Theoretical identities

Immunolabeling for electron microscopy is theoretically identical to immunolabeling for light microscopy. The problems discussed in Chapter 30 describing light microscope immunolabeling are entirely relevant to electron immunocytochemistiy. 

The same lattice-theoretic identities hold as in the affine case. Moreover, we define irreducible algebraic sets exactly as in the affine case. And we obtain the analog of Proposition 2 ... 

Another quaternary alkyl piridinium salt (36) was isolated from an extract of the Micronesian sponge Callyspongia fibrosa [37]. A cyclic structure for this compound was first proposed on the basis of ion-spray mass spectrometry. However, a theoretically identical sample (36a) produced by an efficient synthetic route (see Scheme 7) revealed that the EGF active constituent must be a large oligomer or polymer of (36). 

Wettability measurements indicated a similar surface energy for PDMS 6 and 17, before and after extraction, close to 27 mj irT, with a dispersive component equal to 27 mJ m and a nondispersive component equal to zero. The identical surface energy and chemical composition showed that the ability of both polymers to interact with the substrate was then theoretically identical. 

As I mentioned, Kim, Lewis, Chalmers, and Jackson all have a rather diflferent picture of theoretical identity than the one sketched here. Focusing on Kim, as I explained earlier Kim sees the role of identities as really a matter of specifying a realizer of the functional role of a mental state rather than capturing the metaphysical nature of a mental state. And this difference reflects a view of reductive explanation in which the role of reduction of, say, water, is not to find the physical ground of water but rather a matter of finding what plays the water role here and now. 

Kim (2005) has objected to pictures of the epistemology of theoretical identity of the sort that I have been sketching. He says that identities such as freezing = lattice formation serve only as rewrite rules, and they are not implicated in the explanatory activity (p. 145). He allows that identities are important in the derivation of explanatory and causal claims mentioned... 

Thinking of reductive physicalism in terms of theoretical identities is more conducive to grounding than the picture of reductive physicalism embedded in the Canberra Plan. But identities are not grounding claims. Identity is symmetrical and grounding is not. The identity claim that... 

The added amount of reagent is fixed well in the aliquot containing the highest total concentration of analyte (substoichiometric regime), but it is in excess in the aliquot containing the lowest total amount of substance. The ratio of the activities of the isolated fractions from the second series (which are theoretically identical) and the activities of the isolated fractions of particular members of the first series are plotted as a function of the dilution increment and the mass of analyte is determined from this plot [2], [73J. [89]. 

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 la/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). 

The role identity plays in these models is similar to the role it plays in Schaffner s model. First of all, cross-theoretic identities form a limiting case. Moreover, for monistic worlds, this limiting case will be the relevant case. Accordingly, cases of reduction relevant for the monist will be identity-cases of this model. Reduction as based on cross-theoretic identities is required to make sense of at least some reductions that go together with correction. The way correction is conceived in New Wave reductionism is captured by Fig. 7.2 ... 

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 ... 

In contrast to creep or stress relaxation, DMA involves applying a sinusoidal strain (or stress) to a sample and measuring the corresponding stress (or strain) developed. Both approaches are theoretically identical. Consider what happens if a sinusoidal strain is applied to an ideal elastic solid ... 

LaPorte, 2010] J. LaPorte. Theoretical identity statements, their truth and their discovery. In Helen Beebee Nigel Sabbarton-Leary (eds.) The Semantics and Metaphysics of Natural Kinds (New York Routledge), pp. 104-124, 2010. 

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