Identity Based Theory Reduction

Whereas in the philosophy of mind the notion of reduction is frequently treated as the basis for ontological reductionism, this is a thesis that is not of primary interest for most parts of current philosophy of science. The distinction between reduction debates in the philosophy of science and in the philosophy of mind rests on an idealization, but it nicely illustrates two different tendencies in the two fields. One of the main differences between the philosophy of science debate and the debate in the philosophy of mind becomes apparent when we read the very first sentence of Jerry Fodor s (1974) seminal paper  

A typical thesis of positivistic Philosophy of Science is that aU tme theories in the special 

van Riel, The Concept of Reduction, Philosophical Studies Series 121, 

For Fodor, reduction is an expression that can be used to describe a certain metaphysical picture of the organization of sciences, just like it was for the early positivists. It is this picture which survived in the philosophy of mind but which was seemingly abandoned in the philosophy of science, although, as will be pointed out below, it still lurks within every single model of reduction on the market. This difference is reflected by the fact that in the philosophy of science, reduction is usually explicated in terms of a relation that primarily holds between theories, or representational devices, rather than non-representational worldly objects. Attempts to characterize the reduction-relation go back to the early years of logical positivism. Carnap s reductionism states that  

Reduction in the philosophy of science is usually regarded as a relation instantiated by pairs of theories, or scientific models, rather than by pairs of properties, event-types or states of affairs. Recall the distinction between theory reduction and ontological reduction introduced in Sect. 2.1.7  

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Principle Identity-Based Theory-Reduction) If Tr reduces to Tb, then the (relevant part of) the ontology of Tr belongs to the ontology of Tb. 

Recall the characterization of identity-based theory-reduction ... 

If the kind-terms of the respective theories determine a theory s ontology, then we have defined a notion of identity-based theory-reduction. The next chapter argues that this is how we should conceive of theory reduction. 

The notion of identity-based reduction this book focuses on thus fits monistic realism The concept of reduction is supposed to reconcile diversity and directionality (mirrored by the idea of levels) with strong unity (mirrored by the idea of monism), without relying on (metaphysical) elimination (that is the idea of realism). But isn t this target, or this description of the target obviously ill conceived Apparently, it does not do justice to the fact that in the philosophy of science, reduction is commonly regarded as a relation holding primarily between theories. 

The thesis is, then, this Reductive explanation is constitutive explanation plus identity. If identity comes with constitutive explanation for free (a question not to be pursued here), then reductive explanation just is constitutive explanation (with the contention that partial reductions, as defined below, do not amount to, but can be defined in terms of identity-based reduction). But how does constitutive explanation relate to the grammatical aspect of theories of mechanistic explanation ... 

The present chapter proceeds in two parts. In Sects. 6.2, 6.3 and 6.4,1 will walk us through the successive stages of different versions of identity-theories about the mind, in order to shed light onto their relevance regarding issues of identity-based reduction, and to show how the explication proposed here can be applied to these versions of identity-theories. Section 6.5 summarizes the main points, before turning to a characterization of functional reduction in Sect. 6.6, where functional reduction will be tied to identity-based reduction. 

Now, type identity theories have been extensively criticized. Physicalists opposed to type-identity theory usually conceive of themselves as non-reducHve physicalists. Interestingly, understanding what non-reductive physicalism consists in requires us to understand what this doctrine is opposed to - namely, reductionism about (mental) types. Moreover, non-reductive physicalists often describe themselves as token-identity theorists, they assume that mental tokens reduce to physical tokens, so that there is strong unity at the token-level. Again, a notion of identity-based reduction is required to hilly understand this idea. The explication offered here cannot only be fruitfully applied in the context of type identity theory. The next section is dedicated to the connection between the explication of reduction and token identity theories. 

The concept of identity-based reduction, which underlies the puzzle of reduction discussed in Chap. 3, can partly be characterized as follows a reduces to b only if a = b. Now, obviously, if a theory t reduces to a theory t, then it is not the case that t = t. The so explicated notion of theory-reduction does not, aU by itself, give an idea of how identity-based reduction may enter a model of theory reduction. But in fact, identity-based reduction comes in two forms, as a theory-variant as well as an ontological variant. For the ontological version of identity-based reduction, we get the following principle ... 

We have thus sketched the four most prominent suggestions for defining reduction in the philosophy of science. All these characterizations at least cover a case of identity-based reduction. However, it is not obvious how they should fit the explication proposed in Chaps. 4 and 5 all these characterizations are characterizations of a relation the primary relata of which are theories, or other scientific representational devices, rather than properties or other non-representational worldly objects. The next section offers a notion of theory reduction that is derivative on the notion explicated above. In Chap. 8 it will be argued that in fact, notions of theory reduction are derivative on notions of property reduction, that is it will be shown that the procedure to obtain a notion of theory reduction from a notion of ontological reduction proposed in the next section is in fact adequate. 

The explication proposed in the first part of this book can be used to characterize a notion of theory reduction this is a notion of theory reduction that is based on cross-theoretic identities. It has been shown that the identity-case of theory reduction is covered by a number of prominent models of reduction in the philosophy of science. The explication thus sheds light on the identity-case of theory reduction, which is crucial for an understanding of Nagelian, Structuralist and New-wave models of reduction. We are still here ... 

The idea of holism that accounts for ontological reduction in terms of theory reduction is this If a reduces to b expresses a truth, then it does so because a is relevantly related to a theory t and b is relevantly related to a theory t, and t reduces to t. I will now argue that for a term a to be relevantly related to a theory is for it to have specific semantic properties other than reference (namely, those that are relevant for reduction as construed above), that are relevantly related to t. Thus, it follows that those who embrace this form of holism are committed to the assumption that the relevant semantic facts play a crucial role in reduction-statements. Since the accounts of theory reduction we are familiar with are, on the identity reading, also committed to the tmth of the corresponding metaphysical claims (those expressed by or rendering tme bridge-laws, or statements about analog relations or isomorphisms), holism based on these accounts does not come cheaper than the account presented above. 

The first group of theories was based on the superposition approximation (SA) used for truncation of an infinite hierarchy of equations for a reduced distribution function at the pair distribution level [239,240], It was generalized and applied to the reversible reactions by Lee and Karplus [139] and their successors [145,174,176]. After linearization over deviations from equilibrium [52,63], the theory became simpler and finally was recognized as one identical to IET, provided the reduction to the phenomenological equations is not done [31,175], This is why the linearized superposition approach (LSA) provides exactly the same kernel as IET. 

The next two chapters apply the core notion and a few derivative notions to reduction debates in the philosophy of mind (Chap. 6) and the philosophy of science (Chap. 7). Type-identity theories, token-identity theories, conceptions of non-reductive physicalism, and the model of functional reduction can easily be reconstructed based on the explication proposed here, sometimes in an improved form (for example, on the view presented here, it becomes immediately clear where the directionality stems from - an aspect that has been ignored in the heat of the... 

This book is not about reductionism and, accordingly, not about the question of whether or not arguments from multiple realizability affect the truth of type-identity theory. However, this book assumes that the concept of reduction is relevant. If the argument from multiple realizability goes through, and if token-identity theories are in some sense non-reductive, then one might wonder whether the concept of reduction is relevant. Let me thus show that token-identity theories employ a notion of reduction similar to the one employed by type-identity theories - a notion that can, again, be defined based on the explication offered above. 

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