This paper develops an account of explanation in biology which does not involve appeal to laws of nature, at least as traditionally conceived. Explanatory generalizations in biology must satisfy a requirement that I call invariance, but need not satisfy most of the other standard criteria for lawfulness. Once this point is recognized, there is little motivation for regarding such generalizations as laws of nature. Some of the differences between invariance and the related notions of stability and resiliency, due respectively to Sandra Mitchell and Brian Skyrms, are explored.

The problem of scientific disregard is the problem of accounting for why some putative theories that appear to be well-supported by empirical evidence nevertheless play no role in the scientific enterprise. Laudan and Leplin suggest (and Hoefer and Rosenberg concur) that at least some of these putative theories fail to be genuine theoretical rivals because they lack some non-empirical property of theoreticity. This solution also supports their repudiation of the thesis of underdetermination. I argue that the attempt to provide criteria of theoreticity fails, that there is a Bayesian solution to the problem of scientific disregard that fares better, and that this successful solution supports a distinctively Bayesian version of the underdetermination thesis.

Following Nancy Cartwright and others, I suggest that most (if not all) theories incorporate, or depend on, one or more idealizing assumptions. I then argue that such theories ought to be regimented as counterfactuals, the antecedents of which are simplifying assumptions. If this account of the logical form of theories is granted, then a serious problem arises for Bayesians concerning the prior probabilities of theories that have counterfactual form. If no such probabilities can be assigned, then posterior probabilities will be undefined, as the latter are defined in terms of the former. I argue here that the most plausible attempts to address the problem of probabilities of conditionals fail to help Bayesians, and, hence, that Bayesians are faced with a new problem. In so far as these proposed solutions fail, I argue that Bayesians must give up Bayesianism or accept the counterintuitive view that no theories that incorporate any idealizations have ever really been confirmed to any extent whatsoever. Moreover, as it appears that the latter horn of this dilemma is highly implausible, we are left with the conclusion that Bayesianism should be rejected, at least as it stands.

Many areas of science develop by discovering mechanisms and role functions. Cummins' (1975) analysis of role functions—according to which an item's role function is a capacity of that item that appears in an analytic explanation of the capacity of some containing system—captures one important sense of “function” in the biological sciences and elsewhere. Here I synthesize Cummins' account with recent work on mechanisms and causal/mechanical explanation. The synthesis produces an analysis of specifically mechanistic role functions, one that uses the characteristic active, spatial, temporal, and hierarchical organization of mechanisms to add precision and content to Cummins' original suggestion. This synthesis also shows why the discovery of role functions is a scientific achievement. Discovering a role function (i) contributes to the interlevel integration of multilevel mechanisms, and (ii) provides a unique, contextual variety of causal/mechanical explanation.

In this paper we examine the following problems: How many concepts of function are there in biology, social science, and technology? Are they logically related and if so, how? Which of these function concepts effect a functional explanation as opposed to a mere functional account? What are the consequences of a pluralist view of functions for functionalism? We submit that there are five concepts of function in biology, which are logically related in a particular way, and six function concepts in social science and technology. Only two of them may help effect a genuine functional explanation. Finally, our synthetic approach allows us to distinguish four different varieties of functionalism in biology, psychology, social science, and technology: formalist, black boxist, adaptationist, and teleological. And only one of them is explanatory in the strong sense defended here.

How does deductive logic constrain probability? This question is difficult for subjectivistic approaches, according to which probability is just strength of (prudent) partial belief, for this presumes logical omniscience. This paper proposes that the way in which probability lies always between possibility and necessity can be made precise by exploiting a minor theorem of de Finetti: In any finite set of propositions the expected number of truths is the sum of the probabilities over the set. This is generalized to apply to denumerable languages. It entails that the sum of probabilities can neither exceed nor be exceeded by the cardinalities of all consistent and closed (within the set) subsets. In general any numerical function on sentences is said to be logically coherent if it satisfies this condition. Logical coherence allows the relativization of necessity: A function p on a language is coherent with respect to the concept T of necessity iff there is no set of sentences on which the sum of p exceeds or is exceeded by the cardinality of every T-consistent and T-closed (within the set) subset of the set. Coherence is easily applied as well to sets on which the sum of p does not converge.

Probability should also be relativized by necessity: A T-probability assigns one to every T-necessary sentence and is additive over disjunctions of pairwise T-incompatible sentences. Logical T-coherence is then equivalent to T-probability: All and only T-coherent functions are T-probabilities.

Many of the “counterintuitive” features of relativistic quantum field theory have their formal root in the Reeh-Schlieder theorem, which in particular entails that local operations applied to the vacuum state can produce any state of the entire field. It is of great interest then that I. E. Segal and, more recently, G. Fleming (in a paper entitled “Reeh-Schlieder meets Newton-Wigner”) have proposed an alternative “Newton-Wigner” localization scheme that avoids the Reeh-Schlieder theorem. In this paper, I reconstruct the Newton-Wigner localization scheme and clarify the limited extent to which it avoids the counterintuitive consequences of the Reeh-Schlieder theorem. I also argue that there is no coherent interpretation of the Newton-Wigner localization scheme that renders it free from act-outcome correlations at spacelike separation.