Abstract
This chapter addresses the puzzle of reduction, paving the way for the explication of the notion of reduction proposed in Chaps. 3 and 4. The concept of reduction, as understood here, reconciles diversity and directionality with strong unity, without relying on elimination. But how can we reconcile strong unity, i.e. unity that is based on identity, with directionality? Identity is symmetric and reflexive. Directionality seemingly goes together with asymmetry and irreflexivity. Hence, the concept of reduction, so characterized, appears to be inconsistent. I propose a solution to this problem according to which ‘_reduces to_’ generates hyper-intensional contexts and, thus, is sensitive to the conceptual or descriptive contents under which the reduced or reducing item is presented. We thus get a better idea of what diversity consists in: It is conceptual or descriptive diversity, which goes together with unity in that one and the same entity, say, pain, is presented under different concepts, say, the concept of pain and the concept of C-fiber firing.
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Notes
- 1.
- 2.
Sensitivity to conceptual presentation has not loomed large in the philosophy of science-debate on reduction. There are some exceptions, or so it seems. Fritz Rohrlich incorporated a conceptual aspect in his approach to reduction (Rohrlich 1988). The basic idea of his is that theories at different levels differ in that they have different cognitive values. According to Rohrlich, at a higher level, we can speak of ‘cognitive emergence’ of objects in the sense that these objects “[…differ] perceptively in essential ways from anything that there was at any of the earlier stages […]” (Rohrlich 1988, 298). This cognitive emergence is mimicked by the need for different conceptual structures. Unfortunately, Rohrlich is silent about how to conceive of these conceptual differences. The following suggestion makes it hard to uncover how conceptual structure is supposed to differ from ontological structure: “The two ontologies are associated with different cognitive levels [which, in turn, depend on different conceptual schemes, RvR]. On each level the theory gives us a different ‘model of the world’ which has characteristic features that cannot be expressed by any other level […]” (Rohrlich 1988, 310). He explicitly argues in favor of plural ontologies. More straightforwardly, Ager et~al. (1974) argue that we should conceive of the relation between temperature and mean kinetic energy in terms of identity, though the expressions used (‘temperature’ and ‘mean kinetic energy’) as well as the concepts expressed (the concept of temperature and the concept of mean kinetic energy) are different (Ager et~al. 1974, 125 f.). They explicitly describe the field of the kinetic theory of gases as the field that tries to describe its target systems in terms of a certain list of properties (Ager et~al. 1974, 123). This mimics, to a certain degree, the idea pursued here. However in (Ager et~al. 1974) this idea is left sketchy. The authors have a different target, namely, the alleged necessity of bridge-laws for reductions (that is: the role of bridge-laws is discussed in the context of achieving reductions, rather than in the context of some reduction relation which holds independent of whether or not the reduction is actually carried out). Note that this idea is not to be conflated with the idea that different representational schemes amount to different explanatory links and hierarchies – as long as these are spelled out in purely ontological terms. Sarkar (1998), Bechtel and Richardson (1993), and Wimsatt (1974) describe the idea of different representational schemes, which are individuated via the relations they refer to within the system to be represented (for example, functional vs. structural relations in mechanistic explanations). There is also one strand in the philosophy of mind that can be illuminated building on this notion of reduction: The qualia-problem has been stated in a number of different forms (Jackson 1982, 1986; Davidson 1986; Shoemaker 1982). One prominent reaction to this problem roughly runs as follows: Difference in conceptualization does not imply a difference in ontology (Levine 1998; Papineau 2002, 2007; Tye 1999). Thus, one might suggest that qualia-reduction requires a difference in conceptual presentation and, at the same time, identity of properties.
- 3.
If there are contingent identities that are metaphysically contingent under every possible reading, and if such identity statements play a role in reduction, the account would have to be slightly adjusted, so as to capture a merely intensional interpretation of ‘_reduces to_’. This would, I submit, best be captured by distinguishing between a weak and a strong version of identity-based reduction – the former merely requiring contingent identities, whereas the latter requires necessary identities. The former could accommodate the assumption that a statue reduces to the clay it is formed of, but that this is merely a contingent identity.
