The purpose of this paper is to test the contemporary concept of biological species against some of the problems caused by treating species as spatiotemporally extended entities governed by criteria of persistence, identity, etc. After outlining the general problem of symmetric division in natural objects, I set out some useful distinctions (section 1) and confirm that species are not natural kinds (section 2). Section 3 takes up the separate issue of species definition, focusing on the Biological Species Concept (BSC). Sections 4 and 5 examine the matter of species identity over space and time respectively, as determined by the BSC. Both gradualistic and punctuated equilibrium models of speciation are discussed. In section 6 I argue that the BSC fails to determine adequate criteria for dealing with certain kinds of speciation. Section 7 moves speculatively beyond the BSC to a brief examination of alternatives.

The formal time symmetry of the quantum measurement process is extensively discussed. Then, the origin of the alleged association between a fixed temporal direction and quantum measurements is investigated. It is shown that some features of such an association might arise from epistemological rather than purely physical assumptions. In particular, it is brought out that a sequence of statements bearing on quantum measurements may display intrinsic asymmetric properties, irrespective of the location of corresponding measurements in time t of the Schrödinger equation. The situation of an observer performing two measurements in two opposite directions of t is eventually investigated. Essential differences are found between two descriptions of this situation: the internal one (taking only into account what is recorded in the observer's memory) and the external one (whereby the observer is considered as a quantum system ruled by the Schrödinger equation). Finally, a method allowing several observers to establish a correspondence between their memory sizes is analyzed. The most important facts that usually lead to the associating of a preferential temporal direction with quantum measurements may be inferred from this correspondence.

A plurality of axiomatic systems can be interpreted as referring to one and the same mathematical object. In this paper we examine the relationship between axiomatic systems and their models, the relationships among the various axiomatic systems that refer to the same model, and the role of an intelligent user of an axiomatic system. We ask whether these relationships and this role can themselves be formalized.

Fine has recently proved the surprising result that satisfaction of the Bell inequality in a Clauser-Horne experiment implies the existence of joint probabilities for pairs of noncommuting observables in the experiment. In this paper we show that if probabilities are interpreted in the von Mises-Church sense of relative frequencies on random sequences, a proof of the Bell inequality is nonetheless possible in which such joint probabilities are assumed not to exist. We also argue that Fine's theorem and related results do not impugn the common view that local realists are committed to the Bell inequality.

Support functions s(h,e) = p(h|e) – p(h) are widely used in discussion of explanation, causality and, recently, in connection with the possibility or otherwise of probabilistic induction. With this latter application in view, a rather complete analysis of the variety of support functions, their interrelationships and their “non-deductive” and “inductive” components is presented. With the restriction to two propositions, three variable probabilities are enough to discuss such problems. The analysis is illustrated by graphs, a Venn diagram and by using the Laplace Rule of Succession as an illustrative example. It is concluded that within this framework one cannot prove or disprove the possibility of probabilistic induction.

In this paper, I will defend Paul Feyerabend's claim—that there are some scientific theories that cannot be refuted unless one of their rivals is first confirmed—by criticizing Ronald Laymon's well-known attack on Feyerabend's claim. In particular, I will argue both that the Second Law of Thermodynamics was not refuted before the Kinetic Theory's predictions were confirmed, and that it could not have been refuted without the confirmation of the remarkable predictions of some rival theory.

In this paper I argue against Sober's claim that natural selection does not explain the traits of individuals. Sober argues that natural selection only explains the distribution of traits in a population. My point is that the explanation of an individual's traits involves us in a description of the individual's ancestry, and in an explanation of the distribution of traits in that ancestral population. Thus Sober is wrong, natural selection is part of the explanation of the traits of individuals.

In her “Species Are Individuals” (1985), Mary Williams offers informal arguments and a sketched proof which allegedly show that species are individuals with respect to evolutionary theory. In this paper, I suggest that her informal arguments are insufficient for showing that clans are not sets and that species are individuals. I also argue that her sketched proof depends on three questionable assumptions.

Harvey Siegel's (1985) attempts to revive the traditional epistemological formulation of the rationality of science. Contending that “a general commitment to evidence” is constitutive of method and rationality in science, Siegel advances its compatibility with specific, historically attuned formulations of principles of evidential support as a virtue of his aprioristic candidate for science's rationality. In point of fact, this account is compatible with virtually any formulation of evidential support, which runs afoul of Siegel's claim that scientific beliefs must be evaluated with respect to their rationality. The unwelcome consequence of Siegel's view is that most any belief, scientific or pseudoscientific, can be defended as rational. Indeed, if we want to furnish a warrant for rational choice, we must turn to the very historically informed principles of evidential support that are dismissed by Siegel as providing a misleading portrait of science's rationality.

In his (1988), Brian Baigrie criticizes my earlier discussion of the rationality of science (Siegel 1985). In this response, I argue that (1) Baigrie misses the point of my tripartite distinction between different questions one can ask about science's rationality, (2) Baigrie's argument that the history of the development of methodological principles is crucial to philosophical discussion of the rationality of science is flawed, and (3) Baigrie's charge that my view is “anemic” rests on a failure to appreciate the point of my tripartite distinction.

It is argued that models of H. Jeffreys' axioms of probability (Jeffreys [1939] 1967) are not monotone even with I. J. Good's proposed modification (Good 1950). Hence the additivity axiom seems essential to a theory of probability as it is with Kolmogorov's system (Kolmogorov 1950).

In a recent commendable article, Quentin Smith (1987) exposes fatal flaws in several recent attempts to demonstrate that it is logically impossible for the past to be infinite. However, his analysis of one of these flawed arguments—involving an interesting version of Russell's “Tristram Shandy paradox”—is off the mark, as I show in this paper.

N. Maxwell (1985) has claimed that special relativity and “probabilism” are incompatible; “probabilism” he defines as the doctrine that “the universe is such that, at any instant, there is only one past but many alternative possible futures”. Thus defined, the doctrine is evidently prerelativistic as it depends on the notion of a universal instant of the universe. In this note I show, however, that there is a straightforward relativistic generalization, and that therefore Maxwell's conclusion that the special theory of relativity should be amended is unwarranted. I leave open the question whether or not probabilism (or the related doctrine of the flow of time) is true, but argue that the special theory of relativity has no fundamental significance for this question.

The usual objections to infinite numbers, and classes, and series, and the notion that the infinite as such is self-contradictory, may ... be dismissed as groundless. There remains, however, a very grave difficulty, connected with the contradiction [of the class of all classes not members of themselves]. This difficulty does not concern the infinite as such, but only certain very large infinite classes.

—Bertrand Russell, The Principles of Mathematics, p. 362