities. As I have argued in (van Riel 2011) the term ‘contingent’ in Nagel’s sense is an epistemological term. The epistemological or psychological role of bridge-laws is not of interest to us, and it is this role Kim focuses on. Marras (2005, 351) and Block and Stalnaker (1999, 28) have pointed out that bridge-principles acquire their epistemological status after the reduction has been carried out (this is also the point of New Wave reductionism).
- 17.
For a detailed introduction, see chapter 1 and 2 of Bickle’s (1998).
- 18.
Bickle (1998) gave a semantic interpretation of New-Wave reduction which is not listed here. As it stands, it seems to inherit problems of both, semantic approaches and classical ways of framing New-Wave reduction. Bickle seems to suppose that the semantic interpretation matches the intuitive one which forms our target.
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van Riel, R. (2014). Conceptions of Reduction in the Philosophy of Science. In: The Concept of Reduction. Philosophical Studies Series, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-319-04162-9_7
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