- 4.
Note that this has an interesting consequence for the application of Leibniz’ Law: Just because ‘a exemplifies F-ness’ expresses a truth, and ‘b exemplifies F-ness’ expresses a falsehood, it does not follow that a ≠ b.Schnieder (2006c) has made a similar point about pragmatic aspects of substitution of co-referential expressions. The point made here is semantic in nature, as will become apparent below. Independent of considerations about Leibniz law, a pragmatic interpretation of substitution failures would blur the distinction. Such a strategy has been pursued by Recanati in his (2000), concerning substitution failures in belief-contexts.
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- 6.
Alternatively, you could replace this premise and talk about the relation between a sentence’s being true and the corresponding tuple of objects belonging to the relevant extension (across worlds). Or, even simpler, that precisely this tuple has the property if the sentence is true, and does not have the property if the sentence is false, and nothing has and does not have the property at the same time.
- 7.
I am confident that a modal version of the argument could be given. Moreover, I will ignore sentences in which we quantify into an argument position, which is within the scope of a hyper-intensional predicate.
- 8.
This principle hinges on the assumption that no hyper-intensional predicates are such that they have true or false instances only; if there are, we need to go modal and hope that there are no hyper-intensional predicates that necessarily have true or false instances only. Cases like ‘2 + 2 = 5 and _reduces to_’ can probably be coped with, by requiring that any argument be erased, or be the possible candidate for substitution, or by requiring predicates to occur in atomic sentences. Moreover, it is assumed that for any hyper-intensional predicate, there is, at least in principle, a test for hyper-intensionality.
- 9.
What about sentences that contain terms seemingly referring to fictional entities? This is a more general problem, and whatever the correct solution might be, there seems to be no reason to believe that it cannot be accommodated within the present framework. Similarly, I will ignore possible hidden indexicals concerning contexts or the actual world; then, these would add to the arity of the relation. One prominent interpretation of hyper-intensionality is itself a variant of a hidden-indexical approach (see, for example, Forbes 2006). The argument presented here can be seen as showing that something along these lines must be correct for hyper-intensional expressions.
- 10.
This supports Jenkin’s (2011) point: From the fact that an instance of ‘a is grounded in b’ implies the corresponding instance of ‘b is not grounded in a’, it does not follow, without further ado, that the grounding relation is asymmetric.
- 11.
I would like to thank Marta Campdelacreu for pointing out this argument to me, during a discussion of this argument in a Logos-Seminar in Barcelona in 2012. Jenkins (2011) discusses a somewhat similar alternative (without adopting it): That the semantic values of the terms occurring in the scope of hyper-intensional expressions may designate tuples of objects, one element of which is the ordinary object signified or referred to by the expression. This view will yield an equivalent result; we have to decide between postulating systematic reference shift and postulating that systematically, the arity of some predicates does not reflect the arity of the relation they express.
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- 13.
Here is one general remark: Given these problems for an application of the Frege-picture to the case of reduction, one might feel tempted to ask in response: Why should ‘believes (that)’ function differently? What would be the price to pay when ‘Peter beliefs that snow is white’ should be paraphrased as ‘Peter believes (the fact or state of affairs) that snow is white as presented in that specific way’?
- 14.
Note that this is, maybe, a misguided interpretation of the relevant sort of asymmetry. Consider a (very odd) language where meaning is at least partly determined by position in a sentence, so that in ‘p because q’, p has the meaning of q and q has the meaning of p in ‘q because p’. Then, ‘because’ is not asymmetrical in the sense specified above. We should thus not work with substitutional quantification without, additionally, invoking conditions on the meanings of the relevant expressions. What does this show? It does not show that the characterization fails for English. But it shows that the characterization maybe does not capture the feature it is supposed to capture. It adequately models the “asymmetry” of ‘because’ and other expressions just because our English (and other natural languages) does not contain rules that allow for disambiguation in the way just sketched.
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van Riel, R. (2014). The Puzzle of Reduction. In: The Concept of Reduction. Philosophical Studies Series, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-319-04162-9_3
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