The metaphysical question

Explanation, for the unificationist, begins with the set of accepted beliefs K.

K is identified with the current state of the scientific knowledge of a discipline at a given moment in time. The set of beliefs K, then, can be identified with classical Newtonian mechanics, Mendelian genetics, the kinetic theory of gases, and so on.²⁵ Given the set of beliefs K, the first problem for the unificationist consists in identifying the set of derivations that best systematizesK, called theexplanatory store over K, E(K).²⁶

The explanatory store E(K) is responsible for carrying out the derivation of a

description of a phenomenon. The systematization criteria for entrenching E(K) is, in Kitcher’s own words, “a set of derivations that makes the best tradeoff between minimizing the number of patterns of derivation employed and maximizing the num-ber of conclusions generated” (Kitcher, 1989, 432). E(K), then, explains following the principle of unifying a multiplicity of phenomena using the smallest number of argument patterns. In plain words, E(K) is the minimal set of schemata that best captures the natural kinds and objective dependencies used for the scientific description of a phenomenon. Explanation, then, consists in exhibiting how such a phenomenon shares certain patterns with a greater theoretical framework such as a model or a theory. Although the terminology might be a bit unfamiliar at this point, these definitions will become clearer as I advance in the analysis of unificatory explanation.

Let me begin by specifying what constitutes the explanatory storeE(K). Kitcher considers four elements, namely:

1. Schematic sentence: “an expression obtained by replacing some, but not neces-sarily all, the nonlogical expressions occurring in a sentence by dummy letters”

(Kitcher, 1989, 432). To use Kitcher’s own example, the sentence “Organisms homozygous for the sickling allele develop sickle cell anemia” (Kitcher, 1989, 432) is associated with a number of schematic sentences, including “Organisms homozygous for A develop P” (Kitcher, 1989, 432) and “For all x, if x is O and Athen x isP” (Kitcher, 1989, 432).

(a) Schematic argument: “is a sequence of schematic sentences” (Kitcher, 1989, 432).

2. Filling instructions: (for a schematic sentence) “a set of directions for replac-ing the dummy letters of the schematic sentence, such that, for each dummy letter, there is a direction that tells us how it should be replaced. For the schematic sentence ‘Organisms homozygous for A develop P,’ the filling in-structions might specify thatA be replaced by the name of an allele andP by the name of a phenotypic trait” (Kitcher, 1989, 432). Let it be noted that the filling instructions are semantic in nature, rather than syntactic. The terms that replace a particular dummy letter need not have precisely the same log-ical form, but they must belong to a similar semantic category. For instance, a filling instruction for a pattern based on Newtonian mechanics must spec-ify that the term to replace a dummy letter refer to a body or to a position within a Cartesian coordinate system. The filling instructions, then, have the

important function of facilitating the semantic connection between schematic sentences and the world;

3. Classification: (for a schematic argument) “a set of statements describing the inferential characteristics of the schematic argument: it tells us which terms of the sequence are to be regarded as premises, which are inferred from which, what rules of inference are used, and so forth” (Kitcher, 1989, 432)

4. The Comments section plays the fundamental role of being a ‘repository’ for the information that could not be rendered as a schematic sentence but is still relevant for a successful explanation. Strictly speaking, the comments section is not part of the general argument pattern, understood as “a triple consist-ing of a schematic argument, a set of sets of fillconsist-ing instructions, one for each term of the schematic argument, and a classification for the schematic argu-ment” (Kitcher, 1989, 432). However, it does play a relevant role in the overall explanation of phenomena. For instance, Kitcher presents two examples on how to explain hereditary phenotypic traits through pedigree using Mendelian Genetics: ‘Mendel’ and ‘Refined Mendel.’ The first explanatory pattern is limited to one locus and two allele cases with complete dominance. The sec-ond explanatory pattern fixes this limitation by producing a more complete schema that covers a broader class of cases. ‘Refined Mendel,’ then, overcomes the limitations of the first schemata, explaining more phenomena with fewer patterns. Kitcher later asserts that ‘Refined Mendel’ “does not take account of linkage and recombination. The next step is to build these in” (Kitcher, 1989, 440) indicating, in this way, that the comments section includes the ex-planatory limitations of the general argument pattern, future changes to be implemented, further considerations, and the like.

The comments section brings up an important question that can be addressed now.

That is, what are the criteria for entrenching thebest systematization ofK? In other words, what are the criteria that lodges ‘Refined Mendel’ as more explanatory than

‘Mendel’? Kitcher’s solution is elegant, although a bit cumbersome, and consists in the evaluation of the unifying power of each pattern that has been employed in the systematization ofK.

The solution can be outlined in the following way: find all the acceptable argu-ments that are relative toK (e.g., all the theories, principles, laws, etc., of a scientific theory) and call it the ‘⌃i = the set of arguments overK.’ Then, from each⌃i, find

generating set.’ The next step is to select the set with the greatest unifying power and call it the ‘Bi = the basis of K.’ The basis with the greatest unifying power is the explanatory store E(K) that best systematizes our corpus of beliefs K (see Figure 5.1). This is the reason why ‘Refined Mendel’ is a more suitable explanatory store E(K) than ‘Mendel’: the former has greater unifying power than the latter (i.e., it explains more phenomena with fewer patterns).²⁸

Figure 5.1: If B_k is the basis with the greatest unifying power then E(K) = ⌃_k (Kitcher, 1981, 520)

Systematizations, sets of arguments accept-able relative toK.

Complete generating sets. ⇧i,j is a generat-ing set for⌃_iwhich is complete with respect to K.

