Mathematical progress: Between reason and society

It is shown how the historiographic purport of Lakatosian methodology of mathematics is structured on the theme of analysis and synthesis. This theme is explored and extended to the revolutionary phase around 1800. On the basis of this historical investigation it is argued that major innovations, crucial to the appraisal of mathematical progress, defy reconstruction as irreducibly rational processes and should instead essentially be understood as processes of social-cognitive interaction. A model of conceptual change is developed whose essential ingredients are the variability of rational responses to new intellectual and practical challenges arising in the cultural environment of mathematics, and the shifting selective pressure of society. The resulting view of mathematical development is compared with Kuhn's theory of scientific paradigms in the light of some personal communications.     

After Lakatos

The work of the philosopher of science Imre Lakatos has been highly influential upon scholars of science and religion, especially persons who want to demonstrate how theological inquiry may meet the intellectual standards of science. I first argue against Lakatos' position, showing how it fails to meet its own ambitions of providing clear and public criteria for assessing scientific theories. I then argue that the same weaknesses will manifest themselves in the work of his followers, using Nancey Murphy's early work as an example. I conclude by affirming Murphy's recent shift towards Alasdair MacIntyre's theory of rationality.     

MAINTAINING RESPECTABILITY: RESPONSE TO NICHOLAOS JONES

Nicholaos Jones argues that theology is not a respectable discipline because of its inability to meet the standards of contemporary science. Although Jones makes a bold claim, I suggest that he has not made his case by focusing on the question of defining science and metaphysics appropriately, the analysis of the literature he cites, and his central claim that theology presupposes the absolute certainty of God.     

SCIENCE AND RELIGION: MOVING BEYOND THE CREDIBILITY STRATEGY

Reeves condemns the recruitment of scientific methods by representative theologians to lend credibility to their theological claims. His treatment of Nancey Murphy's use of Lakatosian research programme methodology is focused on here, and his proposal that science and religion scholars might act as “historians of the present” to advance the field is explored. The “credibility strategy” is set in historical context with an exploration of some of the science and religion field's original commitments and goals, particularly in terms of the emphasis on rationalism and corresponding neglect of the imagination, and the value of more creative input in promoting better dialogue between science and religion is highlighted.     

FROM CRITICAL REALISM TO A METHODOLOGICAL APPROACH: RESPONSE TO ROBBINS, VAN HUYSSTEEN, AND HEFNER

Abstract. Critical realism is a problematic philosophical doctrine that unnecessarily complicates attempts to relate theology and science. A more satisfactory approach employs the scientific methodology of Imre Lakatos for the reconstruction of theology along scientific lines. Theological research programs would automatically include auxiliary hypotheses of both theological and scientific origin.     

THE ROLE OF SCIENCE IN PANNENBERG'S THEOGICAL THINKING

Abstract. Employing categories derived from the philosopher of science Imre Lakatos, this essay analyzes the theological thought of Wolfhart Pannenberg, with the aim of showing that he is engaged in a research program that takes seriously the various sciences and their understanding of the world on the one hand and the traditions of Christian faith and theology on the other. The course of the argument demonstrates that Pannenberg's thought extends comprehensively to provide a conceptuality that centers on the phenomena of contingency and field and encompasses nearly every realm of science and the breadth of biblical and theological traditions.     

The Intelligent‐Design Movement: Science or Ideology?

The past decade has seen the rise of a new wave of criticism of evolutionary biology, led by claims that it should be replaced by a new science of intelligent design. While the general question of inferring design may fairly be considered worthy of attention, claims that intelligent-design theory (IDT) constitutes a biological science are highly problematic. This article briefly summarizes the assertions made about IDT as a biological science and indicates why they do not stand up to analysis. While claiming that IDT is a biological science, its advocates have failed to actually produce a research program that merits serious attention. As such, it is clear that IDT is more driven by ideological considerations than by attention to actual scientific research.     

Inference to the Best Explanation

The common role of research programs in science and religion is now widely accepted. The next step in the methodology debate is to specify more concretely the shared standards for adequate explanations. The article presents a detailed account of the method of inference to the best explanation and gives examples of how the method can structure the philosophical and theological interaction with science. The resulting approach dispenses with deductive and inductive proofs of religious propositions and limits itself to initially plausible hypotheses that are to be assessed according to their explanatory power. Only when a domain of data and a particular explanatory task have been specified can any serious claim be made that religious theories are equal or superior to their naturalistic alternatives.     

Conceptual engineering for mathematical concepts

In this paper I investigate how conceptual engineering applies to mathematical concepts in particular. I begin with a discussion of Waismann’s notion of open texture, and compare it to Shapiro’s modern usage of the term. Next I set out the position taken by Lakatos which sees mathematical concepts as dynamic and open to improvement and development, arguing that Waismann’s open texture applies to mathematical concepts too. With the perspective of mathematics as open-textured, I make the case that this allows us to deploy the tools of conceptual engineering in mathematics. I will examine Cappelen’s recent argument that there are no conceptual safe spaces and consider whether mathematics constitutes a counterexample. I argue that it does not, drawing on Haslanger’s distinction between manifest and operative concepts, and applying this in a novel way to set-theoretic foundations. I then set out some of the questions that need to be engaged with to establish mathematics as involving a kind of conceptual engineering. I finish with a case study of how the tools of conceptual engineering will give us a way to progress in the debate between advocates of the Universe view and the Multiverse view in set theory.     

On Holisms: Insular, Inclusivist, and Postmodern

Nancey Murphy's offer to take us “beyond liberalism and fundamentalism” is an exciting one: Who wants to be caught in the clutches of a fruitless theological dispute? She argues that the key to our escape is “Anglo-American postmodernity.” I analyze what Murphy means by this term and why it may turn out to be a more precarious escape route than one might think. Holism or “post-foundationalism” is indeed inescapable for science/religion discussions today, but an inclusivist holism is preferable to Murphy's insular holism