Stephen George Simpson. with definition 1.2.3 and the discussion following it. For example, taking 90(n) to be the formula n §E Y, we have an instance of comprehension, VYEIXVn(n€X<—>n¢Y), asserting that for any given set Y there exists a ...

We have argued elsewhere that: (A) Natural selection is not a cause of evolution. (B) A resolution-of-forces (or vector addition) model does not provide us with a proper understanding of how natural selection combines with other evolutionary influences. These propositions have come in for criticism recently, and here we clarify and defend them. We do so within the broad framework of our own “hierarchical realization model” of how evolutionary influences combine.

The concept of fitness began its career in biology long before evolutionary theory was mathematized. Fitness was used to describe an organism’s vigor, or the degree to which organisms “fit” into their environments. An organism’s success in avoiding predators and in building a nest obviously contribute to its fitness and to the fitness of its offspring, but the peacock’s gaudy tail seemed to be in an entirely different line of work. Fitness, as a term in ordinary language (as in “physical (...) fitness”) and in its original biological meaning, applied to the survival of an organism and its offspring, not to sheer reproductive output (Paul ////; Cronin 1991). Darwin’s separation of natural from sexual selection may sound odd from a modern perspective, but it made sense from this earlier point of view. (shrink)

Recent discussions in the philosophy of biology have brought into question some fundamental assumptions regarding evolutionary processes, natural selection in particular. Some authors argue that natural selection is nothing but a population-level, statistical consequence of lower-level events (Matthen and Ariew [2002]; Walsh et al. [2002]). On this view, natural selection itself does not involve forces. Other authors reject this purely statistical, population-level account for an individual-level, causal account of natural selection (Bouchard and Rosenberg [2004]). I argue that each of these (...) positions is right in one way, but wrong in another; natural selection indeed takes place at the level of populations, but it is a causal process nonetheless. (shrink)

Brian Skyrms has studied the evolutionary dynamics of a simple bargaining game. Fair-dealing is the strategy 'demand 1/2', competing with the more modest strategy 'demand 1/3' and the greedier strategy 'demand 2/3'. Individuals leave offspring in proportion to their accumulated payoffs. The rules for payoffs from encounters penalize low- and high-demanders. The result is a significant basin of attraction for fair-dealing as an evolutionarily stable strategy. From these considerations Skyrms concludes that a disposition to fair-dealing could have evolved. A very (...) different picture emerges, however, when one considers genetic bases for the dispositions involved. A simple two-allele sexual model produces very different stable equilibria in the distribution of behavioral phenotypes. The equilibria for Skyrms's purely phenotypic selection process will not in general be attainable once one enters some simple genetic considerations. (shrink)

Both biologists and philosophers often make use of simple verbal formulations of necessary and sufficient conditions for evolution by natural selection (ENS). Such summaries go back to Darwin's Origin of Species (especially the "Recapitulation"), but recent ones are more compact.1 Perhaps the most commonly cited formulation is due to Lewontin.2 These summaries tend to have three or four conditions, where the core requirement is a combination of variation, heredity, and fitness differences. The summaries are employed in several ways. First, they (...) are often used in pedagogical contexts, and in showing the coherence of evolutionary theory in response to attacks from outside biology. Second, they are important in discussions of extensions of evolutionary principles to new domains, such as cultural change. The summaries also have intrinsic scientific and philosophical interest as attempts to capture some core principles of evolutionary theory in a highly concise way. Despite their prominence, both the proper formulation and status of these summaries are unclear. Standard formulations are subject to counterexamples, and their relations to formal models of evolutionary change are not straightforward. Here I look closely at these verbal summaries, and at how they relate to formal models. Are the summaries merely rough approximations that have no theoretical role of their own? Perhaps they could operate as theoretical statements in Darwin's time, but have now been superseded by more exact treatments. (shrink)

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

In this pithy and highly readable book, Brian Skyrms, a recognised authority on game and decision theory, investigates traditional problems of the social contract in terms of evolutionary dynamics. Game theory is skilfully employed to offer new interpretations of a wide variety of social phenomena, including justice, mutual aid, commitment, convention and meaning. The author eschews any grand, unified theory. Rather, he presents the reader with tools drawn from evolutionary game theory for the purpose of analysing and coming to understand (...) the social contract. The book is not technical and requires no special background knowledge. As such, it could be enjoyed by students and professionals in a wide range of disciplines: political science, philosophy, decision theory, economics and biology. (shrink)

We present a logically detailed case-study of explanation and prediction in Newtonian mechanics. The case in question is that of a planet's elliptical orbit in the Sun's gravitational field. Care is taken to distinguish the respective contributions of the mathematics that is being applied, and of the empirical hypotheses that receive a mathematical formulation. This enables one to appreciate how in this case the overall logical structure of scientific explanation and prediction is exactly in accordance with the hypotheticodeductive model.

A coherent treatment of the flow of ideas throughout Darwin's works, this volume presents a unified theoretical system that explains Darwin's investigations, evaluating the literature from a historical, scientific, and philosophical perspective.

The present edition provides a detailed and accessible discussion ofhis theories and adds an account of the immediate responses to the book on publication.

‘Natural selection’ is, it seems, an ambiguous term. It is sometimes held to denote a consequence of variation, heredity, and environment, while at other times as denoting a force that creates adaptations. I argue that the latter, the force interpretation, is a redundant notion of natural selection. I will point to difficulties in making sense of this linguistic practise, and argue that it is frequently at odds with standard interpretations of evolutionary theory. I provide examples to show this; one example (...) involving the relation between adaptations and other traits, and a second involving the relation between selection and drift. (shrink)