Bases. B_i is the basis for ⌃_i, and is selected as the best of the⇧_i,j on the basis of unifying power. (Kitcher, 1981, 520)

Admittedly, the process of finding the best E(K) is a bit cumbersome. For this reason I will assume that the explanatory storeE(K)used for explaining phenomena is, indeed, the best possible systematization of K. With this assumption in place, there is no need to search for the basis with the greatest unifying power. In fact, Kitcher himself makes the same assumptions, all of which I take as unproblematic.²⁹ Choosing the best systematization of K is related to the changes on the corpus of scientific beliefs, and on whether such changes affect the unificationist theory of explanation.³⁰ The general outline for the explanatory process, however, is the same for a fixed set of beliefs as it is for a changing one. Therefore, and for the sake of simplicity, I will focus my efforts on a fixed body of knowledgeK.

To explain, then, consists in deriving descriptions of different phenomena using as few and as stringent argument patterns as possible. The fewer the patterns used, the more stringent they become. The greater the range of different conclusions derived, the more unified the phenomena are. And the more we use the same argument patterns over and over again, the simpler and more transparent the world appears to us. Kitcher puts this idea in the following way: “E(K) is a set of derivations that

make the best tradeoff between minimizing the number of patterns of derivation employed and maximizing the number of conclusions generated” (Kitcher, 1989, 432)

Let me illustrate these claims with the example of explaining the expected dis-tribution of progeny phenotypes in a cross between two individuals using Mendelian genetics. Kitcher presents the example in the following way:

Classical genetics is centrally focused on (though by no means confined to) a family of problems about the transmission of traits. I shall call them pedi-gree problems, for they are problems of identifying the expected distributions of traits in cases where there are several generations of organisms related by specified connections of descent. The questions that arise can take any of a number of forms: What is the expected distribution of phenotypes in a partic-ular generation? Why should we expect to get that distribution? What is the probability that a particular phenotype will result from a particular mating?, and so forth. Classical genetics answers such questions by making hypothe-ses about the relevant genes, their phenotypic effects, and their distribution among the individuals in the pedigree. [...]

(1) There are two alleles A,a. A is dominant, arecessive.

(2) AA(andAa) individuals have traitP,aa individuals have trait P⁰ (3) The genotypes of the individuals in the pedigree are as follows: i₁ is G₁, i₂ is G₂, ...,i_N isG_N. {(3) is accompanied by a demonstration that (2) and (3) are consistent with the phenotypic ascriptions in the pedigree.}

(4) For any individual x and any alleles yz if x has yz then the probability that xwill transmit y to any one of its springs is ¹₂.

(5) The expected distribution of progeny genotypes in a cross betweeni_jandi_k is D; the expected distribution of progeny genotypes in a cross ... {continued for all pairs for which crosses occur}

(6) The expected distribution of progeny phenotypes in a crossi_j and i_k isE; the expected distribution of progeny phenotypes in a cross ... {continued for all pairs in which crosses occur}

Filling instructions: A,a are to be replaced with names of alleles, P, P⁰ are to be replaced with names of phenotypic traits,i₁, i₂, ..., i_N are to be replaced with names of individuals in the pedigree, G₁, G₂, ..., G_N are to be replaced with names of allelic combinations (e.g., AA, Aa, or aa), D is replaced with an explicit characterization of a function that assigns relative frequencies to genotypes (allelic combinations), andEis to be replaced with an explicit char-acterization of a function that assigns relative frequencies to phenotypes.

Classification: (1), (2), and (3) are premises; the demonstration appended to (3) proceeds by showing that, for each individual i in the pedigree, the phe-notype assigned to iby the conjunction of (2) and (3) is that assigned in the pedigree; (4) is a premise; (5) is obtained from (3) and (4) using the principles of probability; (6) is derived from (5) and (2).

4. Comments: Mendel is limited to one locus, two allele cases with complete dominance. We can express this limitation by pointing out that the pattern above does not have a correct instantiation for examples which do not conform to these conditions. By refining Mendel, we produce a more complete schema, one that has correct instantiations in a broader class of cases. (Kitcher, 1989, 439)

This explanatory pattern shows how an explanation-seeking question about the transmission of traits through pedigrees is addressed within the genetic theory.

Specifically, we can answer questions about why we should expect to find a particular distribution in a specified generation. Explanation then consists in exhibiting (via derivation) how patterns (such as the distribution of progeny phenotypes) can be subsumed under a unified framework such as Mendelian genetics.³¹ In more general terms, the process of explaining a phenomenon consists in exhibiting how natural kinds, objective causal relationships, natural necessities, and the like of that phe-nomenon can be derived and therefore unified into a larger theoretical framework.

Let us note that the derivation must also fulfill some conditions in order to be ex-planatory. Kitcher indicates that aparticular derivation instantiates an explanatory store (or general argument pattern) in case that:

1. The derivation has the same number of terms as the schematic argument of the general argument pattern;

2. Each sentence or formula in the derivation can be obtained from the cor-responding schematic sentence in accordance with the filling instructions for that schematic sentence;

3. The terms of the derivation have the properties assigned by the classification to corresponding members of the schematic argument. (Kitcher, 1989, 433)

These conditions are set as the epistemic guarantee that the derivation belongs to the explanatory store and, as such, is explanatory. Kitcher’s basic strategy is to show that the derivations we regard as successful explanations are instances of patterns that, taken together, ‘score’ better than the patterns instantiated by the derivations we regard as defective explanations. Showing that a particular derivation is a good or successful explanation is, then, a matter of showing that it belongs to the explana-tory storeE(K). Similarly, explanation in computer simulations will also consist in showing how a particular simulated phenomenon belongs to the explanatory store E(K). However, and before entering into the discussion on explanation in computer simulations, let me finish the analysis of the unificationist account by addressing Kim’s epistemic question.