Clark Glymour

The use of ceteris paribus clauses in philosophy and in the sciences has a long and fascinating history. Persky (1990) traces the use by economists of ceteris paribus clauses in qualifying generalizations as far back as William Petty’s Treatise of Taxes and Contributions (1662). John Cairnes’ The Character and Logical Method of Political Economy (1857) is credited with enunciating the idea that the conclusions of economic investigations hold “only in the absence of disturbing causes”.1 His Leading Principles (1874) contains the classic example of a ceteris paribus law: “The rate of wage, other things being equal, varies inversely with the supply of labour”. Carines’ ideas were popularized by Alfred Marshall in his Principles of Economics (1890) where he argued for a methodology that involved holding disturbing causes “in a pound called Caeteris Paribus”. It is unclear when the notion of ceteris paribus laws made its appearance in the philosophical literature; but in the nineteenth century it is to be found in Mill’s System of Logic (1843), and in the twentieth century it gained prominence in the Hempel-inspired debates of the 1950’s over the role of general laws in historical explanations, albeit under other labels such as quasi-laws (Rescher) or grounded generalizations (Scriven).

Through their transcript products genes regulate the rates at which an immense variety of transcripts and subsequent proteins occur. Understanding the mechanisms that determine which genes are expressed, and when they are expressed, is one of the keys to genetic manipulation for many purposes, including the development of new treatments for disease. Viewing each gene in a genome as a distinct variable that is either on or off, or more realistically as a continuous variable, the values of some of these variables influence the values of others through the regulatory proteins they express, including, of course, the possibility that the rate of expression of a gene at one time may, in various circumstances, influence the rate of expression of that same gene at a later time. If we imagine an arrow drawn from each gene expression variable at a given time to a gene variable whose expression it influences a short while after, the result is a network, technically a directed acyclic graph. For example, the DAG in Figure 1 is a representation of a system in which the expression level of gene G1 at time 1 ) causes the expression level of G2, which in turn causes the expression level of G3. The arrows in Figure 1 which do not have a variable at their tails are “error terms” which represent all of the causes of a variable other than the ones explicitly represented in the DAG. The DAG describes more than associations—it describes causal connections among gene expression rates. A shock to a cell—by mutation, heating, chemical treatment, etc. may alter the DAG describing the relations among gene expressions, for example by activating a gene that was otherwise not expressed, producing a cascade of new expression effects. Although “knockout” experiments can reveal some of the underlying causal network of gene expression levels, unless guided by information from other sources, such experiments are limited in how much of the network structure they can reveal, due to the sheer number of possible combinations of experimental manipulations of genes necessary to reveal the complete causal network. Recent developments have made it possible to compare quantitatively the expression of tens of thousands of genes in cells from different sources in a single experiment, and to trace gene expression over time in thousands of genes simultaneously. cDNA microarrays are already producing extensive data, much of it available on the web. Thus there are calls for analytic software that can be applied to microarray and other data to help infer regulatory networks. In this paper we will review current techniques that are available for searching for the causal relations between variables, describe algorithmic and data gathering obstacles to applying these techniques to gene expression levels, and describe the prospects for overcoming these obstacles

The notion of reduction in the natural sciences has been assimilated to the notion of inter-theoretical explanation. Many philosophers of science (following Nagel) have held that the apparently ontological issues involved in reduction should be replaced by analyses of the syntactic and semantic connections involved in explaining one theory on the basis of another. The replacement does not seem to have been especially successful, for we still lack a plausible account of inter-theoretical explanation. I attempt to provide one