Although the introduction of the modern axiomatic method in physics is attributed to Hilbert, it is only recently that physicists and mathematicians have applied it significantly, i.e. on a basis extensive enough to promise fruitful results. Carnap, for one, stresses the importance of the axiomatic method, yet he considers its application in physics as a task for the future.

I analyze the two main theses of Helmholtz's “The Applicability of the Axioms to the Physical World,” in which he argued that the axioms of Euclidean geometry are not, as his neo-Kantian opponents had argued, binding on any experience of the external world. This required two argumentative steps: 1) a new account of the structure of our representations which was consistent both with the experience of our (for him) Euclidean world and with experience of a non-Euclidean one, and 2) a demonstration of why geometric propositions are essentially connected to material and temporal aspects of experience. The effect of Helmholtz's discussion is to throw into relief an intermediate category of metrological objects—objects which are required for the properly theoretical activity of doing physical science (in this sense, a priori requirements for doing science), all while being recognizably contingent aspects of experience.

Agreement between “independent” measurements of a theoretically posited quantity is intuitively compelling evidence that a theory is, loosely speaking, on the right track. But exactly what conclusion is warranted by such agreement? I propose a new account of the phenomenon’s epistemic significance within the framework of Bayesian epistemology. I contrast my proposal with the standard Bayesian treatment, which lumps the phenomenon under the heading of “evidential diversity.”

Professor Feigl's admirably lucid and concise appraisal of the major considerations which are still significant in the controversy between realism and phenomenalism includes the important reminder that the problem at hand should be viewed as concerning, not the truth or falsity of two conflicting hypotheses, but rather the comparative adequacy of two alternative proposals for the rational reconstruction of scientific knowledge. Feigl advocates the approach of semantic realism in preference to a phenomenalistic type of reconstruction on the grounds that in his critical examination, the latter has been “found wanting,” whereas semantic realism—and only semantic realism—can provide a satisfactory systematic account of the meaning and the experiential foundation of scientific hypotheses. While I fully agree with Feigl's general appraisal of the issues involved, I have doubts as to the superiority of the proposed realistic interpretation, and I should like to state these here in outline.

Physics presents us with a symphony of natural constants: $G$, ℏ, $c$, and so forth. Up to this point, constants have received comparatively little philosophical attention. In this article, I provide an account of dimensionful constants, in particular the gravitational constant. I propose that they represent interquantity structure in the form of relations between quantities with different dimensions. I use this account of $G$ to settle a debate over whether mass scalings are symmetries of Newtonian gravitation. I argue that they are not, but only if we interpret mass anti-quidditistically. This is analogous to anti-haecceitism in the presence of spacetime symmetries.

Frank has recently argued for an information-theoretic interpretation of natural selection. This interpretation is based on the identification of a measure related to the Malthusian parameter (for population change) with the Jeffreys divergence between the present allelic distribution of the population and that distribution in the next generation. It is pointed out in this analysis that this identification only holds if the mean fitness of the population is a constant, that is, there is no selection. This problem is used to argue for the superiority of the standard dynamical interpretation of natural selection over its information-theoretic counterpart.

The axiom of comparability has been a fundamental part of mathematical choice theory from its beginnings. This axiom was a natural first assumption for a theory of choice originally constructed to explain decision making where other assumptions such as continuous divisibility of choice spaces could legitimately also be made. Once the generality of application of formal choice theory becomes apparent, it also becomes apparent that both continuity assumptions and the axiom of comparability may be unduly restrictive and lead to the neglect of decision situations which are important and which can be handled on a modified axiom set. These considerations bear on the philosophical analysis of the concept of rational decision.

The science of the 19th and early 20th century permitted the view that all human experience is subject to the deterministic laws of physics. Reality was conformable with these laws, and the laws could be used to designate what is real.

The controversy which has raged between those who accept Aristotelian Logic and those who reject it, seems to continue. It is, I believe, advisable to consider the arguments on both sides. Modern Logicians for the most part insist that Aristotelian Logic breaks down, i.e. it is not true for all meanings of the terms. On the other hand there are those who insist on the validity of Aristotelian Logic claiming that those values for which it fails are not permissible values. But there is one who stands almost entirely alone in his position—namely Professor H. B. Smith—who maintains that Aristotelian Logic breaks down because and only because its interpretation into Boolean terms has been accomplished by means of a definition that is not forced upon us and which, since it gives up desirable principles, is to be rejected.

This article unpacks a particular use of ‘cases’ within developmental biology, namely as a means of describing the typical or canonical patterns of phenomena. The article explores how certain cases have come to be established within the field and argues that although they were initially selected for reasons of convenience or ease of experimental manipulation, these cases come to serve as key reference points within the field because of the epistemological structures imposed on them by the scientists using them and, hence, become usable in a wider variety of circumstances including future theory development.

