Online research in philosophy

The theory of random propositions is a theory of confirmation that contains the Bayesian and Shafer—Dempster theories as special cases, while extending both in ways that resolve many of their outstanding problems. The theory resolves the Bayesian problem of the priors and provides an extension of Dempster's rule of combination for partially dependent evidence. The standard probability calculus can be generated from the calculus of frequencies among infinite sequences of outcomes. The theory of random propositions is generated analogously from the calculus of frequencies among pairs of infinite sequences of suitably generalized outcomes and in a way that precludes the inclusion of contrived orad hoc elements. The theory is also formulated as an uninterpreted calculus.

I sketch a new objective interpretation of probability, called "mechanistic probability", and more specifically what I call "far-flung frequency (FFF) mechanistic probability". FFF mechanistic probability is defined in terms of facts about the causal structure of devices and certain sets of collections of frequencies in the actual world. The relevant kind of causal structure is a generalization of what Strevens (2003) calls microconstancy. Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories. It at least partly explains stable frequencies, which will usually be close to the values of corresponding mechanistic probabilities; FFF mechanistic probability thus satisfies what in my view is a core desideratum for any objective interpretation. However, FFF mechanistic probabilities are not single case probabilities, and FFF mechanistic probability explains stable frequencies directly rather than by inference from combinations of single case probabilities.

Evolutionary models can explain the dynamics of populations, how genetic, genotypic, or phenotypic frequencies change with time. Models incorporating chance, or drift, predict specific patterns of change. These are illustrated using classic work on blood types by Cavalli-Sforza and his collaborators in the Parma Valley of Italy, in which the theoretically predicted patterns are exhibited in human populations. These data and the models display properties of ensembles of populations. The explanatory problem needs to be understood in terms of how likely an observed change, in either a population or an ensemble, would be under drift alone; this is fundamentally a matter of chance. Understood in this way, issues of drift and chance undercut most recent philosophical, but not biological, discussions of the role of "genetic drift.".

Variational evolutionary theory as advocated by Darwin is not a single theory, but a bundle of related but independent theories, namely: (a) variational evolution; (b) gradualism rather than large leaps; (c) processes of phyletic evolution and of speciation; (d) causes for the formation of varying individuals in populations and for the action of selective agents; and (e) all organisms evolved from a common ancestor. The first four are nomological-deductive explanations and the fifth is historical-narrative. Therefore evolutionary theory must be divided into nomological and historical theories which are both testable against objective empirical observations. To be scientific, historical evolutionary theories must be based on well corroborated nomological theories, both evolutionary and functional. Nomological and general historical evolutionary theories are well tested and must be considered as strongly corroborated scientific theories. Opponents of evolutionary theory are concerned only with historical evolutionary theories, having little interest in nomological theory. Yet given a well corroborated nomological evolutionary theory, historical evolutionary theories follow automatically. If understood correctly, both forms of evolutionary theories stand on their own as corroborated scientific theories and should not be labeled as facts.

A law about frequencies would be a law of nature that imposes a constraint on one or more (actual, global) frequencies. On any of the leading philosophical approaches to laws of nature, there could be laws about frequencies. Hypotheses that posit laws about frequencies turn out to behave very similarly to hypotheses that posit corresponding laws about probabilities or chances -- they make the same predictions, provide similar explanations, and are confirmed or disconfirmed by empirical evidence in the same ways. This makes it interesting to consider the possibility of interpreting probabilistic laws from scientific theories as laws about frequencies. This is surprising proposal, but I argue that the resulting view (which I call 'nomic frequentism') is able to overcome all of the standard objections to frequentist interpretation of objective probabilities.

I argue that results from foraging theory give us good reason to think some evolutionary phenomena are indeterministic and hence that evolutionary theory must be probabilistic. Foraging theory implies that random search is sometimes selectively advantageous, and experimental work suggests that it is employed by a variety of organisms. There are reasons to think such search will sometimes be genuinely indeterministic. If it is, then individual reproductive success will also be indeterministic, and so too will frequency change in populations of organisms employing such search.

This paper investigates the conception of causation required in order to make sense of natural selection as a causal explanation of changes in traits or allele frequencies. It claims that under a counterfactual account of causation, natural selection is constituted by the causal relevance of traits and alleles to the variation in traits and alleles frequencies. The “statisticalist” view of selection (Walsh, Matthen, Ariew, Lewens) has shown that natural selection is not a cause superadded to the causal interactions between individual organisms. It also claimed that the only causation at work is those aggregated individual interactions, natural selection being only predictive and explanatory, but it is implicitly committed to a process-view of causation. I formulate a counterfactual construal of the causal statements underlying selectionist explanations, and show that they hold because of the reference they make to ecological reliable factors. Considering case studies, I argue that this counterfactual view of causal relevance proper to natural selection captures more salient features of evolutionary explanations than the statisticalist view, and especially makes sense of the difference between selection and drift. I eventually establish equivalence between causal relevance of traits and natural selection itself as a cause.

Philosophers have explored objective interpretations of probability mainly by considering empirical probability statements. Because of this focus, it is widely believed that the logical interpretation and the actual-frequency interpretation are unsatisfactory and the hypothetical-frequency interpretation is not much better. Probabilistic assertions in pure mathematics present a new challenge. Mathematicians prove theorems in number theory that assign probabilities. The most natural interpretation of these probabilities is that they describe actual frequencies in finite sets and limits of actual frequencies in infinite sets. This interpretation vindicates part of what the logical interpretation of probability aimed to establish.

Biologists often define evolution as a change in allele frequencies. Consideration of the evolution of the pocket mouse will show that it is possible to have evolution without any change in the allele frequencies in a population (through change in the genotype frequencies). The implications of this for genic selectionism are then discussed. Sober and Lewontin (1982) have constructed an example to demonstrate the blindness of genic selectionism in certain cases. Sterelny and Kitcher (1988) offer a defense against these arguments which assumes a conventionalist approach to populations. The example considered here will be shown to offer a more plausible and far-reaching argument against the view that alleles can always be seen as the units of selection.

When applied to a family of sets, the term differentiation designates a measure of the totality of those members which appear in only one of the sets. This basic set theoretic concept involves the formation of intersections, unions, and complements of sets. However, populations as special kinds of sets may share types, but they do not share the carriers of these types; intersections of different populations are thus always empty. The resulting conceptual dilemma is resolved by considering the joint representation of members of different populations that have the same type; populations then intersect with respect to joint representation of types. Two forms of representation reflect relative and absolute characteristics of differentiation by accounting for the distributions of types as relative frequencies within populations (as is commonly done) and as absolute frequencies (including effects of population sizes on differentiation), respectively. Corresponding classes of differentiation measures are developed, and existing measures are discussed in relation to these classes. In particular, the affinity of the measurement of distances between populations and the special case of differentiation of two-population families is examined in order to distinguish between the notions of distance and differentiation.