Understanding the role mechanistic constraints play in shaping evolution can relieve the tension between the generally accepted intuition that there are no strict laws in biology and empirical findings showing that evolutionary processes are biased toward preferred outcomes. Mechanistic constraints explain why some evolutionary outcomes are more probable than others and allow for predictions in specific lineages. At the same time, mechanistic constraints are neither necessary nor universal in the way laws are traditionally characterized: they remain contingent on the past evolution of the biological mechanisms underpinning them and only constrain the future evolution of the organisms possessing them.

I explore the evolution of strategies in an Augmented Stag Hunt game that adds a punishing strategy to the ordinary Stag Hunt strategies of cooperating, which aims for optimality, and defecting, which “plays it safe.” Cooperating weakly dominates punishing and defecting is the unique evolutionarily stable strategy (ESS). Nevertheless, for a wide class of Augmented Stag Hunts, polymorphic strategies combining punishing and cooperating collectively have greater attracting power for replicator dynamics than that of the ESS. The analysis here lends theoretical support to the altruistic punishment hypothesis in the social sciences.

“Accessibility” is a crucial concept of possible worlds semantics. The simplest approach to accessibility is the “magical theory” that construes this relation as analogous to spatial or temporal relations. In this paper I give a nonmagical structural account of the accessibility relation that can be used to give a necessitarian account of kinds and laws. Laws are characterized in a structural way as stable invariants of the world's gestalt. Finally, I point out how the structural approach can be embedded in a general representational theory of modality.

1. Introduction. Attempts to utilize the probability calculus to prove or disprove various inductive or inductive skeptical theses are, I believe, highly problematic. Inductivism and inductive skepticism are substantive (logically consistent) philosophical positions that do not allow of merely formal proofs or disproofs. Often the problems with particular alleged formal proofs of inductive or inductive sceptical theses turn on subtle technical considerations. In the following I highlight such considerations in pointing out the flaws of two proofs, one an alleged proof of an inductive sceptical conclusion due to Karl Popper, the other an alleged proof of an inductivist thesis originally due to Harold Jeffreys and later advocated by John Earman. Surprisingly, in examining Popper's argument it is shown that certain apparently weak premises, often embraced by both inductivists and deductivists, lend themselves to inductive conclusions. However it is argued that those premises are still philosophically substantive and not amenable to a purely formal demonstration. The lesson to be learnt here is twofold. First, we need to be very careful in determining which formal theses entail, and which are entailed by, inductive skepticism and inductivism. Second, we need to take great care in laying out and examining the assumptions presumed in formal arguments directed for and against such formal theses. In a follow up article I will consider various attempts by David Stove and Karl Popper and David Miller to identify the exact content of inductive skepticism and propose a new identification based on the theory of content developed in Gemes 1994. Finally I will compare this new version with that proposed recently in Alberto Mura 1990.

When scientists are asked to give expert advice on risk-related questions, such as the authorization of medical drugs, deliberation often does not eliminate all disagreements. I propose to model these remaining discrepancies as differences in risk assessments and/or in risk acceptability thresholds. The normative question I consider, then, is how the individual expert views should best be aggregated. I discuss what “best” could mean, with an eye to some robustness considerations. I argue that the majority rule, which is currently often used in expert panels, has significant drawbacks.

The first part deals with the problem of the external form of ostensive definition. It is concluded that the definition statement is not complete. The proper form of this statement is not a sentence, but a sentential function, namely a sentential function of the type: “IIx [N(x) = x is in the respect R and in the degree D such as A, B ... and not such as K, L ...]” where “N” stands for the term being defined.

Thus the ostensive definition informs about the criteria of applicability of the defined term in a partial way only, and the rest must be supplied by the addressee for whom the given definition was destined.

In the second part the conditions are analysed on which depends the possibility of solving that problem, and consequently the conditions on which depend the informational value and the efficacy of ostensive definition. The concluding remarks deal with the properties of the terms introduced by the ostensive method.

Biology deals, notoriously, with complex systems. In discussing biological methodology, all three papers in this symposium honor the complexity of biological subject matter by preferring models and theories built to reflect the details of complex systems to models based on broad general principles or laws. Rheinberger's paper, the most programmatic of the three, provides a framework for the epistemology of discovery in complex systems. A fundamental problem is raised for Rheinberger's epistemology, namely, how to understand the referential continuity of the theoretical terms and concepts employed in typical case studies involving complex systems.

When can a Bayesian investigator select an hypothesis H and design an experiment (or a sequence of experiments) to make certain that, given the experimental outcome(s), the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspective of an onlooker who agrees with the investigator about the statistical model for the data but who holds a different prior probability for the statistical parameters of that model. We consider, specifically, one-sided and two-sided statistical hypotheses involving i.i.d. Normal data with conjugate priors. In a concluding section, using an “improper” prior, we illustrate how the preceding results depend upon the assumption that probability is countably additive.